| Rfc | 6716 |
|---|
| Title | Definition of the Opus Audio Codec |
|---|
| Author | JM. Valin, K. Vos, T.
Terriberry |
|---|
| Date | September 2012 |
|---|
| Format: | TXT, HTML |
|---|
| Updated by | RFC8251 |
|---|
| Status: | PROPOSED STANDARD |
|---|
|
Internet Engineering Task Force (IETF) JM. Valin
Request for Comments: 6716 Mozilla Corporation
Category: Standards Track K. Vos
ISSN: 2070-1721 Skype Technologies S.A.
T. Terriberry
Mozilla Corporation
September 2012
Definition of the Opus Audio Codec
Abstract
This document defines the Opus interactive speech and audio codec.
Opus is designed to handle a wide range of interactive audio
applications, including Voice over IP, videoconferencing, in-game
chat, and even live, distributed music performances. It scales from
low bitrate narrowband speech at 6 kbit/s to very high quality stereo
music at 510 kbit/s. Opus uses both Linear Prediction (LP) and the
Modified Discrete Cosine Transform (MDCT) to achieve good compression
of both speech and music.
Status of This Memo
This is an Internet Standards Track document.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Further information on
Internet Standards is available in Section 2 of RFC 5741.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
http://www.rfc-editor.org/info/rfc6716.
Copyright Notice
Copyright (c) 2012 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(http://trustee.ietf.org/license-info) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document. Code Components extracted from this document must
include Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
The licenses granted by the IETF Trust to this RFC under Section 3.c
of the Trust Legal Provisions shall also include the right to extract
text from Sections 1 through 8 and Appendix A and Appendix B of this
RFC and create derivative works from these extracts, and to copy,
publish, display and distribute such derivative works in any medium
and for any purpose, provided that no such derivative work shall be
presented, displayed or published in a manner that states or implies
that it is part of this RFC or any other IETF Document.
Table of Contents
1. Introduction ....................................................5
1.1. Notation and Conventions ...................................6
2. Opus Codec Overview .............................................8
2.1. Control Parameters ........................................10
2.1.1. Bitrate ............................................10
2.1.2. Number of Channels (Mono/Stereo) ...................11
2.1.3. Audio Bandwidth ....................................11
2.1.4. Frame Duration .....................................11
2.1.5. Complexity .........................................11
2.1.6. Packet Loss Resilience .............................12
2.1.7. Forward Error Correction (FEC) .....................12
2.1.8. Constant/Variable Bitrate ..........................12
2.1.9. Discontinuous Transmission (DTX) ...................13
3. Internal Framing ...............................................13
3.1. The TOC Byte ..............................................13
3.2. Frame Packing .............................................16
3.2.1. Frame Length Coding ................................16
3.2.2. Code 0: One Frame in the Packet ....................16
3.2.3. Code 1: Two Frames in the Packet, Each with
Equal Compressed Size ..............................17
3.2.4. Code 2: Two Frames in the Packet, with
Different Compressed Sizes .........................17
3.2.5. Code 3: A Signaled Number of Frames in the Packet ..18
3.3. Examples ..................................................21
3.4. Receiving Malformed Packets ...............................22
4. Opus Decoder ...................................................23
4.1. Range Decoder .............................................23
4.1.1. Range Decoder Initialization .......................25
4.1.2. Decoding Symbols ...................................25
4.1.3. Alternate Decoding Methods .........................27
4.1.4. Decoding Raw Bits ..................................29
4.1.5. Decoding Uniformly Distributed Integers ............29
4.1.6. Current Bit Usage ..................................30
4.2. SILK Decoder ..............................................32
4.2.1. SILK Decoder Modules ...............................32
4.2.2. LP Layer Organization ..............................33
4.2.3. Header Bits ........................................35
4.2.4. Per-Frame LBRR Flags ...............................36
4.2.5. LBRR Frames ........................................36
4.2.6. Regular SILK Frames ................................37
4.2.7. SILK Frame Contents ................................37
4.2.7.1. Stereo Prediction Weights .................40
4.2.7.2. Mid-Only Flag .............................42
4.2.7.3. Frame Type ................................43
4.2.7.4. Subframe Gains ............................44
4.2.7.5. Normalized Line Spectral Frequency
(LSF) and Linear Predictive Coding (LPC)
Coeffieients ..............................46
4.2.7.6. Long-Term Prediction (LTP) Parameters .....74
4.2.7.7. Linear Congruential Generator (LCG) Seed ..86
4.2.7.8. Excitation ................................86
4.2.7.9. SILK Frame Reconstruction .................98
4.2.8. Stereo Unmixing ...................................102
4.2.9. Resampling ........................................103
4.3. CELT Decoder .............................................104
4.3.1. Transient Decoding ................................108
4.3.2. Energy Envelope Decoding ..........................108
4.3.3. Bit Allocation ....................................110
4.3.4. Shape Decoding ....................................116
4.3.5. Anti-collapse Processing ..........................120
4.3.6. Denormalization ...................................121
4.3.7. Inverse MDCT ......................................121
4.4. Packet Loss Concealment (PLC) ............................122
4.4.1. Clock Drift Compensation ..........................122
4.5. Configuration Switching ..................................123
4.5.1. Transition Side Information (Redundancy) ..........124
4.5.2. State Reset .......................................127
4.5.3. Summary of Transitions ............................128
5. Opus Encoder ..................................................131
5.1. Range Encoder ............................................132
5.1.1. Encoding Symbols ..................................133
5.1.2. Alternate Encoding Methods ........................134
5.1.3. Encoding Raw Bits .................................135
5.1.4. Encoding Uniformly Distributed Integers ...........135
5.1.5. Finalizing the Stream .............................135
5.1.6. Current Bit Usage .................................136
5.2. SILK Encoder .............................................136
5.2.1. Sample Rate Conversion ............................137
5.2.2. Stereo Mixing .....................................137
5.2.3. SILK Core Encoder .................................138
5.3. CELT Encoder .............................................150
5.3.1. Pitch Pre-filter ..................................150
5.3.2. Bands and Normalization ...........................151
5.3.3. Energy Envelope Quantization ......................151
5.3.4. Bit Allocation ....................................151
5.3.5. Stereo Decisions ..................................152
5.3.6. Time-Frequency Decision ...........................153
5.3.7. Spreading Values Decision .........................153
5.3.8. Spherical Vector Quantization .....................154
6. Conformance ...................................................155
6.1. Testing ..................................................155
6.2. Opus Custom ..............................................156
7. Security Considerations .......................................157
8. Acknowledgements ..............................................158
9. References ....................................................159
9.1. Normative References .....................................159
9.2. Informative References ...................................159
Appendix A. Reference Implementation .............................163
A.1. Extracting the Source ....................................164
A.2. Up-to-Date Implementation ................................164
A.3. Base64-Encoded Source Code ...............................164
A.4. Test Vectors .............................................321
Appendix B. Self-Delimiting Framing ..............................321
1. Introduction
The Opus codec is a real-time interactive audio codec designed to
meet the requirements described in [REQUIREMENTS]. It is composed of
a layer based on Linear Prediction (LP) [LPC] and a layer based on
the Modified Discrete Cosine Transform (MDCT) [MDCT]. The main idea
behind using two layers is as follows: in speech, linear prediction
techniques (such as Code-Excited Linear Prediction, or CELP) code low
frequencies more efficiently than transform (e.g., MDCT) domain
techniques, while the situation is reversed for music and higher
speech frequencies. Thus, a codec with both layers available can
operate over a wider range than either one alone and can achieve
better quality by combining them than by using either one
individually.
The primary normative part of this specification is provided by the
source code in Appendix A. Only the decoder portion of this software
is normative, though a significant amount of code is shared by both
the encoder and decoder. Section 6 provides a decoder conformance
test. The decoder contains a great deal of integer and fixed-point
arithmetic that needs to be performed exactly, including all rounding
considerations, so any useful specification requires domain-specific
symbolic language to adequately define these operations.
Additionally, any conflict between the symbolic representation and
the included reference implementation must be resolved. For the
practical reasons of compatibility and testability, it would be
advantageous to give the reference implementation priority in any
disagreement. The C language is also one of the most widely
understood, human-readable symbolic representations for machine
behavior. For these reasons, this RFC uses the reference
implementation as the sole symbolic representation of the codec.
While the symbolic representation is unambiguous and complete, it is
not always the easiest way to understand the codec's operation. For
this reason, this document also describes significant parts of the
codec in prose and takes the opportunity to explain the rationale
behind many of the more surprising elements of the design. These
descriptions are intended to be accurate and informative, but the
limitations of common English sometimes result in ambiguity, so it is
expected that the reader will always read them alongside the symbolic
representation. Numerous references to the implementation are
provided for this purpose. The descriptions sometimes differ from
the reference in ordering or through mathematical simplification
wherever such deviation makes an explanation easier to understand.
For example, the right shift and left shift operations in the
reference implementation are often described using division and
multiplication in the text. In general, the text is focused on the
"what" and "why" while the symbolic representation most clearly
provides the "how".
1.1. Notation and Conventions
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [RFC2119].
Various operations in the codec require bit-exact fixed-point
behavior, even when writing a floating point implementation. The
notation "Q<n>", where n is an integer, denotes the number of binary
digits to the right of the decimal point in a fixed-point number.
For example, a signed Q14 value in a 16-bit word can represent values
from -2.0 to 1.99993896484375, inclusive. This notation is for
informational purposes only. Arithmetic, when described, always
operates on the underlying integer. For example, the text will
explicitly indicate any shifts required after a multiplication.
Expressions, where included in the text, follow C operator rules and
precedence, with the exception that the syntax "x**y" indicates x
raised to the power y. The text also makes use of the following
functions.
1.1.1. min(x,y)
The smallest of two values x and y.
1.1.2. max(x,y)
The largest of two values x and y.
1.1.3. clamp(lo,x,hi)
clamp(lo,x,hi) = max(lo,min(x,hi))
With this definition, if lo > hi, then lo is returned.
1.1.4. sign(x)
The sign of x, i.e.,
( -1, x < 0
sign(x) = < 0, x == 0
( 1, x > 0
1.1.5. abs(x)
The absolute value of x, i.e.,
abs(x) = sign(x)*x
1.1.6. floor(f)
The largest integer z such that z <= f.
1.1.7. ceil(f)
The smallest integer z such that z >= f.
1.1.8. round(f)
The integer z nearest to f, with ties rounded towards negative
infinity, i.e.,
round(f) = ceil(f - 0.5)
1.1.9. log2(f)
The base-two logarithm of f.
1.1.10. ilog(n)
The minimum number of bits required to store a positive integer n in
binary, or 0 for a non-positive integer n.
( 0, n <= 0
ilog(n) = <
( floor(log2(n))+1, n > 0
Examples:
o ilog(-1) = 0
o ilog(0) = 0
o ilog(1) = 1
o ilog(2) = 2
o ilog(3) = 2
o ilog(4) = 3
o ilog(7) = 3
2. Opus Codec Overview
The Opus codec scales from 6 kbit/s narrowband mono speech to
510 kbit/s fullband stereo music, with algorithmic delays ranging
from 5 ms to 65.2 ms. At any given time, either the LP layer, the
MDCT layer, or both, may be active. It can seamlessly switch between
all of its various operating modes, giving it a great deal of
flexibility to adapt to varying content and network conditions
without renegotiating the current session. The codec allows input
and output of various audio bandwidths, defined as follows:
+----------------------+-----------------+-------------------------+
| Abbreviation | Audio Bandwidth | Sample Rate (Effective) |
+----------------------+-----------------+-------------------------+
| NB (narrowband) | 4 kHz | 8 kHz |
| | | |
| MB (medium-band) | 6 kHz | 12 kHz |
| | | |
| WB (wideband) | 8 kHz | 16 kHz |
| | | |
| SWB (super-wideband) | 12 kHz | 24 kHz |
| | | |
| FB (fullband) | 20 kHz (*) | 48 kHz |
+----------------------+-----------------+-------------------------+
Table 1
(*) Although the sampling theorem allows a bandwidth as large as half
the sampling rate, Opus never codes audio above 20 kHz, as that is
the generally accepted upper limit of human hearing.
Opus defines super-wideband (SWB) with an effective sample rate of
24 kHz, unlike some other audio coding standards that use 32 kHz.
This was chosen for a number of reasons. The band layout in the MDCT
layer naturally allows skipping coefficients for frequencies over
12 kHz, but does not allow cleanly dropping just those frequencies
over 16 kHz. A sample rate of 24 kHz also makes resampling in the
MDCT layer easier, as 24 evenly divides 48, and when 24 kHz is
sufficient, it can save computation in other processing, such as
Acoustic Echo Cancellation (AEC). Experimental changes to the band
layout to allow a 16 kHz cutoff (32 kHz effective sample rate) showed
potential quality degradations at other sample rates, and, at typical
bitrates, the number of bits saved by using such a cutoff instead of
coding in fullband (FB) mode is very small. Therefore, if an
application wishes to process a signal sampled at 32 kHz, it should
just use FB.
The LP layer is based on the SILK codec [SILK]. It supports NB, MB,
or WB audio and frame sizes from 10 ms to 60 ms, and requires an
additional 5 ms look-ahead for noise shaping estimation. A small
additional delay (up to 1.5 ms) may be required for sampling rate
conversion. Like Vorbis [VORBIS-WEBSITE] and many other modern
codecs, SILK is inherently designed for variable bitrate (VBR)
coding, though the encoder can also produce constant bitrate (CBR)
streams. The version of SILK used in Opus is substantially modified
from, and not compatible with, the stand-alone SILK codec previously
deployed by Skype. This document does not serve to define that
format, but those interested in the original SILK codec should see
[SILK] instead.
The MDCT layer is based on the Constrained-Energy Lapped Transform
(CELT) codec [CELT]. It supports NB, WB, SWB, or FB audio and frame
sizes from 2.5 ms to 20 ms, and requires an additional 2.5 ms look-
ahead due to the overlapping MDCT windows. The CELT codec is
inherently designed for CBR coding, but unlike many CBR codecs, it is
not limited to a set of predetermined rates. It internally allocates
bits to exactly fill any given target budget, and an encoder can
produce a VBR stream by varying the target on a per-frame basis. The
MDCT layer is not used for speech when the audio bandwidth is WB or
less, as it is not useful there. On the other hand, non-speech
signals are not always adequately coded using linear prediction.
Therefore, the MDCT layer should be used for music signals.
A "Hybrid" mode allows the use of both layers simultaneously with a
frame size of 10 or 20 ms and an SWB or FB audio bandwidth. The LP
layer codes the low frequencies by resampling the signal down to WB.
The MDCT layer follows, coding the high frequency portion of the
signal. The cutoff between the two lies at 8 kHz, the maximum WB
audio bandwidth. In the MDCT layer, all bands below 8 kHz are
discarded, so there is no coding redundancy between the two layers.
The sample rate (in contrast to the actual audio bandwidth) can be
chosen independently on the encoder and decoder side, e.g., a
fullband signal can be decoded as wideband, or vice versa. This
approach ensures a sender and receiver can always interoperate,
regardless of the capabilities of their actual audio hardware.
Internally, the LP layer always operates at a sample rate of twice
the audio bandwidth, up to a maximum of 16 kHz, which it continues to
use for SWB and FB. The decoder simply resamples its output to
support different sample rates. The MDCT layer always operates
internally at a sample rate of 48 kHz. Since all the supported
sample rates evenly divide this rate, and since the decoder may
easily zero out the high frequency portion of the spectrum in the
frequency domain, it can simply decimate the MDCT layer output to
achieve the other supported sample rates very cheaply.
After conversion to the common, desired output sample rate, the
decoder simply adds the output from the two layers together. To
compensate for the different look-ahead required by each layer, the
CELT encoder input is delayed by an additional 2.7 ms. This ensures
that low frequencies and high frequencies arrive at the same time.
This extra delay may be reduced by an encoder by using less look-
ahead for noise shaping or using a simpler resampler in the LP layer,
but this will reduce quality. However, the base 2.5 ms look-ahead in
the CELT layer cannot be reduced in the encoder because it is needed
for the MDCT overlap, whose size is fixed by the decoder.
Both layers use the same entropy coder, avoiding any waste from
"padding bits" between them. The hybrid approach makes it easy to
support both CBR and VBR coding. Although the LP layer is VBR, the
bit allocation of the MDCT layer can produce a final stream that is
CBR by using all the bits left unused by the LP layer.
2.1. Control Parameters
The Opus codec includes a number of control parameters that can be
changed dynamically during regular operation of the codec, without
interrupting the audio stream from the encoder to the decoder. These
parameters only affect the encoder since any impact they have on the
bitstream is signaled in-band such that a decoder can decode any Opus
stream without any out-of-band signaling. Any Opus implementation
can add or modify these control parameters without affecting
interoperability. The most important encoder control parameters in
the reference encoder are listed below.
2.1.1. Bitrate
Opus supports all bitrates from 6 kbit/s to 510 kbit/s. All other
parameters being equal, higher bitrate results in higher quality.
For a frame size of 20 ms, these are the bitrate "sweet spots" for
Opus in various configurations:
o 8-12 kbit/s for NB speech,
o 16-20 kbit/s for WB speech,
o 28-40 kbit/s for FB speech,
o 48-64 kbit/s for FB mono music, and
o 64-128 kbit/s for FB stereo music.
2.1.2. Number of Channels (Mono/Stereo)
Opus can transmit either mono or stereo frames within a single
stream. When decoding a mono frame in a stereo decoder, the left and
right channels are identical, and when decoding a stereo frame in a
mono decoder, the mono output is the average of the left and right
channels. In some cases, it is desirable to encode a stereo input
stream in mono (e.g., because the bitrate is too low to encode stereo
with sufficient quality). The number of channels encoded can be
selected in real-time, but by default the reference encoder attempts
to make the best decision possible given the current bitrate.
2.1.3. Audio Bandwidth
The audio bandwidths supported by Opus are listed in Table 1. Just
like for the number of channels, any decoder can decode audio that is
encoded at any bandwidth. For example, any Opus decoder operating at
8 kHz can decode an FB Opus frame, and any Opus decoder operating at
48 kHz can decode an NB frame. Similarly, the reference encoder can
take a 48 kHz input signal and encode it as NB. The higher the audio
bandwidth, the higher the required bitrate to achieve acceptable
quality. The audio bandwidth can be explicitly specified in real-
time, but, by default, the reference encoder attempts to make the
best bandwidth decision possible given the current bitrate.
2.1.4. Frame Duration
Opus can encode frames of 2.5, 5, 10, 20, 40, or 60 ms. It can also
combine multiple frames into packets of up to 120 ms. For real-time
applications, sending fewer packets per second reduces the bitrate,
since it reduces the overhead from IP, UDP, and RTP headers.
However, it increases latency and sensitivity to packet losses, as
losing one packet constitutes a loss of a bigger chunk of audio.
Increasing the frame duration also slightly improves coding
efficiency, but the gain becomes small for frame sizes above 20 ms.
For this reason, 20 ms frames are a good choice for most
applications.
2.1.5. Complexity
There are various aspects of the Opus encoding process where trade-
offs can be made between CPU complexity and quality/bitrate. In the
reference encoder, the complexity is selected using an integer from 0
to 10, where 0 is the lowest complexity and 10 is the highest.
Examples of computations for which such trade-offs may occur are:
o The order of the pitch analysis whitening filter [WHITENING],
o The order of the short-term noise shaping filter,
o The number of states in delayed decision quantization of the
residual signal, and
o The use of certain bitstream features such as variable time-
frequency resolution and the pitch post-filter.
2.1.6. Packet Loss Resilience
Audio codecs often exploit inter-frame correlations to reduce the
bitrate at a cost in error propagation: after losing one packet,
several packets need to be received before the decoder is able to
accurately reconstruct the speech signal. The extent to which Opus
exploits inter-frame dependencies can be adjusted on the fly to
choose a trade-off between bitrate and amount of error propagation.
2.1.7. Forward Error Correction (FEC)
Another mechanism providing robustness against packet loss is the in-
band Forward Error Correction (FEC). Packets that are determined to
contain perceptually important speech information, such as onsets or
transients, are encoded again at a lower bitrate and this re-encoded
information is added to a subsequent packet.
2.1.8. Constant/Variable Bitrate
Opus is more efficient when operating with variable bitrate (VBR),
which is the default. When low-latency transmission is required over
a relatively slow connection, then constrained VBR can also be used.
This uses VBR in a way that simulates a "bit reservoir" and is
equivalent to what MP3 (MPEG 1, Layer 3) and AAC (Advanced Audio
Coding) call CBR (i.e., not true CBR due to the bit reservoir). In
some (rare) applications, constant bitrate (CBR) is required. There
are two main reasons to operate in CBR mode:
o When the transport only supports a fixed size for each compressed
frame, or
o When encryption is used for an audio stream that is either highly
constrained (e.g., yes/no, recorded prompts) or highly sensitive
[SRTP-VBR].
Bitrate may still be allowed to vary, even with sensitive data, as
long as the variation is not driven by the input signal (for example,
to match changing network conditions). To achieve this, an
application should still run Opus in CBR mode, but change the target
rate before each packet.
2.1.9. Discontinuous Transmission (DTX)
Discontinuous Transmission (DTX) reduces the bitrate during silence
or background noise. When DTX is enabled, only one frame is encoded
every 400 milliseconds.
3. Internal Framing
The Opus encoder produces "packets", which are each a contiguous set
of bytes meant to be transmitted as a single unit. The packets
described here do not include such things as IP, UDP, or RTP headers,
which are normally found in a transport-layer packet. A single
packet may contain multiple audio frames, so long as they share a
common set of parameters, including the operating mode, audio
bandwidth, frame size, and channel count (mono vs. stereo). This
section describes the possible combinations of these parameters and
the internal framing used to pack multiple frames into a single
packet. This framing is not self-delimiting. Instead, it assumes
that a lower layer (such as UDP or RTP [RFC3550] or Ogg [RFC3533] or
Matroska [MATROSKA-WEBSITE]) will communicate the length, in bytes,
of the packet, and it uses this information to reduce the framing
overhead in the packet itself. A decoder implementation MUST support
the framing described in this section. An alternative, self-
delimiting variant of the framing is described in Appendix B.
Support for that variant is OPTIONAL.
All bit diagrams in this document number the bits so that bit 0 is
the most significant bit of the first byte, and bit 7 is the least
significant. Bit 8 is thus the most significant bit of the second
byte, etc. Well-formed Opus packets obey certain requirements,
marked [R1] through [R7] below. These are summarized in Section 3.4
along with appropriate means of handling malformed packets.
3.1. The TOC Byte
A well-formed Opus packet MUST contain at least one byte [R1]. This
byte forms a table-of-contents (TOC) header that signals which of the
various modes and configurations a given packet uses. It is composed
of a configuration number, "config", a stereo flag, "s", and a frame
count code, "c", arranged as illustrated in Figure 1. A description
of each of these fields follows.
0
0 1 2 3 4 5 6 7
+-+-+-+-+-+-+-+-+
| config |s| c |
+-+-+-+-+-+-+-+-+
Figure 1: The TOC Byte
The top five bits of the TOC byte, labeled "config", encode one of 32
possible configurations of operating mode, audio bandwidth, and frame
size. As described, the LP (SILK) layer and MDCT (CELT) layer can be
combined in three possible operating modes:
1. A SILK-only mode for use in low bitrate connections with an audio
bandwidth of WB or less,
2. A Hybrid (SILK+CELT) mode for SWB or FB speech at medium
bitrates, and
3. A CELT-only mode for very low delay speech transmission as well
as music transmission (NB to FB).
The 32 possible configurations each identify which one of these
operating modes the packet uses, as well as the audio bandwidth and
the frame size. Table 2 lists the parameters for each configuration.
+-----------------------+-----------+-----------+-------------------+
| Configuration | Mode | Bandwidth | Frame Sizes |
| Number(s) | | | |
+-----------------------+-----------+-----------+-------------------+
| 0...3 | SILK-only | NB | 10, 20, 40, 60 ms |
| | | | |
| 4...7 | SILK-only | MB | 10, 20, 40, 60 ms |
| | | | |
| 8...11 | SILK-only | WB | 10, 20, 40, 60 ms |
| | | | |
| 12...13 | Hybrid | SWB | 10, 20 ms |
| | | | |
| 14...15 | Hybrid | FB | 10, 20 ms |
| | | | |
| 16...19 | CELT-only | NB | 2.5, 5, 10, 20 ms |
| | | | |
| 20...23 | CELT-only | WB | 2.5, 5, 10, 20 ms |
| | | | |
| 24...27 | CELT-only | SWB | 2.5, 5, 10, 20 ms |
| | | | |
| 28...31 | CELT-only | FB | 2.5, 5, 10, 20 ms |
+-----------------------+-----------+-----------+-------------------+
Table 2: TOC Byte Configuration Parameters
The configuration numbers in each range (e.g., 0...3 for NB SILK-
only) correspond to the various choices of frame size, in the same
order. For example, configuration 0 has a 10 ms frame size and
configuration 3 has a 60 ms frame size.
One additional bit, labeled "s", signals mono vs. stereo, with 0
indicating mono and 1 indicating stereo.
The remaining two bits of the TOC byte, labeled "c", code the number
of frames per packet (codes 0 to 3) as follows:
o 0: 1 frame in the packet
o 1: 2 frames in the packet, each with equal compressed size
o 2: 2 frames in the packet, with different compressed sizes
o 3: an arbitrary number of frames in the packet
This document refers to a packet as a code 0 packet, code 1 packet,
etc., based on the value of "c".
3.2. Frame Packing
This section describes how frames are packed according to each
possible value of "c" in the TOC byte.
3.2.1. Frame Length Coding
When a packet contains multiple VBR frames (i.e., code 2 or 3), the
compressed length of one or more of these frames is indicated with a
one- or two-byte sequence, with the meaning of the first byte as
follows:
o 0: No frame (Discontinuous Transmission (DTX) or lost packet)
o 1...251: Length of the frame in bytes
o 252...255: A second byte is needed. The total length is
(second_byte*4)+first_byte
The special length 0 indicates that no frame is available, either
because it was dropped during transmission by some intermediary or
because the encoder chose not to transmit it. Any Opus frame in any
mode MAY have a length of 0.
The maximum representable length is 255*4+255=1275 bytes. For 20 ms
frames, this represents a bitrate of 510 kbit/s, which is
approximately the highest useful rate for lossily compressed fullband
stereo music. Beyond this point, lossless codecs are more
appropriate. It is also roughly the maximum useful rate of the MDCT
layer as, shortly thereafter, quality no longer improves with
additional bits due to limitations on the codebook sizes.
No length is transmitted for the last frame in a VBR packet, or for
any of the frames in a CBR packet, as it can be inferred from the
total size of the packet and the size of all other data in the
packet. However, the length of any individual frame MUST NOT exceed
1275 bytes [R2] to allow for repacketization by gateways, conference
bridges, or other software.
3.2.2. Code 0: One Frame in the Packet
For code 0 packets, the TOC byte is immediately followed by N-1 bytes
of compressed data for a single frame (where N is the size of the
packet), as illustrated in Figure 2.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| config |s|0|0| |
+-+-+-+-+-+-+-+-+ |
| Compressed frame 1 (N-1 bytes)... :
: |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 2: A Code 0 Packet
3.2.3. Code 1: Two Frames in the Packet, Each with Equal Compressed
Size
For code 1 packets, the TOC byte is immediately followed by the
(N-1)/2 bytes of compressed data for the first frame, followed by
(N-1)/2 bytes of compressed data for the second frame, as illustrated
in Figure 3. The number of payload bytes available for compressed
data, N-1, MUST be even for all code 1 packets [R3].
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| config |s|0|1| |
+-+-+-+-+-+-+-+-+ :
| Compressed frame 1 ((N-1)/2 bytes)... |
: +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ :
| Compressed frame 2 ((N-1)/2 bytes)... |
: +-+-+-+-+-+-+-+-+
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 3: A Code 1 Packet
3.2.4. Code 2: Two Frames in the Packet, with Different Compressed
Sizes
For code 2 packets, the TOC byte is followed by a one- or two-byte
sequence indicating the length of the first frame (marked N1 in
Figure 4), followed by N1 bytes of compressed data for the first
frame. The remaining N-N1-2 or N-N1-3 bytes are the compressed data
for the second frame. This is illustrated in Figure 4. A code 2
packet MUST contain enough bytes to represent a valid length. For
example, a 1-byte code 2 packet is always invalid, and a 2-byte code
2 packet whose second byte is in the range 252...255 is also invalid.
The length of the first frame, N1, MUST also be no larger than the
size of the payload remaining after decoding that length for all code
2 packets [R4]. This makes, for example, a 2-byte code 2 packet with
a second byte in the range 1...251 invalid as well (the only valid
2-byte code 2 packet is one where the length of both frames is zero).
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| config |s|1|0| N1 (1-2 bytes): |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ :
| Compressed frame 1 (N1 bytes)... |
: +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |
| Compressed frame 2... :
: |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 4: A Code 2 Packet
3.2.5. Code 3: A Signaled Number of Frames in the Packet
Code 3 packets signal the number of frames, as well as additional
padding, called "Opus padding" to indicate that this padding is added
at the Opus layer rather than at the transport layer. Code 3 packets
MUST have at least 2 bytes [R6,R7]. The TOC byte is followed by a
byte encoding the number of frames in the packet in bits 2 to 7
(marked "M" in Figure 5), with bit 1 indicating whether or not Opus
padding is inserted (marked "p" in Figure 5), and bit 0 indicating
VBR (marked "v" in Figure 5). M MUST NOT be zero, and the audio
duration contained within a packet MUST NOT exceed 120 ms [R5]. This
limits the maximum frame count for any frame size to 48 (for 2.5 ms
frames), with lower limits for longer frame sizes. Figure 5
illustrates the layout of the frame count byte.
0
0 1 2 3 4 5 6 7
+-+-+-+-+-+-+-+-+
|v|p| M |
+-+-+-+-+-+-+-+-+
Figure 5: The frame count byte
When Opus padding is used, the number of bytes of padding is encoded
in the bytes following the frame count byte. Values from 0...254
indicate that 0...254 bytes of padding are included, in addition to
the byte(s) used to indicate the size of the padding. If the value
is 255, then the size of the additional padding is 254 bytes, plus
the padding value encoded in the next byte. There MUST be at least
one more byte in the packet in this case [R6,R7]. The additional
padding bytes appear at the end of the packet and MUST be set to zero
by the encoder to avoid creating a covert channel. The decoder MUST
accept any value for the padding bytes, however.
Although this encoding provides multiple ways to indicate a given
number of padding bytes, each uses a different number of bytes to
indicate the padding size and thus will increase the total packet
size by a different amount. For example, to add 255 bytes to a
packet, set the padding bit, p, to 1, insert a single byte after the
frame count byte with a value of 254, and append 254 padding bytes
with the value zero to the end of the packet. To add 256 bytes to a
packet, set the padding bit to 1, insert two bytes after the frame
count byte with the values 255 and 0, respectively, and append 254
padding bytes with the value zero to the end of the packet. By using
the value 255 multiple times, it is possible to create a packet of
any specific, desired size. Let P be the number of header bytes used
to indicate the padding size plus the number of padding bytes
themselves (i.e., P is the total number of bytes added to the
packet). Then, P MUST be no more than N-2 [R6,R7].
In the CBR case, let R=N-2-P be the number of bytes remaining in the
packet after subtracting the (optional) padding. Then, the
compressed length of each frame in bytes is equal to R/M. The value
R MUST be a non-negative integer multiple of M [R6]. The compressed
data for all M frames follows, each of size R/M bytes, as illustrated
in Figure 6.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| config |s|1|1|0|p| M | Padding length (Optional) :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 1 (R/M bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 2 (R/M bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: ... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame M (R/M bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: Opus Padding (Optional)... |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 6: A CBR Code 3 Packet
In the VBR case, the (optional) padding length is followed by M-1
frame lengths (indicated by "N1" to "N[M-1]" in Figure 7), each
encoded in a one- or two-byte sequence as described above. The
packet MUST contain enough data for the M-1 lengths after removing
the (optional) padding, and the sum of these lengths MUST be no
larger than the number of bytes remaining in the packet after
decoding them [R7]. The compressed data for all M frames follows,
each frame consisting of the indicated number of bytes, with the
final frame consuming any remaining bytes before the final padding,
as illustrated in Figure 6. The number of header bytes (TOC byte,
frame count byte, padding length bytes, and frame length bytes), plus
the signaled length of the first M-1 frames themselves, plus the
signaled length of the padding MUST be no larger than N, the total
size of the packet.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| config |s|1|1|1|p| M | Padding length (Optional) :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: N1 (1-2 bytes): N2 (1-2 bytes): ... : N[M-1] |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 1 (N1 bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 2 (N2 bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: ... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame M... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: Opus Padding (Optional)... |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 7: A VBR Code 3 Packet
3.3. Examples
Simplest case, one NB mono 20 ms SILK frame:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 1 |0|0|0| compressed data... :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 8
Two FB mono 5 ms CELT frames of the same compressed size:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 29 |0|0|1| compressed data... :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 9
Two FB mono 20 ms Hybrid frames of different compressed size:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 15 |0|1|1|1|0| 2 | N1 | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |
| compressed data... :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 10
Four FB stereo 20 ms CELT frames of the same compressed size:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 31 |1|1|1|0|0| 4 | compressed data... :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 11
3.4. Receiving Malformed Packets
A receiver MUST NOT process packets that violate any of the rules
above as normal Opus packets. They are reserved for future
applications, such as in-band headers (containing metadata, etc.).
Packets that violate these constraints may cause implementations of
_this_ specification to treat them as malformed and discard them.
These constraints are summarized here for reference:
[R1] Packets are at least one byte.
[R2] No implicit frame length is larger than 1275 bytes.
[R3] Code 1 packets have an odd total length, N, so that (N-1)/2 is
an integer.
[R4] Code 2 packets have enough bytes after the TOC for a valid
frame length, and that length is no larger than the number of
bytes remaining in the packet.
[R5] Code 3 packets contain at least one frame, but no more than
120 ms of audio total.
[R6] The length of a CBR code 3 packet, N, is at least two bytes,
the number of bytes added to indicate the padding size plus the
trailing padding bytes themselves, P, is no more than N-2, and
the frame count, M, satisfies the constraint that (N-2-P) is a
non-negative integer multiple of M.
[R7] VBR code 3 packets are large enough to contain all the header
bytes (TOC byte, frame count byte, any padding length bytes,
and any frame length bytes), plus the length of the first M-1
frames, plus any trailing padding bytes.
4. Opus Decoder
The Opus decoder consists of two main blocks: the SILK decoder and
the CELT decoder. At any given time, one or both of the SILK and
CELT decoders may be active. The output of the Opus decode is the
sum of the outputs from the SILK and CELT decoders with proper sample
rate conversion and delay compensation on the SILK side, and optional
decimation (when decoding to sample rates less than 48 kHz) on the
CELT side, as illustrated in the block diagram below.
+---------+ +------------+
| SILK | | Sample |
+->| Decoder |--->| Rate |----+
Bit- +---------+ | | | | Conversion | v
stream | Range |---+ +---------+ +------------+ /---\ Audio
------->| Decoder | | + |------>
| |---+ +---------+ +------------+ \---/
+---------+ | | CELT | | Decimation | ^
+->| Decoder |--->| (Optional) |----+
| | | |
+---------+ +------------+
4.1. Range Decoder
Opus uses an entropy coder based on range coding [RANGE-CODING]
[MARTIN79], which is itself a rediscovery of the FIFO arithmetic code
introduced by [CODING-THESIS]. It is very similar to arithmetic
encoding, except that encoding is done with digits in any base
instead of with bits, so it is faster when using larger bases (i.e.,
a byte). All of the calculations in the range coder must use bit-
exact integer arithmetic.
Symbols may also be coded as "raw bits" packed directly into the
bitstream, bypassing the range coder. These are packed backwards
starting at the end of the frame, as illustrated in Figure 12. This
reduces complexity and makes the stream more resilient to bit errors,
as corruption in the raw bits will not desynchronize the decoding
process, unlike corruption in the input to the range decoder. Raw
bits are only used in the CELT layer.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Range coder data (packed MSB to LSB) -> :
+ +
: :
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: | <- Boundary occurs at an arbitrary bit position :
+-+-+-+ +
: <- Raw bits data (packed LSB to MSB) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Legend:
LSB = Least Significant Bit
MSB = Most Significant Bit
Figure 12: Illustrative Example of Packing Range Coder
and Raw Bits Data
Each symbol coded by the range coder is drawn from a finite alphabet
and coded in a separate "context", which describes the size of the
alphabet and the relative frequency of each symbol in that alphabet.
Suppose there is a context with n symbols, identified with an index
that ranges from 0 to n-1. The parameters needed to encode or decode
symbol k in this context are represented by a three-tuple
(fl[k], fh[k], ft), all 16-bit unsigned integers, with
0 <= fl[k] < fh[k] <= ft <= 65535. The values of this tuple are
derived from the probability model for the symbol, represented by
traditional "frequency counts". Because Opus uses static contexts,
those are not updated as symbols are decoded. Let f[i] be the
frequency of symbol i. Then, the three-tuple corresponding to symbol
k is given by the following:
k-1 n-1
__ __
fl[k] = \ f[i], fh[k] = fl[k] + f[k], ft = \ f[i]
/_ /_
i=0 i=0
The range decoder extracts the symbols and integers encoded using the
range encoder in Section 5.1. The range decoder maintains an
internal state vector composed of the two-tuple (val, rng), where val
represents the difference between the high end of the current range
and the actual coded value, minus one, and rng represents the size of
the current range. Both val and rng are 32-bit unsigned integer
values.
4.1.1. Range Decoder Initialization
Let b0 be an 8-bit unsigned integer containing first input byte (or
containing zero if there are no bytes in this Opus frame). The
decoder initializes rng to 128 and initializes val to (127 -
(b0>>1)), where (b0>>1) is the top 7 bits of the first input byte.
It saves the remaining bit, (b0&1), for use in the renormalization
procedure described in Section 4.1.2.1, which the decoder invokes
immediately after initialization to read additional bits and
establish the invariant that rng > 2**23.
4.1.2. Decoding Symbols
Decoding a symbol is a two-step process. The first step determines a
16-bit unsigned value fs, which lies within the range of some symbol
in the current context. The second step updates the range decoder
state with the three-tuple (fl[k], fh[k], ft) corresponding to that
symbol.
The first step is implemented by ec_decode() (entdec.c), which
computes
val
fs = ft - min(------ + 1, ft)
rng/ft
The divisions here are integer division.
The decoder then identifies the symbol in the current context
corresponding to fs; i.e., the value of k whose three-tuple
(fl[k], fh[k], ft) satisfies fl[k] <= fs < fh[k]. It uses this tuple
to update val according to
rng
val = val - --- * (ft - fh[k])
ft
If fl[k] is greater than zero, then the decoder updates rng using
rng
rng = --- * (fh[k] - fl[k])
ft
Otherwise, it updates rng using
rng
rng = rng - --- * (ft - fh[k])
ft
Using a special case for the first symbol (rather than the last
symbol, as is commonly done in other arithmetic coders) ensures that
all the truncation error from the finite precision arithmetic
accumulates in symbol 0. This makes the cost of coding a 0 slightly
smaller, on average, than its estimated probability indicates and
makes the cost of coding any other symbol slightly larger. When
contexts are designed so that 0 is the most probable symbol, which is
often the case, this strategy minimizes the inefficiency introduced
by the finite precision. It also makes some of the special-case
decoding routines in Section 4.1.3 particularly simple.
After the updates, implemented by ec_dec_update() (entdec.c), the
decoder normalizes the range using the procedure in the next section,
and returns the index k.
4.1.2.1. Renormalization
To normalize the range, the decoder repeats the following process,
implemented by ec_dec_normalize() (entdec.c), until rng > 2**23. If
rng is already greater than 2**23, the entire process is skipped.
First, it sets rng to (rng<<8). Then, it reads the next byte of the
Opus frame and forms an 8-bit value sym, using the leftover bit
buffered from the previous byte as the high bit and the top 7 bits of
the byte just read as the other 7 bits of sym. The remaining bit in
the byte just read is buffered for use in the next iteration. If no
more input bytes remain, it uses zero bits instead. See
Section 4.1.1 for the initialization used to process the first byte.
Then, it sets
val = ((val<<8) + (255-sym)) & 0x7FFFFFFF
It is normal and expected that the range decoder will read several
bytes into the data of the raw bits (if any) at the end of the frame
by the time the frame is completely decoded, as illustrated in
Figure 13. This same data MUST also be returned as raw bits when
requested. The encoder is expected to terminate the stream in such a
way that the range decoder will decode the intended values regardless
of the data contained in the raw bits. Section 5.1.5 describes a
procedure for doing this. If the range decoder consumes all of the
bytes belonging to the current frame, it MUST continue to use zero
when any further input bytes are required, even if there is
additional data in the current packet from padding or other frames.
n n+1 n+2 n+3
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: | <----------- Overlap region ------------> | :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
^ ^
| End of data buffered by the range coder |
...-----------------------------------------------+
|
| End of data consumed by raw bits
+-------------------------------------------------------...
Figure 13: Illustrative Example of Raw Bits Overlapping
Range Coder Data
4.1.3. Alternate Decoding Methods
The reference implementation uses three additional decoding methods
that are exactly equivalent to the above but make assumptions and
simplifications that allow for a more efficient implementation.
4.1.3.1. ec_decode_bin()
The first is ec_decode_bin() (entdec.c), defined using the parameter
ftb instead of ft. It is mathematically equivalent to calling
ec_decode() with ft = (1<<ftb), but it avoids one of the divisions.
4.1.3.2. ec_dec_bit_logp()
The next is ec_dec_bit_logp() (entdec.c), which decodes a single
binary symbol, replacing both the ec_decode() and ec_dec_update()
steps. The context is described by a single parameter, logp, which
is the absolute value of the base-2 logarithm of the probability of a
"1". It is mathematically equivalent to calling ec_decode() with
ft = (1<<logp), followed by ec_dec_update() with the 3-tuple
(fl[k] = 0, fh[k] = (1<<logp) - 1, ft = (1<<logp)) if the returned
value of fs is less than (1<<logp) - 1 (a "0" was decoded), and with
(fl[k] = (1<<logp) - 1, fh[k] = ft = (1<<logp)) otherwise (a "1" was
decoded). The implementation requires no multiplications or
divisions.
4.1.3.3. ec_dec_icdf()
The last is ec_dec_icdf() (entdec.c), which decodes a single symbol
with a table-based context of up to 8 bits, also replacing both the
ec_decode() and ec_dec_update() steps, as well as the search for the
decoded symbol in between. The context is described by two
parameters, an icdf ("inverse" cumulative distribution function)
table and ftb. As with ec_decode_bin(), (1<<ftb) is equivalent to
ft. idcf[k], on the other hand, stores (1<<ftb)-fh[k], which is equal
to (1<<ftb) - fl[k+1]. fl[0] is assumed to be 0, and the table is
terminated by a value of 0 (where fh[k] == ft).
The function is mathematically equivalent to calling ec_decode() with
ft = (1<<ftb), using the returned value fs to search the table for
the first entry where fs < (1<<ftb)-icdf[k], and calling
ec_dec_update() with fl[k] = (1<<ftb) - icdf[k-1] (or 0 if k == 0),
fh[k] = (1<<ftb) - idcf[k], and ft = (1<<ftb). Combining the search
with the update allows the division to be replaced by a series of
multiplications (which are usually much cheaper), and using an
inverse CDF allows the use of an ftb as large as 8 in an 8-bit table
without any special cases. This is the primary interface with the
range decoder in the SILK layer, though it is used in a few places in
the CELT layer as well.
Although icdf[k] is more convenient for the code, the frequency
counts, f[k], are a more natural representation of the probability
distribution function (PDF) for a given symbol. Therefore, this
document lists the latter, not the former, when describing the
context in which a symbol is coded as a list, e.g., {4, 4, 4, 4}/16
for a uniform context with four possible values and ft = 16. The
value of ft after the slash is always the sum of the entries in the
PDF, but is included for convenience. Contexts with identical
probabilities, f[k]/ft, but different values of ft (or equivalently,
ftb) are not the same, and cannot, in general, be used in place of
one another. An icdf table is also not capable of representing a PDF
where the first symbol has 0 probability. In such contexts,
ec_dec_icdf() can decode the symbol by using a table that drops the
entries for any initial zero-probability values and by adding the
constant offset of the first value with a non-zero probability to its
return value.
4.1.4. Decoding Raw Bits
The raw bits used by the CELT layer are packed at the end of the
frame, with the least significant bit of the first value packed in
the least significant bit of the last byte, filling up to the most
significant bit in the last byte, continuing on to the least
significant bit of the penultimate byte, and so on. The reference
implementation reads them using ec_dec_bits() (entdec.c). Because
the range decoder must read several bytes ahead in the stream, as
described in Section 4.1.2.1, the input consumed by the raw bits may
overlap with the input consumed by the range coder, and a decoder
MUST allow this. The format should render it impossible to attempt
to read more raw bits than there are actual bits in the frame, though
a decoder may wish to check for this and report an error.
4.1.5. Decoding Uniformly Distributed Integers
The function ec_dec_uint() (entdec.c) decodes one of ft equiprobable
values in the range 0 to (ft - 1), inclusive, each with a frequency
of 1, where ft may be as large as (2**32 - 1). Because ec_decode()
is limited to a total frequency of (2**16 - 1), it splits up the
value into a range coded symbol representing up to 8 of the high
bits, and, if necessary, raw bits representing the remainder of the
value. The limit of 8 bits in the range coded symbol is a trade-off
between implementation complexity, modeling error (since the symbols
no longer truly have equal coding cost), and rounding error
introduced by the range coder itself (which gets larger as more bits
are included). Using raw bits reduces the maximum number of
divisions required in the worst case, but means that it may be
possible to decode a value outside the range 0 to (ft - 1),
inclusive.
ec_dec_uint() takes a single, positive parameter, ft, which is not
necessarily a power of two, and returns an integer, t, whose value
lies between 0 and (ft - 1), inclusive. Let ftb = ilog(ft - 1),
i.e., the number of bits required to store (ft - 1) in two's
complement notation. If ftb is 8 or less, then t is decoded with
t = ec_decode(ft), and the range coder state is updated using the
three-tuple (t, t + 1, ft).
If ftb is greater than 8, then the top 8 bits of t are decoded using
t = ec_decode(((ft - 1) >> (ftb - 8)) + 1)
the decoder state is updated using the three-tuple (t, t + 1, ((ft -
1) >> (ftb - 8)) + 1), and the remaining bits are decoded as raw
bits, setting
t = (t << (ftb - 8)) | ec_dec_bits(ftb - 8)
If, at this point, t >= ft, then the current frame is corrupt. In
that case, the decoder should assume there has been an error in the
coding, decoding, or transmission and SHOULD take measures to conceal
the error (e.g., saturate to ft-1 or use the Packet Loss Concealment
(PLC)) and/or report to the application that the error has occurred.
4.1.6. Current Bit Usage
The bit allocation routines in the CELT decoder need a conservative
upper bound on the number of bits that have been used from the
current frame thus far, including both range coder bits and raw bits.
This drives allocation decisions that must match those made in the
encoder. The upper bound is computed in the reference implementation
to whole-bit precision by the function ec_tell() (entcode.h) and to
fractional 1/8th bit precision by the function ec_tell_frac()
(entcode.c). Like all operations in the range coder, it must be
implemented in a bit-exact manner, and it must produce exactly the
same value returned by the same functions in the encoder after
encoding the same symbols.
ec_tell() is guaranteed to return ceil(ec_tell_frac()/8.0). In
various places, the codec will check to ensure there is enough room
to contain a symbol before attempting to decode it. In practice,
although the number of bits used so far is an upper bound, decoding a
symbol whose probability model suggests it has a worst-case cost of p
1/8th bits may actually advance the return value of ec_tell_frac() by
p-1, p, or p+1 1/8th bits, due to approximation error in that upper
bound, truncation error in the range coder, and for large values of
ft, modeling error in ec_dec_uint().
However, this error is bounded, and periodic calls to ec_tell() or
ec_tell_frac() at precisely defined points in the decoding process
prevent it from accumulating. For a range coder symbol that requires
a whole number of bits (i.e., for which ft/(fh[k] - fl[k]) is a power
of two), where there are at least p 1/8th bits available, decoding
the symbol will never cause ec_tell() or ec_tell_frac() to exceed the
size of the frame ("bust the budget"). In this case, the return
value of ec_tell_frac() will only advance by more than p 1/8th bits
if there were an additional, fractional number of bits remaining, and
it will never advance beyond the next whole-bit boundary, which is
safe, since frames always contain a whole number of bits. However,
when p is not a whole number of bits, an extra 1/8th bit is required
to ensure that decoding the symbol will not bust the budget.
The reference implementation keeps track of the total number of whole
bits that have been processed by the decoder so far in the variable
nbits_total, including the (possibly fractional) number of bits that
are currently buffered, but not consumed, inside the range coder.
nbits_total is initialized to 9 just before the initial range
renormalization process completes (or equivalently, it can be
initialized to 33 after the first renormalization). The extra two
bits over the actual amount buffered by the range coder guarantees
that it is an upper bound and that there is enough room for the
encoder to terminate the stream. Each iteration through the range
coder's renormalization loop increases nbits_total by 8. Reading raw
bits increases nbits_total by the number of raw bits read.
4.1.6.1. ec_tell()
The whole number of bits buffered in rng may be estimated via
lg = ilog(rng). ec_tell() then becomes a simple matter of removing
these bits from the total. It returns (nbits_total - lg).
In a newly initialized decoder, before any symbols have been read,
this reports that 1 bit has been used. This is the bit reserved for
termination of the encoder.
4.1.6.2. ec_tell_frac()
ec_tell_frac() estimates the number of bits buffered in rng to
fractional precision. Since rng must be greater than 2**23 after
renormalization, lg must be at least 24. Let
r_Q15 = rng >> (lg-16)
so that 32768 <= r_Q15 < 65536, an unsigned Q15 value representing
the fractional part of rng. Then, the following procedure can be
used to add one bit of precision to lg. First, update
r_Q15 = (r_Q15*r_Q15) >> 15
Then, add the 16th bit of r_Q15 to lg via
lg = 2*lg + (r_Q15 >> 16)
Finally, if this bit was a 1, reduce r_Q15 by a factor of two via
r_Q15 = r_Q15 >> 1
so that it once again lies in the range 32768 <= r_Q15 < 65536. This
procedure is repeated three times to extend lg to 1/8th bit
precision. ec_tell_frac() then returns (nbits_total*8 - lg).
4.2. SILK Decoder
The decoder's LP layer uses a modified version of the SILK codec
(herein simply called "SILK"), which runs a decoded excitation signal
through adaptive long-term and short-term prediction synthesis
filters. It runs at NB, MB, and WB sample rates internally. When
used in a SWB or FB Hybrid frame, the LP layer itself still only runs
in WB.
4.2.1. SILK Decoder Modules
An overview of the decoder is given in Figure 14.
+---------+ +------------+
-->| Range |--->| Decode |---------------------------+
1 | Decoder | 2 | Parameters |----------+ 5 |
+---------+ +------------+ 4 | |
3 | | |
\/ \/ \/
+------------+ +------------+ +------------+
| Generate |-->| LTP |-->| LPC |
| Excitation | | Synthesis | | Synthesis |
+------------+ +------------+ +------------+
^ |
| |
+-------------------+----------------+
| 6
| +------------+ +-------------+
+-->| Stereo |-->| Sample Rate |-->
| Unmixing | 7 | Conversion | 8
+------------+ +-------------+
1: Range encoded bitstream
2: Coded parameters
3: Pulses, LSBs, and signs
4: Pitch lags, Long-Term Prediction (LTP) coefficients
5: Linear Predictive Coding (LPC) coefficients and gains
6: Decoded signal (mono or mid-side stereo)
7: Unmixed signal (mono or left-right stereo)
8: Resampled signal
Figure 14: SILK Decoder
The decoder feeds the bitstream (1) to the range decoder from
Section 4.1 and then decodes the parameters in it (2) using the
procedures detailed in Sections 4.2.3 through 4.2.7.8.5. These
parameters (3, 4, 5) are used to generate an excitation signal (see
Section 4.2.7.8.6), which is fed to an optional Long-Term Prediction
(LTP) filter (voiced frames only, see Section 4.2.7.9.1) and then a
short-term prediction filter (see Section 4.2.7.9.2), producing the
decoded signal (6). For stereo streams, the mid-side representation
is converted to separate left and right channels (7). The result is
finally resampled to the desired output sample rate (e.g., 48 kHz) so
that the resampled signal (8) can be mixed with the CELT layer.
4.2.2. LP Layer Organization
Internally, the LP layer of a single Opus frame is composed of either
a single 10 ms regular SILK frame or between one and three 20 ms
regular SILK frames. A stereo Opus frame may double the number of
regular SILK frames (up to a total of six), since it includes
separate frames for a mid channel and, optionally, a side channel.
Optional Low Bit-Rate Redundancy (LBRR) frames, which are reduced-
bitrate encodings of previous SILK frames, may be included to aid in
recovery from packet loss. If present, these appear before the
regular SILK frames. They are, in most respects, identical to
regular, active SILK frames, except that they are usually encoded
with a lower bitrate. This document uses "SILK frame" to refer to
either one and "regular SILK frame" if it needs to draw a distinction
between the two.
Logically, each SILK frame is, in turn, composed of either two or
four 5 ms subframes. Various parameters, such as the quantization
gain of the excitation and the pitch lag and filter coefficients can
vary on a subframe-by-subframe basis. Physically, the parameters for
each subframe are interleaved in the bitstream, as described in the
relevant sections for each parameter.
All of these frames and subframes are decoded from the same range
coder, with no padding between them. Thus, packing multiple SILK
frames in a single Opus frame saves, on average, half a byte per SILK
frame. It also allows some parameters to be predicted from prior
SILK frames in the same Opus frame, since this does not degrade
packet loss robustness (beyond any penalty for merely using fewer,
larger packets to store multiple frames).
Stereo support in SILK uses a variant of mid-side coding, allowing a
mono decoder to simply decode the mid channel. However, the data for
the two channels is interleaved, so a mono decoder must still unpack
the data for the side channel. It would be required to do so anyway
for Hybrid Opus frames or to support decoding individual 20 ms
frames.
Table 3 summarizes the overall grouping of the contents of the LP
layer. Figures 15 and 16 illustrate the ordering of the various SILK
frames for a 60 ms Opus frame, for both mono and stereo,
respectively.
+-----------------------------------+---------------+---------------+
| Symbol(s) | PDF(s) | Condition |
+-----------------------------------+---------------+---------------+
| Voice Activity Detection (VAD) | {1, 1}/2 | |
| Flags | | |
| | | |
| LBRR Flag | {1, 1}/2 | |
| | | |
| Per-Frame LBRR Flags | Table 4 | Section 4.2.4 |
| | | |
| LBRR Frame(s) | Section 4.2.7 | Section 4.2.4 |
| | | |
| Regular SILK Frame(s) | Section 4.2.7 | |
+-----------------------------------+---------------+---------------+
Table 3: Organization of the SILK layer of an Opus Frame
+---------------------------------+
| VAD Flags |
+---------------------------------+
| LBRR Flag |
+---------------------------------+
| Per-Frame LBRR Flags (Optional) |
+---------------------------------+
| LBRR Frame 1 (Optional) |
+---------------------------------+
| LBRR Frame 2 (Optional) |
+---------------------------------+
| LBRR Frame 3 (Optional) |
+---------------------------------+
| Regular SILK Frame 1 |
+---------------------------------+
| Regular SILK Frame 2 |
+---------------------------------+
| Regular SILK Frame 3 |
+---------------------------------+
Figure 15: A 60 ms Mono Frame
+---------------------------------------+
| Mid VAD Flags |
+---------------------------------------+
| Mid LBRR Flag |
+---------------------------------------+
| Side VAD Flags |
+---------------------------------------+
| Side LBRR Flag |
+---------------------------------------+
| Mid Per-Frame LBRR Flags (Optional) |
+---------------------------------------+
| Side Per-Frame LBRR Flags (Optional) |
+---------------------------------------+
| Mid LBRR Frame 1 (Optional) |
+---------------------------------------+
| Side LBRR Frame 1 (Optional) |
+---------------------------------------+
| Mid LBRR Frame 2 (Optional) |
+---------------------------------------+
| Side LBRR Frame 2 (Optional) |
+---------------------------------------+
| Mid LBRR Frame 3 (Optional) |
+---------------------------------------+
| Side LBRR Frame 3 (Optional) |
+---------------------------------------+
| Mid Regular SILK Frame 1 |
+---------------------------------------+
| Side Regular SILK Frame 1 (Optional) |
+---------------------------------------+
| Mid Regular SILK Frame 2 |
+---------------------------------------+
| Side Regular SILK Frame 2 (Optional) |
+---------------------------------------+
| Mid Regular SILK Frame 3 |
+---------------------------------------+
| Side Regular SILK Frame 3 (Optional) |
+---------------------------------------+
Figure 16: A 60 ms Stereo Frame
4.2.3. Header Bits
The LP layer begins with two to eight header bits, decoded in
silk_Decode() (dec_API.c). These consist of one Voice Activity
Detection (VAD) bit per frame (up to 3), followed by a single flag
indicating the presence of LBRR frames. For a stereo packet, these
first flags correspond to the mid channel, and a second set of flags
is included for the side channel.
Because these are the first symbols decoded by the range coder and
because they are coded as binary values with uniform probability,
they can be extracted directly from the most significant bits of the
first byte of compressed data. Thus, a receiver can determine if an
Opus frame contains any active SILK frames without the overhead of
using the range decoder.
4.2.4. Per-Frame LBRR Flags
For Opus frames longer than 20 ms, a set of LBRR flags is decoded for
each channel that has its LBRR flag set. Each set contains one flag
per 20 ms SILK frame. 40 ms Opus frames use the 2-frame LBRR flag PDF
from Table 4, and 60 ms Opus frames use the 3-frame LBRR flag PDF.
For each channel, the resulting 2- or 3-bit integer contains the
corresponding LBRR flag for each frame, packed in order from the LSB
to the MSB.
+------------+-------------------------------------+
| Frame Size | PDF |
+------------+-------------------------------------+
| 40 ms | {0, 53, 53, 150}/256 |
| | |
| 60 ms | {0, 41, 20, 29, 41, 15, 28, 82}/256 |
+------------+-------------------------------------+
Table 4: LBRR Flag PDFs
A 10 or 20 ms Opus frame does not contain any per-frame LBRR flags,
as there may be at most one LBRR frame per channel. The global LBRR
flag in the header bits (see Section 4.2.3) is already sufficient to
indicate the presence of that single LBRR frame.
4.2.5. LBRR Frames
The LBRR frames, if present, contain an encoded representation of the
signal immediately prior to the current Opus frame as if it were
encoded with the current mode, frame size, audio bandwidth, and
channel count, even if those differ from the prior Opus frame. When
one of these parameters changes from one Opus frame to the next, this
implies that the LBRR frames of the current Opus frame may not be
simple drop-in replacements for the contents of the previous Opus
frame.
For example, when switching from 20 ms to 60 ms, the 60 ms Opus frame
may contain LBRR frames covering up to three prior 20 ms Opus frames,
even if those frames already contained LBRR frames covering some of
the same time periods. When switching from 20 ms to 10 ms, the 10 ms
Opus frame can contain an LBRR frame covering at most half the prior
20 ms Opus frame, potentially leaving a hole that needs to be
concealed from even a single packet loss (see Section 4.4). When
switching from mono to stereo, the LBRR frames in the first stereo
Opus frame MAY contain a non-trivial side channel.
In order to properly produce LBRR frames under all conditions, an
encoder might need to buffer up to 60 ms of audio and re-encode it
during these transitions. However, the reference implementation opts
to disable LBRR frames at the transition point for simplicity. Since
transitions are relatively infrequent in normal usage, this does not
have a significant impact on packet loss robustness.
The LBRR frames immediately follow the LBRR flags, prior to any
regular SILK frames. Section 4.2.7 describes their exact contents.
LBRR frames do not include their own separate VAD flags. LBRR frames
are only meant to be transmitted for active speech, thus all LBRR
frames are treated as active.
In a stereo Opus frame longer than 20 ms, although the per-frame LBRR
flags for the mid channel are coded as a unit before the per-frame
LBRR flags for the side channel, the LBRR frames themselves are
interleaved. The decoder parses an LBRR frame for the mid channel of
a given 20 ms interval (if present) and then immediately parses the
corresponding LBRR frame for the side channel (if present), before
proceeding to the next 20 ms interval.
4.2.6. Regular SILK Frames
The regular SILK frame(s) follow the LBRR frames (if any).
Section 4.2.7 describes their contents, as well. Unlike the LBRR
frames, a regular SILK frame is coded for each time interval in an
Opus frame, even if the corresponding VAD flags are unset. For
stereo Opus frames longer than 20 ms, the regular mid and side SILK
frames for each 20 ms interval are interleaved, just as with the LBRR
frames. The side frame may be skipped by coding an appropriate flag,
as detailed in Section 4.2.7.2.
4.2.7. SILK Frame Contents
Each SILK frame includes a set of side information that encodes
o The frame type and quantization type (Section 4.2.7.3),
o Quantization gains (Section 4.2.7.4),
o Short-term prediction filter coefficients (Section 4.2.7.5),
o A Line Spectral Frequencies (LSFs) interpolation weight
(Section 4.2.7.5.5),
o LTP filter lags and gains (Section 4.2.7.6), and
o A Linear Congruential Generator (LCG) seed (Section 4.2.7.7).
The quantized excitation signal (see Section 4.2.7.8) follows these
at the end of the frame. Table 5 details the overall organization of
a SILK frame.
+---------------------------+-------------------+-------------------+
| Symbol(s) | PDF(s) | Condition |
+---------------------------+-------------------+-------------------+
| Stereo Prediction Weights | Table 6 | Section 4.2.7.1 |
| | | |
| Mid-only Flag | Table 8 | Section 4.2.7.2 |
| | | |
| Frame Type | Section 4.2.7.3 | |
| | | |
| Subframe Gains | Section 4.2.7.4 | |
| | | |
| Normalized LSF Stage-1 | Table 14 | |
| Index | | |
| | | |
| Normalized LSF Stage-2 | Section 4.2.7.5.2 | |
| Residual | | |
| | | |
| Normalized LSF | Table 26 | 20 ms frame |
| Interpolation Weight | | |
| | | |
| Primary Pitch Lag | Section 4.2.7.6.1 | Voiced frame |
| | | |
| Subframe Pitch Contour | Table 32 | Voiced frame |
| | | |
| Periodicity Index | Table 37 | Voiced frame |
| | | |
| LTP Filter | Table 38 | Voiced frame |
| | | |
| LTP Scaling | Table 42 | Section 4.2.7.6.3 |
| | | |
| LCG Seed | Table 43 | |
| | | |
| Excitation Rate Level | Table 45 | |
| | | |
| Excitation Pulse Counts | Table 46 | |
| | | |
| Excitation Pulse | Section 4.2.7.8.3 | Non-zero pulse |
| Locations | | count |
| | | |
| Excitation LSBs | Table 51 | Section 4.2.7.8.2 |
| | | |
| Excitation Signs | Table 52 | |
+---------------------------+-------------------+-------------------+
Table 5: Order of the Symbols in an Individual SILK Frame
4.2.7.1. Stereo Prediction Weights
A SILK frame corresponding to the mid channel of a stereo Opus frame
begins with a pair of side channel prediction weights, designed such
that zeros indicate normal mid-side coupling. Since these weights
can change on every frame, the first portion of each frame linearly
interpolates between the previous weights and the current ones, using
zeros for the previous weights if none are available. These
prediction weights are never included in a mono Opus frame, and the
previous weights are reset to zeros on any transition from mono to
stereo. They are also not included in an LBRR frame for the side
channel, even if the LBRR flags indicate the corresponding mid
channel was not coded. In that case, the previous weights are used,
again substituting in zeros if no previous weights are available
since the last decoder reset (see Section 4.5.2).
To summarize, these weights are coded if and only if
o This is a stereo Opus frame (Section 3.1), and
o The current SILK frame corresponds to the mid channel.
The prediction weights are coded in three separate pieces, which are
decoded by silk_stereo_decode_pred() (stereo_decode_pred.c). The
first piece jointly codes the high-order part of a table index for
both weights. The second piece codes the low-order part of each
table index. The third piece codes an offset used to linearly
interpolate between table indices. The details are as follows.
Let n be an index decoded with the 25-element stage-1 PDF in Table 6.
Then, let i0 and i1 be indices decoded with the stage-2 and stage-3
PDFs in Table 6, respectively, and let i2 and i3 be two more indices
decoded with the stage-2 and stage-3 PDFs, all in that order.
+-------+-----------------------------------------------------------+
| Stage | PDF |
+-------+-----------------------------------------------------------+
| Stage | {7, 2, 1, 1, 1, 10, 24, 8, 1, 1, 3, 23, 92, 23, 3, 1, 1, |
| 1 | 8, 24, 10, 1, 1, 1, 2, 7}/256 |
| | |
| Stage | {85, 86, 85}/256 |
| 2 | |
| | |
| Stage | {51, 51, 52, 51, 51}/256 |
| 3 | |
+-------+-----------------------------------------------------------+
Table 6: Stereo Weight PDFs
Then, use n, i0, and i2 to form two table indices, wi0 and wi1,
according to
wi0 = i0 + 3*(n/5)
wi1 = i2 + 3*(n%5)
where the division is integer division. The range of these indices
is 0 to 14, inclusive. Let w_Q13[i] be the i'th weight from Table 7.
Then, the two prediction weights, w0_Q13 and w1_Q13, are
w1_Q13 = w_Q13[wi1]
+ (((w_Q13[wi1+1] - w_Q13[wi1])*6554) >> 16)*(2*i3 + 1)
w0_Q13 = w_Q13[wi0]
+ (((w_Q13[wi0+1] - w_Q13[wi0])*6554) >> 16)*(2*i1 + 1)
- w1_Q13
N.B., w1_Q13 is computed first here, because w0_Q13 depends on it.
The constant 6554 is approximately 0.1 in Q16. Although wi0 and wi1
only have 15 possible values, Table 7 contains 16 entries to allow
interpolation between entry wi0 and (wi0 + 1) (and likewise for wi1).
+-------+--------------+
| Index | Weight (Q13) |
+-------+--------------+
| 0 | -13732 |
| | |
| 1 | -10050 |
| | |
| 2 | -8266 |
| | |
| 3 | -7526 |
| | |
| 4 | -6500 |
| | |
| 5 | -5000 |
| | |
| 6 | -2950 |
| | |
| 7 | -820 |
| | |
| 8 | 820 |
| | |
| 9 | 2950 |
| | |
| 10 | 5000 |
| | |
| 11 | 6500 |
| | |
| 12 | 7526 |
| | |
| 13 | 8266 |
| | |
| 14 | 10050 |
| | |
| 15 | 13732 |
+-------+--------------+
Table 7: Stereo Weight Table
4.2.7.2. Mid-Only Flag
A flag appears after the stereo prediction weights that indicates if
only the mid channel is coded for this time interval. It appears
only when
o This is a stereo Opus frame (see Section 3.1),
o The current SILK frame corresponds to the mid channel, and
o Either
* This is a regular SILK frame where the VAD flags (see
Section 4.2.3) indicate that the corresponding side channel is
not active.
* This is an LBRR frame where the LBRR flags (see Sections 4.2.3
and 4.2.4) indicate that the corresponding side channel is not
coded.
It is omitted when there are no stereo weights, for all of the same
reasons. It is also omitted for a regular SILK frame when the VAD
flag of the corresponding side channel frame is set (indicating it is
active). The side channel must be coded in this case, making the
mid-only flag redundant. It is also omitted for an LBRR frame when
the corresponding LBRR flags indicate the side channel is coded.
When the flag is present, the decoder reads a single value using the
PDF in Table 8, as implemented in silk_stereo_decode_mid_only()
(stereo_decode_pred.c). If the flag is set, then there is no
corresponding SILK frame for the side channel, the entire decoding
process for the side channel is skipped, and zeros are fed to the
stereo unmixing process (see Section 4.2.8) instead. As stated
above, LBRR frames still include this flag when the LBRR flag
indicates that the side channel is not coded. In that case, if this
flag is zero (indicating that there should be a side channel), then
Packet Loss Concealment (PLC, see Section 4.4) SHOULD be invoked to
recover a side channel signal. Otherwise, the stereo image will
collapse.
+---------------+
| PDF |
+---------------+
| {192, 64}/256 |
+---------------+
Table 8: Mid-only Flag PDF
4.2.7.3. Frame Type
Each SILK frame contains a single "frame type" symbol that jointly
codes the signal type and quantization offset type of the
corresponding frame. If the current frame is a regular SILK frame
whose VAD bit was not set (an "inactive" frame), then the frame type
symbol takes on a value of either 0 or 1 and is decoded using the
first PDF in Table 9. If the frame is an LBRR frame or a regular
SILK frame whose VAD flag was set (an "active" frame), then the value
of the symbol may range from 2 to 5, inclusive, and is decoded using
the second PDF in Table 9. Table 10 translates between the value of
the frame type symbol and the corresponding signal type and
quantization offset type.
+----------+-----------------------------+
| VAD Flag | PDF |
+----------+-----------------------------+
| Inactive | {26, 230, 0, 0, 0, 0}/256 |
| | |
| Active | {0, 0, 24, 74, 148, 10}/256 |
+----------+-----------------------------+
Table 9: Frame Type PDFs
+------------+-------------+--------------------------+
| Frame Type | Signal Type | Quantization Offset Type |
+------------+-------------+--------------------------+
| 0 | Inactive | Low |
| | | |
| 1 | Inactive | High |
| | | |
| 2 | Unvoiced | Low |
| | | |
| 3 | Unvoiced | High |
| | | |
| 4 | Voiced | Low |
| | | |
| 5 | Voiced | High |
+------------+-------------+--------------------------+
Table 10: Signal Type and Quantization Offset Type from Frame Type
4.2.7.4. Subframe Gains
A separate quantization gain is coded for each 5 ms subframe. These
gains control the step size between quantization levels of the
excitation signal and, therefore, the quality of the reconstruction.
They are independent of and unrelated to the pitch contours coded for
voiced frames. The quantization gains are themselves uniformly
quantized to 6 bits on a log scale, giving them a resolution of
approximately 1.369 dB and a range of approximately 1.94 dB to
88.21 dB.
The subframe gains are either coded independently, or relative to the
gain from the most recent coded subframe in the same channel.
Independent coding is used if and only if
o This is the first subframe in the current SILK frame, and
o Either
* This is the first SILK frame of its type (LBRR or regular) for
this channel in the current Opus frame, or
* The previous SILK frame of the same type (LBRR or regular) for
this channel in the same Opus frame was not coded.
In an independently coded subframe gain, the 3 most significant bits
of the quantization gain are decoded using a PDF selected from
Table 11 based on the decoded signal type (see Section 4.2.7.3).
+-------------+------------------------------------+
| Signal Type | PDF |
+-------------+------------------------------------+
| Inactive | {32, 112, 68, 29, 12, 1, 1, 1}/256 |
| | |
| Unvoiced | {2, 17, 45, 60, 62, 47, 19, 4}/256 |
| | |
| Voiced | {1, 3, 26, 71, 94, 50, 9, 2}/256 |
+-------------+------------------------------------+
Table 11: PDFs for Independent Quantization Gain MSB Coding
The 3 least significant bits are decoded using a uniform PDF:
+--------------------------------------+
| PDF |
+--------------------------------------+
| {32, 32, 32, 32, 32, 32, 32, 32}/256 |
+--------------------------------------+
Table 12: PDF for Independent Quantization Gain LSB Coding
These 6 bits are combined to form a value, gain_index, between 0 and
63. When the gain for the previous subframe is available, then the
current gain is limited as follows:
log_gain = max(gain_index, previous_log_gain - 16)
This may help some implementations limit the change in precision of
their internal LTP history. The indices to which this clamp applies
cannot simply be removed from the codebook, because previous_log_gain
will not be available after packet loss. The clamping is skipped
after a decoder reset, and in the side channel if the previous frame
in the side channel was not coded, since there is no value for
previous_log_gain available. It MAY also be skipped after packet
loss.
For subframes that do not have an independent gain (including the
first subframe of frames not listed as using independent coding
above), the quantization gain is coded relative to the gain from the
previous subframe (in the same channel). The PDF in Table 13 yields
a delta_gain_index value between 0 and 40, inclusive.
+-------------------------------------------------------------------+
| PDF |
+-------------------------------------------------------------------+
| {6, 5, 11, 31, 132, 21, 8, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, |
| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
| 1}/256 |
+-------------------------------------------------------------------+
Table 13: PDF for Delta Quantization Gain Coding
The following formula translates this index into a quantization gain
for the current subframe using the gain from the previous subframe:
log_gain = clamp(0, max(2*delta_gain_index - 16,
previous_log_gain + delta_gain_index - 4), 63)
silk_gains_dequant() (gain_quant.c) dequantizes log_gain for the k'th
subframe and converts it into a linear Q16 scale factor via
gain_Q16[k] = silk_log2lin((0x1D1C71*log_gain>>16) + 2090)
The function silk_log2lin() (log2lin.c) computes an approximation of
2**(inLog_Q7/128.0), where inLog_Q7 is its Q7 input. Let i =
inLog_Q7>>7 be the integer part of inLogQ7 and f = inLog_Q7&127 be
the fractional part. Then,
(1<<i) + ((-174*f*(128-f)>>16)+f)*((1<<i)>>7)
yields the approximate exponential. The final Q16 gain values lies
between 81920 and 1686110208, inclusive (representing scale factors
of 1.25 to 25728, respectively).
4.2.7.5. Normalized Line Spectral Frequency (LSF) and Linear Predictive
Coding (LPC) Coefficients
A set of normalized Line Spectral Frequency (LSF) coefficients follow
the quantization gains in the bitstream and represent the Linear
Predictive Coding (LPC) coefficients for the current SILK frame.
Once decoded, the normalized LSFs form an increasing list of Q15
values between 0 and 1. These represent the interleaved zeros on the
upper half of the unit circle (between 0 and pi, hence "normalized")
in the standard decomposition [SPECTRAL-PAIRS] of the LPC filter into
a symmetric part and an anti-symmetric part (P and Q in
Section 4.2.7.5.6). Because of non-linear effects in the decoding
process, an implementation SHOULD match the fixed-point arithmetic
described in this section exactly. An encoder SHOULD also use the
same process.
The normalized LSFs are coded using a two-stage vector quantizer (VQ)
(Sections 4.2.7.5.1 and 4.2.7.5.2). NB and MB frames use an order-10
predictor, while WB frames use an order-16 predictor. Thus, each of
these two cases uses a different set of tables. After reconstructing
the normalized LSFs (Section 4.2.7.5.3), the decoder runs them
through a stabilization process (Section 4.2.7.5.4), interpolates
them between frames (Section 4.2.7.5.5), converts them back into LPC
coefficients (Section 4.2.7.5.6), and then runs them through further
processes to limit the range of the coefficients (Section 4.2.7.5.7)
and the gain of the filter (Section 4.2.7.5.8). All of this is
necessary to ensure the reconstruction process is stable.
4.2.7.5.1. Normalized LSF Stage 1 Decoding
The first VQ stage uses a 32-element codebook, coded with one of the
PDFs in Table 14, depending on the audio bandwidth and the signal
type of the current SILK frame. This yields a single index, I1, for
the entire frame, which
1. Indexes an element in a coarse codebook,
2. Selects the PDFs for the second stage of the VQ, and
3. Selects the prediction weights used to remove intra-frame
redundancy from the second stage.
The actual codebook elements are listed in Tables 23 and 24, but they
are not needed until the last stages of reconstructing the LSF
coefficients.
+-----------+----------+--------------------------------------------+
| Audio | Signal | PDF |
| Bandwidth | Type | |
+-----------+----------+--------------------------------------------+
| NB or MB | Inactive | {44, 34, 30, 19, 21, 12, 11, 3, 3, 2, 16, |
| | or | 2, 2, 1, 5, 2, 1, 3, 3, 1, 1, 2, 2, 2, 3, |
| | unvoiced | 1, 9, 9, 2, 7, 2, 1}/256 |
| | | |
| NB or MB | Voiced | {1, 10, 1, 8, 3, 8, 8, 14, 13, 14, 1, 14, |
| | | 12, 13, 11, 11, 12, 11, 10, 10, 11, 8, 9, |
| | | 8, 7, 8, 1, 1, 6, 1, 6, 5}/256 |
| | | |
| WB | Inactive | {31, 21, 3, 17, 1, 8, 17, 4, 1, 18, 16, 4, |
| | or | 2, 3, 1, 10, 1, 3, 16, 11, 16, 2, 2, 3, 2, |
| | unvoiced | 11, 1, 4, 9, 8, 7, 3}/256 |
| | | |
| WB | Voiced | {1, 4, 16, 5, 18, 11, 5, 14, 15, 1, 3, 12, |
| | | 13, 14, 14, 6, 14, 12, 2, 6, 1, 12, 12, |
| | | 11, 10, 3, 10, 5, 1, 1, 1, 3}/256 |
+-----------+----------+--------------------------------------------+
Table 14: PDFs for Normalized LSF Stage-1 Index Decoding
4.2.7.5.2. Normalized LSF Stage 2 Decoding
A total of 16 PDFs are available for the LSF residual in the second
stage: the 8 (a...h) for NB and MB frames given in Table 15, and the
8 (i...p) for WB frames given in Table 16. Which PDF is used for
which coefficient is driven by the index, I1, decoded in the first
stage. Table 17 lists the letter of the corresponding PDF for each
normalized LSF coefficient for NB and MB, and Table 18 lists the same
information for WB.
+----------+--------------------------------------+
| Codebook | PDF |
+----------+--------------------------------------+
| a | {1, 1, 1, 15, 224, 11, 1, 1, 1}/256 |
| | |
| b | {1, 1, 2, 34, 183, 32, 1, 1, 1}/256 |
| | |
| c | {1, 1, 4, 42, 149, 55, 2, 1, 1}/256 |
| | |
| d | {1, 1, 8, 52, 123, 61, 8, 1, 1}/256 |
| | |
| e | {1, 3, 16, 53, 101, 74, 6, 1, 1}/256 |
| | |
| f | {1, 3, 17, 55, 90, 73, 15, 1, 1}/256 |
| | |
| g | {1, 7, 24, 53, 74, 67, 26, 3, 1}/256 |
| | |
| h | {1, 1, 18, 63, 78, 58, 30, 6, 1}/256 |
+----------+--------------------------------------+
Table 15: PDFs for NB/MB Normalized LSF Stage-2 Index Decoding
+----------+---------------------------------------+
| Codebook | PDF |
+----------+---------------------------------------+
| i | {1, 1, 1, 9, 232, 9, 1, 1, 1}/256 |
| | |
| j | {1, 1, 2, 28, 186, 35, 1, 1, 1}/256 |
| | |
| k | {1, 1, 3, 42, 152, 53, 2, 1, 1}/256 |
| | |
| l | {1, 1, 10, 49, 126, 65, 2, 1, 1}/256 |
| | |
| m | {1, 4, 19, 48, 100, 77, 5, 1, 1}/256 |
| | |
| n | {1, 1, 14, 54, 100, 72, 12, 1, 1}/256 |
| | |
| o | {1, 1, 15, 61, 87, 61, 25, 4, 1}/256 |
| | |
| p | {1, 7, 21, 50, 77, 81, 17, 1, 1}/256 |
+----------+---------------------------------------+
Table 16: PDFs for WB Normalized LSF Stage-2 Index Decoding
+----+---------------------+
| I1 | Coefficient |
+----+---------------------+
| | 0 1 2 3 4 5 6 7 8 9 |
| 0 | a a a a a a a a a a |
| | |
| 1 | b d b c c b c b b b |
| | |
| 2 | c b b b b b b b b b |
| | |
| 3 | b c c c c b c b b b |
| | |
| 4 | c d d d d c c c c c |
| | |
| 5 | a f d d c c c c b b |
| | |
| g | a c c c c c c c c b |
| | |
| 7 | c d g e e e f e f f |
| | |
| 8 | c e f f e f e g e e |
| | |
| 9 | c e e h e f e f f e |
| | |
| 10 | e d d d c d c c c c |
| | |
| 11 | b f f g e f e f f f |
| | |
| 12 | c h e g f f f f f f |
| | |
| 13 | c h f f f f f g f e |
| | |
| 14 | d d f e e f e f e e |
| | |
| 15 | c d d f f e e e e e |
| | |
| 16 | c e e g e f e f f f |
| | |
| 17 | c f e g f f f e f e |
| | |
| 18 | c h e f e f e f f f |
| | |
| 19 | c f e g h g f g f e |
| | |
| 20 | d g h e g f f g e f |
| | |
| 21 | c h g e e e f e f f |
| | |
| 22 | e f f e g g f g f e |
| | |
| 23 | c f f g f g e g e e |
| | |
| 24 | e f f f d h e f f e |
| | |
| 25 | c d e f f g e f f e |
| | |
| 26 | c d c d d e c d d d |
| | |
| 27 | b b c c c c c d c c |
| | |
| 28 | e f f g g g f g e f |
| | |
| 29 | d f f e e e e d d c |
| | |
| 30 | c f d h f f e e f e |
| | |
| 31 | e e f e f g f g f e |
+----+---------------------+
Table 17: Codebook Selection for NB/MB Normalized LSF Stage-2 Index
Decoding
+----+------------------------------------------------+
| I1 | Coefficient |
+----+------------------------------------------------+
| | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
| | |
| 0 | i i i i i i i i i i i i i i i i |
| | |
| 1 | k l l l l l k k k k k j j j i l |
| | |
| 2 | k n n l p m m n k n m n n m l l |
| | |
| 3 | i k j k k j j j j j i i i i i j |
| | |
| 4 | i o n m o m p n m m m n n m m l |
| | |
| 5 | i l n n m l l n l l l l l l k m |
| | |
| 6 | i i i i i i i i i i i i i i i i |
| | |
| 7 | i k o l p k n l m n n m l l k l |
| | |
| 8 | i o k o o m n m o n m m n l l l |
| | |
| 9 | k j i i i i i i i i i i i i i i |
| | |
| 10 | i j i i i i i i i i i i i i i j |
| | |
| 11 | k k l m n l l l l l l l k k j l |
| | |
| 12 | k k l l m l l l l l l l l k j l |
| | |
| 13 | l m m m o m m n l n m m n m l m |
| | |
| 14 | i o m n m p n k o n p m m l n l |
| | |
| 15 | i j i j j j j j j j i i i i j i |
| | |
| 16 | j o n p n m n l m n m m m l l m |
| | |
| 17 | j l l m m l l n k l l n n n l m |
| | |
| 18 | k l l k k k l k j k j k j j j m |
| | |
| 19 | i k l n l l k k k j j i i i i i |
| | |
| 20 | l m l n l l k k j j j j j k k m |
| | |
| 21 | k o l p p m n m n l n l l k l l |
| | |
| 22 | k l n o o l n l m m l l l l k m |
| | |
| 23 | j l l m m m m l n n n l j j j j |
| | |
| 24 | k n l o o m p m m n l m m l l l |
| | |
| 25 | i o j j i i i i i i i i i i i i |
| | |
| 26 | i o o l n k n n l m m p p m m m |
| | |
| 27 | l l p l n m l l l k k l l l k l |
| | |
| 28 | i i j i i i k j k j j k k k j j |
| | |
| 29 | i l k n l l k l k j i i j i i j |
| | |
| 30 | l n n m p n l l k l k k j i j i |
| | |
| 31 | k l n l m l l l k j k o m i i i |
+----+------------------------------------------------+
Table 18: Codebook Selection for WB Normalized LSF Stage-2 Index
Decoding
Decoding the second stage residual proceeds as follows. For each
coefficient, the decoder reads a symbol using the PDF corresponding
to I1 from either Table 17 or Table 18, and subtracts 4 from the
result to give an index in the range -4 to 4, inclusive. If the
index is either -4 or 4, it reads a second symbol using the PDF in
Table 19, and adds the value of this second symbol to the index,
using the same sign. This gives the index, I2[k], a total range of
-10 to 10, inclusive.
+-------------------------------+
| PDF |
+-------------------------------+
| {156, 60, 24, 9, 4, 2, 1}/256 |
+-------------------------------+
Table 19: PDF for Normalized LSF Index Extension Decoding
The decoded indices from both stages are translated back into
normalized LSF coefficients in silk_NLSF_decode() (NLSF_decode.c).
The stage-2 indices represent residuals after both the first stage of
the VQ and a separate backwards-prediction step. The backwards
prediction process in the encoder subtracts a prediction from each
residual formed by a multiple of the coefficient that follows it.
The decoder must undo this process. Table 20 contains lists of
prediction weights for each coefficient. There are two lists for NB
and MB, and another two lists for WB, giving two possible prediction
weights for each coefficient.
+-------------+-----+-----+-----+-----+
| Coefficient | A | B | C | D |
+-------------+-----+-----+-----+-----+
| 0 | 179 | 116 | 175 | 68 |
| | | | | |
| 1 | 138 | 67 | 148 | 62 |
| | | | | |
| 2 | 140 | 82 | 160 | 66 |
| | | | | |
| 3 | 148 | 59 | 176 | 60 |
| | | | | |
| 4 | 151 | 92 | 178 | 72 |
| | | | | |
| 5 | 149 | 72 | 173 | 117 |
| | | | | |
| 6 | 153 | 100 | 174 | 85 |
| | | | | |
| 7 | 151 | 89 | 164 | 90 |
| | | | | |
| 8 | 163 | 92 | 177 | 118 |
| | | | | |
| 9 | | | 174 | 136 |
| | | | | |
| 10 | | | 196 | 151 |
| | | | | |
| 11 | | | 182 | 142 |
| | | | | |
| 12 | | | 198 | 160 |
| | | | | |
| 13 | | | 192 | 142 |
| | | | | |
| 14 | | | 182 | 155 |
+-------------+-----+-----+-----+-----+
Table 20: Prediction Weights for Normalized LSF Decoding
The prediction is undone using the procedure implemented in
silk_NLSF_residual_dequant() (NLSF_decode.c), which is as follows.
Each coefficient selects its prediction weight from one of the two
lists based on the stage-1 index, I1. Table 21 gives the selections
for each coefficient for NB and MB, and Table 22 gives the selections
for WB. Let d_LPC be the order of the codebook, i.e., 10 for NB and
MB, and 16 for WB, and let pred_Q8[k] be the weight for the k'th
coefficient selected by this process for 0 <= k < d_LPC-1. Then, the
stage-2 residual for each coefficient is computed via
res_Q10[k] = (k+1 < d_LPC ? (res_Q10[k+1]*pred_Q8[k])>>8 : 0)
+ ((((I2[k]<<10) - sign(I2[k])*102)*qstep)>>16) ,
where qstep is the Q16 quantization step size, which is 11796 for NB
and MB and 9830 for WB (representing step sizes of approximately 0.18
and 0.15, respectively).
+----+-------------------+
| I1 | Coefficient |
+----+-------------------+
| | 0 1 2 3 4 5 6 7 8 |
| | |
| 0 | A B A A A A A A A |
| | |
| 1 | B A A A A A A A A |
| | |
| 2 | A A A A A A A A A |
| | |
| 3 | B B B A A A A B A |
| | |
| 4 | A B A A A A A A A |
| | |
| 5 | A B A A A A A A A |
| | |
| 6 | B A B B A A A B A |
| | |
| 7 | A B B A A B B A A |
| | |
| 8 | A A B B A B A B B |
| | |
| 9 | A A B B A A B B B |
| | |
| 10 | A A A A A A A A A |
| | |
| 11 | A B A B B B B B A |
| | |
| 12 | A B A B B B B B A |
| | |
| 13 | A B B B B B B B A |
| | |
| 14 | B A B B A B B B B |
| | |
| 15 | A B B B B B A B A |
| | |
| 16 | A A B B A B A B A |
| | |
| 17 | A A B B B A B B B |
| | |
| 18 | A B B A A B B B A |
| | |
| 19 | A A A B B B A B A |
| | |
| 20 | A B B A A B A B A |
| | |
| 21 | A B B A A A B B A |
| | |
| 22 | A A A A A B B B B |
| | |
| 23 | A A B B A A A B B |
| | |
| 24 | A A A B A B B B B |
| | |
| 25 | A B B B B B B B A |
| | |
| 26 | A A A A A A A A A |
| | |
| 27 | A A A A A A A A A |
| | |
| 28 | A A B A B B A B A |
| | |
| 29 | B A A B A A A A A |
| | |
| 30 | A A A B B A B A B |
| | |
| 31 | B A B B A B B B B |
+----+-------------------+
Table 21: Prediction Weight Selection for NB/MB Normalized LSF
Decoding
+----+---------------------------------------------+
| I1 | Coefficient |
+----+---------------------------------------------+
| | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 |
| | |
| 0 | C C C C C C C C C C C C C C D |
| | |
| 1 | C C C C C C C C C C C C C C C |
| | |
| 2 | C C D C C D D D C D D D D C C |
| | |
| 3 | C C C C C C C C C C C C D C C |
| | |
| 4 | C D D C D C D D C D D D D D C |
| | |
| 5 | C C D C C C C C C C C C C C C |
| | |
| 6 | D C C C C C C C C C C D C D C |
| | |
| 7 | C D D C C C D C D D D C D C D |
| | |
| 8 | C D C D D C D C D C D D D D D |
| | |
| 9 | C C C C C C C C C C C C C C D |
| | |
| 10 | C D C C C C C C C C C C C C C |
| | |
| 11 | C C D C D D D D D D D C D C C |
| | |
| 12 | C C D C C D C D C D C C D C C |
| | |
| 13 | C C C C D D C D C D D D D C C |
| | |
| 14 | C D C C C D D C D D D C D D D |
| | |
| 15 | C C D D C C C C C C C C D D C |
| | |
| 16 | C D D C D C D D D D D C D C C |
| | |
| 17 | C C D C C C C D C C D D D C C |
| | |
| 18 | C C C C C C C C C C C C C C D |
| | |
| 19 | C C C C C C C C C C C C D C C |
| | |
| 20 | C C C C C C C C C C C C C C C |
| | |
| 21 | C D C D C D D C D C D C D D C |
| | |
| 22 | C C D D D D C D D C C D D C C |
| | |
| 23 | C D D C D C D C D C C C C D C |
| | |
| 24 | C C C D D C D C D D D D D D D |
| | |
| 25 | C C C C C C C C C C C C C C D |
| | |
| 26 | C D D C C C D D C C D D D D D |
| | |
| 27 | C C C C C D C D D D D C D D D |
| | |
| 28 | C C C C C C C C C C C C C C D |
| | |
| 29 | C C C C C C C C C C C C C C D |
| | |
| 30 | D C C C C C C C C C C D C C C |
| | |
| 31 | C C D C C D D D C C D C C D C |
+----+---------------------------------------------+
Table 22: Prediction Weight Selection for WB Normalized LSF Decoding
4.2.7.5.3. Reconstructing the Normalized LSF Coefficients
Once the stage-1 index I1 and the stage-2 residual res_Q10[] have
been decoded, the final normalized LSF coefficients can be
reconstructed.
The spectral distortion introduced by the quantization of each LSF
coefficient varies, so the stage-2 residual is weighted accordingly,
using the low-complexity Inverse Harmonic Mean Weighting (IHMW)
function proposed in [LAROIA-ICASSP]. The weights are derived
directly from the stage-1 codebook vector. Let cb1_Q8[k] be the k'th
entry of the stage-1 codebook vector from Table 23 or Table 24.
Then, for 0 <= k < d_LPC, the following expression computes the
square of the weight as a Q18 value:
w2_Q18[k] = (1024/(cb1_Q8[k] - cb1_Q8[k-1])
+ 1024/(cb1_Q8[k+1] - cb1_Q8[k])) << 16
where cb1_Q8[-1] = 0 and cb1_Q8[d_LPC] = 256, and the division is
integer division. This is reduced to an unsquared, Q9 value using
the following square-root approximation:
i = ilog(w2_Q18[k])
f = (w2_Q18[k]>>(i-8)) & 127
y = ((i&1) ? 32768 : 46214) >> ((32-i)>>1)
w_Q9[k] = y + ((213*f*y)>>16)
The constant 46214 here is approximately the square root of 2 in Q15.
The cb1_Q8[] vector completely determines these weights, and they may
be tabulated and stored as 13-bit unsigned values (with a range of
1819 to 5227, inclusive) to avoid computing them when decoding. The
reference implementation already requires code to compute these
weights on unquantized coefficients in the encoder, in
silk_NLSF_VQ_weights_laroia() (NLSF_VQ_weights_laroia.c) and its
callers, so it reuses that code in the decoder instead of using a
pre-computed table to reduce the amount of ROM required.
+----+----------------------------------------+
| I1 | Codebook (Q8) |
+----+----------------------------------------+
| | 0 1 2 3 4 5 6 7 8 9 |
| | |
| 0 | 12 35 60 83 108 132 157 180 206 228 |
| | |
| 1 | 15 32 55 77 101 125 151 175 201 225 |
| | |
| 2 | 19 42 66 89 114 137 162 184 209 230 |
| | |
| 3 | 12 25 50 72 97 120 147 172 200 223 |
| | |
| 4 | 26 44 69 90 114 135 159 180 205 225 |
| | |
| 5 | 13 22 53 80 106 130 156 180 205 228 |
| | |
| 6 | 15 25 44 64 90 115 142 168 196 222 |
| | |
| 7 | 19 24 62 82 100 120 145 168 190 214 |
| | |
| 8 | 22 31 50 79 103 120 151 170 203 227 |
| | |
| 9 | 21 29 45 65 106 124 150 171 196 224 |
| | |
| 10 | 30 49 75 97 121 142 165 186 209 229 |
| | |
| 11 | 19 25 52 70 93 116 143 166 192 219 |
| | |
| 12 | 26 34 62 75 97 118 145 167 194 217 |
| | |
| 13 | 25 33 56 70 91 113 143 165 196 223 |
| | |
| 14 | 21 34 51 72 97 117 145 171 196 222 |
| | |
| 15 | 20 29 50 67 90 117 144 168 197 221 |
| | |
| 16 | 22 31 48 66 95 117 146 168 196 222 |
| | |
| 17 | 24 33 51 77 116 134 158 180 200 224 |
| | |
| 18 | 21 28 70 87 106 124 149 170 194 217 |
| | |
| 19 | 26 33 53 64 83 117 152 173 204 225 |
| | |
| 20 | 27 34 65 95 108 129 155 174 210 225 |
| | |
| 21 | 20 26 72 99 113 131 154 176 200 219 |
| | |
| 22 | 34 43 61 78 93 114 155 177 205 229 |
| | |
| 23 | 23 29 54 97 124 138 163 179 209 229 |
| | |
| 24 | 30 38 56 89 118 129 158 178 200 231 |
| | |
| 25 | 21 29 49 63 85 111 142 163 193 222 |
| | |
| 26 | 27 48 77 103 133 158 179 196 215 232 |
| | |
| 27 | 29 47 74 99 124 151 176 198 220 237 |
| | |
| 28 | 33 42 61 76 93 121 155 174 207 225 |
| | |
| 29 | 29 53 87 112 136 154 170 188 208 227 |
| | |
| 30 | 24 30 52 84 131 150 166 186 203 229 |
| | |
| 31 | 37 48 64 84 104 118 156 177 201 230 |
+----+----------------------------------------+
Table 23: NB/MB Normalized LSF Stage-1 Codebook Vectors
+----+------------------------------------------------------------+
| I1 | Codebook (Q8) |
+----+------------------------------------------------------------+
| | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
| | |
| 0 | 7 23 38 54 69 85 100 116 131 147 162 178 193 208 223 239 |
| | |
| 1 | 13 25 41 55 69 83 98 112 127 142 157 171 187 203 220 236 |
| | |
| 2 | 15 21 34 51 61 78 92 106 126 136 152 167 185 205 225 240 |
| | |
| 3 | 10 21 36 50 63 79 95 110 126 141 157 173 189 205 221 237 |
| | |
| 4 | 17 20 37 51 59 78 89 107 123 134 150 164 184 205 224 240 |
| | |
| 5 | 10 15 32 51 67 81 96 112 129 142 158 173 189 204 220 236 |
| | |
| 6 | 8 21 37 51 65 79 98 113 126 138 155 168 179 192 209 218 |
| | |
| 7 | 12 15 34 55 63 78 87 108 118 131 148 167 185 203 219 236 |
| | |
| 8 | 16 19 32 36 56 79 91 108 118 136 154 171 186 204 220 237 |
| | |
| 9 | 11 28 43 58 74 89 105 120 135 150 165 180 196 211 226 241 |
| | |
| 10 | 6 16 33 46 60 75 92 107 123 137 156 169 185 199 214 225 |
| | |
| 11 | 11 19 30 44 57 74 89 105 121 135 152 169 186 202 218 234 |
| | |
| 12 | 12 19 29 46 57 71 88 100 120 132 148 165 182 199 216 233 |
| | |
| 13 | 17 23 35 46 56 77 92 106 123 134 152 167 185 204 222 237 |
| | |
| 14 | 14 17 45 53 63 75 89 107 115 132 151 171 188 206 221 240 |
| | |
| 15 | 9 16 29 40 56 71 88 103 119 137 154 171 189 205 222 237 |
| | |
| 16 | 16 19 36 48 57 76 87 105 118 132 150 167 185 202 218 236 |
| | |
| 17 | 12 17 29 54 71 81 94 104 126 136 149 164 182 201 221 237 |
| | |
| 18 | 15 28 47 62 79 97 115 129 142 155 168 180 194 208 223 238 |
| | |
| 19 | 8 14 30 45 62 78 94 111 127 143 159 175 192 207 223 239 |
| | |
| 20 | 17 30 49 62 79 92 107 119 132 145 160 174 190 204 220 235 |
| | |
| 21 | 14 19 36 45 61 76 91 108 121 138 154 172 189 205 222 238 |
| | |
| 22 | 12 18 31 45 60 76 91 107 123 138 154 171 187 204 221 236 |
| | |
| 23 | 13 17 31 43 53 70 83 103 114 131 149 167 185 203 220 237 |
| | |
| 24 | 17 22 35 42 58 78 93 110 125 139 155 170 188 206 224 240 |
| | |
| 25 | 8 15 34 50 67 83 99 115 131 146 162 178 193 209 224 239 |
| | |
| 26 | 13 16 41 66 73 86 95 111 128 137 150 163 183 206 225 241 |
| | |
| 27 | 17 25 37 52 63 75 92 102 119 132 144 160 175 191 212 231 |
| | |
| 28 | 19 31 49 65 83 100 117 133 147 161 174 187 200 213 227 242 |
| | |
| 29 | 18 31 52 68 88 103 117 126 138 149 163 177 192 207 223 239 |
| | |
| 30 | 16 29 47 61 76 90 106 119 133 147 161 176 193 209 224 240 |
| | |
| 31 | 15 21 35 50 61 73 86 97 110 119 129 141 175 198 218 237 |
+----+------------------------------------------------------------+
Table 24: WB Normalized LSF Stage-1 Codebook Vectors
Given the stage-1 codebook entry cb1_Q8[], the stage-2 residual
res_Q10[], and their corresponding weights, w_Q9[], the reconstructed
normalized LSF coefficients are
NLSF_Q15[k] = clamp(0,
(cb1_Q8[k]<<7) + (res_Q10[k]<<14)/w_Q9[k], 32767)
where the division is integer division. However, nothing in either
the reconstruction process or the quantization process in the encoder
thus far guarantees that the coefficients are monotonically
increasing and separated well enough to ensure a stable filter
[KABAL86]. When using the reference encoder, roughly 2% of frames
violate this constraint. The next section describes a stabilization
procedure used to make these guarantees.
4.2.7.5.4. Normalized LSF Stabilization
The normalized LSF stabilization procedure is implemented in
silk_NLSF_stabilize() (NLSF_stabilize.c). This process ensures that
consecutive values of the normalized LSF coefficients, NLSF_Q15[],
are spaced some minimum distance apart (predetermined to be the 0.01
percentile of a large training set). Table 25 gives the minimum
spacings for NB and MB and those for WB, where row k is the minimum
allowed value of NLSF_Q15[k]-NLSF_Q15[k-1]. For the purposes of
computing this spacing for the first and last coefficient,
NLSF_Q15[-1] is taken to be 0 and NLSF_Q15[d_LPC] is taken to be
32768.
+-------------+-----------+-----+
| Coefficient | NB and MB | WB |
+-------------+-----------+-----+
| 0 | 250 | 100 |
| | | |
| 1 | 3 | 3 |
| | | |
| 2 | 6 | 40 |
| | | |
| 3 | 3 | 3 |
| | | |
| 4 | 3 | 3 |
| | | |
| 5 | 3 | 3 |
| | | |
| 6 | 4 | 5 |
| | | |
| 7 | 3 | 14 |
| | | |
| 8 | 3 | 14 |
| | | |
| 9 | 3 | 10 |
| | | |
| 10 | 461 | 11 |
| | | |
| 11 | | 3 |
| | | |
| 12 | | 8 |
| | | |
| 13 | | 9 |
| | | |
| 14 | | 7 |
| | | |
| 15 | | 3 |
| | | |
| 16 | | 347 |
+-------------+-----------+-----+
Table 25: Minimum Spacing for Normalized LSF Coefficients
The procedure starts off by trying to make small adjustments that
attempt to minimize the amount of distortion introduced. After 20
such adjustments, it falls back to a more direct method that
guarantees the constraints are enforced but may require large
adjustments.
Let NDeltaMin_Q15[k] be the minimum required spacing for the current
audio bandwidth from Table 25. First, the procedure finds the index
i where NLSF_Q15[i] - NLSF_Q15[i-1] - NDeltaMin_Q15[i] is the
smallest, breaking ties by using the lower value of i. If this value
is non-negative, then the stabilization stops; the coefficients
satisfy all the constraints. Otherwise, if i == 0, it sets
NLSF_Q15[0] to NDeltaMin_Q15[0], and if i == d_LPC, it sets
NLSF_Q15[d_LPC-1] to (32768 - NDeltaMin_Q15[d_LPC]). For all other
values of i, both NLSF_Q15[i-1] and NLSF_Q15[i] are updated as
follows:
i-1
__
min_center_Q15 = (NDeltaMin_Q15[i]>>1) + \ NDeltaMin_Q15[k]
/_
k=0
d_LPC
__
max_center_Q15 = 32768 - (NDeltaMin_Q15[i]>>1) - \ NDeltaMin_Q15[k]
/_
k=i+1
center_freq_Q15 = clamp(min_center_Q15[i],
(NLSF_Q15[i-1] + NLSF_Q15[i] + 1)>>1
max_center_Q15[i])
NLSF_Q15[i-1] = center_freq_Q15 - (NDeltaMin_Q15[i]>>1)
NLSF_Q15[i] = NLSF_Q15[i-1] + NDeltaMin_Q15[i]
Then, the procedure repeats again, until it has either executed 20
times or stopped because the coefficients satisfy all the
constraints.
After the 20th repetition of the above procedure, the following
fallback procedure executes once. First, the values of NLSF_Q15[k]
for 0 <= k < d_LPC are sorted in ascending order. Then, for each
value of k from 0 to d_LPC-1, NLSF_Q15[k] is set to
max(NLSF_Q15[k], NLSF_Q15[k-1] + NDeltaMin_Q15[k])
Next, for each value of k from d_LPC-1 down to 0, NLSF_Q15[k] is set
to
min(NLSF_Q15[k], NLSF_Q15[k+1] - NDeltaMin_Q15[k+1])
There is no need to check if the coefficients satisfy all the
constraints before applying this fallback procedure. If they do,
then it will not change their values.
4.2.7.5.5. Normalized LSF Interpolation
For 20 ms SILK frames, the first half of the frame (i.e., the first
two subframes) may use normalized LSF coefficients that are
interpolated between the decoded LSFs for the most recent coded frame
(in the same channel) and the current frame. A Q2 interpolation
factor follows the LSF coefficient indices in the bitstream, which is
decoded using the PDF in Table 26. This happens in
silk_decode_indices() (decode_indices.c). After either
o An uncoded regular SILK frame in the side channel, or
o A decoder reset (see Section 4.5.2),
the decoder still decodes this factor, but ignores its value and
always uses 4 instead. For 10 ms SILK frames, this factor is not
stored at all.
+---------------------------+
| PDF |
+---------------------------+
| {13, 22, 29, 11, 181}/256 |
+---------------------------+
Table 26: PDF for Normalized LSF Interpolation Index
Let n2_Q15[k] be the normalized LSF coefficients decoded by the
procedure in Section 4.2.7.5, n0_Q15[k] be the LSF coefficients
decoded for the prior frame, and w_Q2 be the interpolation factor.
Then, the normalized LSF coefficients used for the first half of a
20 ms frame, n1_Q15[k], are
n1_Q15[k] = n0_Q15[k] + (w_Q2*(n2_Q15[k] - n0_Q15[k]) >> 2)
This interpolation is performed in silk_decode_parameters()
(decode_parameters.c).
4.2.7.5.6. Converting Normalized LSFs to LPC Coefficients
Any LPC filter A(z) can be split into a symmetric part P(z) and an
anti-symmetric part Q(z) such that
d_LPC
__ -k 1
A(z) = 1 - \ a[k] * z = - * (P(z) + Q(z))
/_ 2
k=1
with
-d_LPC-1 -1
P(z) = A(z) + z * A(z )
-d_LPC-1 -1
Q(z) = A(z) - z * A(z )
The even normalized LSF coefficients correspond to a pair of
conjugate roots of P(z), while the odd coefficients correspond to a
pair of conjugate roots of Q(z), all of which lie on the unit circle.
In addition, P(z) has a root at pi and Q(z) has a root at 0. Thus,
they may be reconstructed mathematically from a set of normalized LSF
coefficients, n[k], as
d_LPC/2-1
-1 ___ -1 -2
P(z) = (1 + z ) * | | (1 - 2*cos(pi*n[2*k])*z + z )
k=0
d_LPC/2-1
-1 ___ -1 -2
Q(z) = (1 - z ) * | | (1 - 2*cos(pi*n[2*k+1])*z + z )
k=0
However, SILK performs this reconstruction using a fixed-point
approximation so that all decoders can reproduce it in a bit-exact
manner to avoid prediction drift. The function silk_NLSF2A()
(NLSF2A.c) implements this procedure.
To start, it approximates cos(pi*n[k]) using a table lookup with
linear interpolation. The encoder SHOULD use the inverse of this
piecewise linear approximation, rather than the true inverse of the
cosine function, when deriving the normalized LSF coefficients.
These values are also re-ordered to improve numerical accuracy when
constructing the LPC polynomials.
+-------------+-----------+----+
| Coefficient | NB and MB | WB |
+-------------+-----------+----+
| 0 | 0 | 0 |
| | | |
| 1 | 9 | 15 |
| | | |
| 2 | 6 | 8 |
| | | |
| 3 | 3 | 7 |
| | | |
| 4 | 4 | 4 |
| | | |
| 5 | 5 | 11 |
| | | |
| 6 | 8 | 12 |
| | | |
| 7 | 1 | 3 |
| | | |
| 8 | 2 | 2 |
| | | |
| 9 | 7 | 13 |
| | | |
| 10 | | 10 |
| | | |
| 11 | | 5 |
| | | |
| 12 | | 6 |
| | | |
| 13 | | 9 |
| | | |
| 14 | | 14 |
| | | |
| 15 | | 1 |
+-------------+-----------+----+
Table 27: LSF Ordering for Polynomial Evaluation
The top 7 bits of each normalized LSF coefficient index a value in
the table, and the next 8 bits interpolate between it and the next
value. Let i = (n[k] >> 8) be the integer index and f = (n[k] & 255)
be the fractional part of a given coefficient. Then, the re-ordered,
approximated cosine, c_Q17[ordering[k]], is
c_Q17[ordering[k]] = (cos_Q12[i]*256
+ (cos_Q12[i+1]-cos_Q12[i])*f + 4) >> 3
where ordering[k] is the k'th entry of the column of Table 27
corresponding to the current audio bandwidth and cos_Q12[i] is the
i'th entry of Table 28.
+-----+-------+-------+-------+-------+
| i | +0 | +1 | +2 | +3 |
+-----+-------+-------+-------+-------+
| 0 | 4096 | 4095 | 4091 | 4085 |
| | | | | |
| 4 | 4076 | 4065 | 4052 | 4036 |
| | | | | |
| 8 | 4017 | 3997 | 3973 | 3948 |
| | | | | |
| 12 | 3920 | 3889 | 3857 | 3822 |
| | | | | |
| 16 | 3784 | 3745 | 3703 | 3659 |
| | | | | |
| 20 | 3613 | 3564 | 3513 | 3461 |
| | | | | |
| 24 | 3406 | 3349 | 3290 | 3229 |
| | | | | |
| 28 | 3166 | 3102 | 3035 | 2967 |
| | | | | |
| 32 | 2896 | 2824 | 2751 | 2676 |
| | | | | |
| 36 | 2599 | 2520 | 2440 | 2359 |
| | | | | |
| 40 | 2276 | 2191 | 2106 | 2019 |
| | | | | |
| 44 | 1931 | 1842 | 1751 | 1660 |
| | | | | |
| 48 | 1568 | 1474 | 1380 | 1285 |
| | | | | |
| 52 | 1189 | 1093 | 995 | 897 |
| | | | | |
| 56 | 799 | 700 | 601 | 501 |
| | | | | |
| 60 | 401 | 301 | 201 | 101 |
| | | | | |
| 64 | 0 | -101 | -201 | -301 |
| | | | | |
| 68 | -401 | -501 | -601 | -700 |
| | | | | |
| 72 | -799 | -897 | -995 | -1093 |
| | | | | |
| 76 | -1189 | -1285 | -1380 | -1474 |
| | | | | |
| 80 | -1568 | -1660 | -1751 | -1842 |
| | | | | |
| 84 | -1931 | -2019 | -2106 | -2191 |
| | | | | |
| 88 | -2276 | -2359 | -2440 | -2520 |
| | | | | |
| 92 | -2599 | -2676 | -2751 | -2824 |
| | | | | |
| 96 | -2896 | -2967 | -3035 | -3102 |
| | | | | |
| 100 | -3166 | -3229 | -3290 | -3349 |
| | | | | |
| 104 | -3406 | -3461 | -3513 | -3564 |
| | | | | |
| 108 | -3613 | -3659 | -3703 | -3745 |
| | | | | |
| 112 | -3784 | -3822 | -3857 | -3889 |
| | | | | |
| 116 | -3920 | -3948 | -3973 | -3997 |
| | | | | |
| 120 | -4017 | -4036 | -4052 | -4065 |
| | | | | |
| 124 | -4076 | -4085 | -4091 | -4095 |
| | | | | |
| 128 | -4096 | | | |
+-----+-------+-------+-------+-------+
Table 28: Q12 Cosine Table for LSF Conversion
Given the list of cosine values, silk_NLSF2A_find_poly() (NLSF2A.c)
computes the coefficients of P and Q, described here via a simple
recurrence. Let p_Q16[k][j] and q_Q16[k][j] be the coefficients of
the products of the first (k+1) root pairs for P and Q, with j
indexing the coefficient number. Only the first (k+2) coefficients
are needed, as the products are symmetric. Let
p_Q16[0][0] = q_Q16[0][0] = 1<<16, p_Q16[0][1] = -c_Q17[0],
q_Q16[0][1] = -c_Q17[1], and d2 = d_LPC/2. As boundary conditions,
assume p_Q16[k][j] = q_Q16[k][j] = 0 for all j < 0. Also, assume
p_Q16[k][k+2] = p_Q16[k][k] and q_Q16[k][k+2] = q_Q16[k][k] (because
of the symmetry). Then, for 0 < k < d2 and 0 <= j <= k+1,
p_Q16[k][j] = p_Q16[k-1][j] + p_Q16[k-1][j-2]
- ((c_Q17[2*k]*p_Q16[k-1][j-1] + 32768)>>16)
q_Q16[k][j] = q_Q16[k-1][j] + q_Q16[k-1][j-2]
- ((c_Q17[2*k+1]*q_Q16[k-1][j-1] + 32768)>>16)
The use of Q17 values for the cosine terms in an otherwise Q16
expression implicitly scales them by a factor of 2. The
multiplications in this recurrence may require up to 48 bits of
precision in the result to avoid overflow. In practice, each row of
the recurrence only depends on the previous row, so an implementation
does not need to store all of them.
silk_NLSF2A() uses the values from the last row of this recurrence to
reconstruct a 32-bit version of the LPC filter (without the leading
1.0 coefficient), a32_Q17[k], 0 <= k < d2:
a32_Q17[k] = -(q_Q16[d2-1][k+1] - q_Q16[d2-1][k])
- (p_Q16[d2-1][k+1] + p_Q16[d2-1][k]))
a32_Q17[d_LPC-k-1] = (q_Q16[d2-1][k+1] - q_Q16[d2-1][k])
- (p_Q16[d2-1][k+1] + p_Q16[d2-1][k]))
The sum and difference of two terms from each of the p_Q16 and q_Q16
coefficient lists reflect the (1 + z**-1) and (1 - z**-1) factors of
P and Q, respectively. The promotion of the expression from Q16 to
Q17 implicitly scales the result by 1/2.
4.2.7.5.7. Limiting the Range of the LPC Coefficients
The a32_Q17[] coefficients are too large to fit in a 16-bit value,
which significantly increases the cost of applying this filter in
fixed-point decoders. Reducing them to Q12 precision doesn't incur
any significant quality loss, but still does not guarantee they will
fit. silk_NLSF2A() applies up to 10 rounds of bandwidth expansion to
limit the dynamic range of these coefficients. Even floating-point
decoders SHOULD perform these steps, to avoid mismatch.
For each round, the process first finds the index k such that
abs(a32_Q17[k]) is largest, breaking ties by choosing the lowest
value of k. Then, it computes the corresponding Q12 precision value,
maxabs_Q12, subject to an upper bound to avoid overflow in subsequent
computations:
maxabs_Q12 = min((maxabs_Q17 + 16) >> 5, 163838)
If this is larger than 32767, the procedure derives the chirp factor,
sc_Q16[0], to use in the bandwidth expansion as
(maxabs_Q12 - 32767) << 14
sc_Q16[0] = 65470 - --------------------------
(maxabs_Q12 * (k+1)) >> 2
where the division here is integer division. This is an
approximation of the chirp factor needed to reduce the target
coefficient to 32767, though it is both less than 0.999 and, for
k > 0 when maxabs_Q12 is much greater than 32767, still slightly too
large. The upper bound on maxabs_Q12, 163838, was chosen because it
is equal to ((2**31 - 1) >> 14) + 32767, i.e., the largest value of
maxabs_Q12 that would not overflow the numerator in the equation
above when stored in a signed 32-bit integer.
silk_bwexpander_32() (bwexpander_32.c) performs the bandwidth
expansion (again, only when maxabs_Q12 is greater than 32767) using
the following recurrence:
a32_Q17[k] = (a32_Q17[k]*sc_Q16[k]) >> 16
sc_Q16[k+1] = (sc_Q16[0]*sc_Q16[k] + 32768) >> 16
The first multiply may require up to 48 bits of precision in the
result to avoid overflow. The second multiply must be unsigned to
avoid overflow with only 32 bits of precision. The reference
implementation uses a slightly more complex formulation that avoids
the 32-bit overflow using signed multiplication, but is otherwise
equivalent.
After 10 rounds of bandwidth expansion are performed, they are simply
saturated to 16 bits:
a32_Q17[k] = clamp(-32768, (a32_Q17[k] + 16) >> 5, 32767) << 5
Because this performs the actual saturation in the Q12 domain, but
converts the coefficients back to the Q17 domain for the purposes of
prediction gain limiting, this step must be performed after the 10th
round of bandwidth expansion, regardless of whether or not the Q12
version of any coefficient still overflows a 16-bit integer. This
saturation is not performed if maxabs_Q12 drops to 32767 or less
prior to the 10th round.
4.2.7.5.8. Limiting the Prediction Gain of the LPC Filter
The prediction gain of an LPC synthesis filter is the square root of
the output energy when the filter is excited by a unit-energy
impulse. Even if the Q12 coefficients would fit, the resulting
filter may still have a significant gain (especially for voiced
sounds), making the filter unstable. silk_NLSF2A() applies up to 16
additional rounds of bandwidth expansion to limit the prediction
gain. Instead of controlling the amount of bandwidth expansion using
the prediction gain itself (which may diverge to infinity for an
unstable filter), silk_NLSF2A() uses silk_LPC_inverse_pred_gain_QA()
(LPC_inv_pred_gain.c) to compute the reflection coefficients
associated with the filter. The filter is stable if and only if the
magnitude of these coefficients is sufficiently less than one. The
reflection coefficients, rc[k], can be computed using a simple
Levinson recurrence, initialized with the LPC coefficients a[d_LPC-
1][n] = a[n], and then updated via
rc[k] = -a[k][k] ,
a[k][n] - a[k][k-n-1]*rc[k]
a[k-1][n] = ---------------------------
2
1 - rc[k]
However, silk_LPC_inverse_pred_gain_QA() approximates this using
fixed-point arithmetic to guarantee reproducible results across
platforms and implementations. Since small changes in the
coefficients can make a stable filter unstable, it takes the real Q12
coefficients that will be used during reconstruction as input. Thus,
let
a32_Q12[n] = (a32_Q17[n] + 16) >> 5
be the Q12 version of the LPC coefficients that will eventually be
used. As a simple initial check, the decoder computes the DC
response as
d_PLC-1
__
DC_resp = \ a32_Q12[n]
/_
n=0
and if DC_resp > 4096, the filter is unstable.
Increasing the precision of these Q12 coefficients to Q24 for
intermediate computations allows more accurate computation of the
reflection coefficients, so the decoder initializes the recurrence
via
inv_gain_Q30[d_LPC] = 1 << 30
a32_Q24[d_LPC-1][n] = a32_Q12[n] << 12
Then, for each k from d_LPC-1 down to 0, if
abs(a32_Q24[k][k]) > 16773022, the filter is unstable and the
recurrence stops. The constant 16773022 here is approximately
0.99975 in Q24. Otherwise, the inverse of the prediction gain,
inv_gain_Q30[k], is updated via
rc_Q31[k] = -a32_Q24[k][k] << 7
div_Q30[k] = (1<<30) - (rc_Q31[k]*rc_Q31[k] >> 32)
inv_gain_Q30[k] = (inv_gain_Q30[k+1]*div_Q30[k] >> 32) << 2
and if inv_gain_Q30[k] < 107374, the filter is unstable and the
recurrence stops. The constant 107374 here is approximately 1/10000
in Q30. If neither of these checks determine that the filter is
unstable and k > 0, row k-1 of a32_Q24 is computed from row k as
b1[k] = ilog(div_Q30[k])
b2[k] = b1[k] - 16
(1<<29) - 1
inv_Qb2[k] = -----------------------
div_Q30[k] >> (b2[k]+1)
err_Q29[k] = (1<<29)
- ((div_Q30[k]<<(15-b2[k]))*inv_Qb2[k] >> 16)
gain_Qb1[k] = ((inv_Qb2[k] << 16)
+ (err_Q29[k]*inv_Qb2[k] >> 13))
num_Q24[k-1][n] = a32_Q24[k][n]
- ((a32_Q24[k][k-n-1]*rc_Q31[k] + (1<<30)) >> 31)
a32_Q24[k-1][n] = (num_Q24[k-1][n]*gain_Qb1[k]
+ (1<<(b1[k]-1))) >> b1[k]
where 0 <= n < k. In the above, rc_Q31[k] are the reflection
coefficients. div_Q30[k] is the denominator for each iteration, and
gain_Qb1[k] is its multiplicative inverse (with b1[k] fractional
bits, where b1[k] ranges from 20 to 31). inv_Qb2[k], which ranges
from 16384 to 32767, is a low-precision version of that inverse (with
b2[k] fractional bits). err_Q29[k] is the residual error, ranging
from -32763 to 32392, which is used to improve the accuracy. The
values t_Q24[k-1][n] for each n are the numerators for the next row
of coefficients in the recursion, and a32_Q24[k-1][n] is the final
version of that row. Every multiply in this procedure except the one
used to compute gain_Qb1[k] requires more than 32 bits of precision,
but otherwise all intermediate results fit in 32 bits or less. In
practice, because each row only depends on the next one, an
implementation does not need to store them all.
If abs(a32_Q24[k][k]) <= 16773022 and inv_gain_Q30[k] >= 107374 for
0 <= k < d_LPC, then the filter is considered stable. However, the
problem of determining stability is ill-conditioned when the filter
contains several reflection coefficients whose magnitude is very
close to one. This fixed-point algorithm is not mathematically
guaranteed to correctly classify filters as stable or unstable in
this case, though it does very well in practice.
On round i, 0 <= i < 16, if the filter passes these stability checks,
then this procedure stops, and the final LPC coefficients to use for
reconstruction in Section 4.2.7.9.2 are
a_Q12[k] = (a32_Q17[k] + 16) >> 5
Otherwise, a round of bandwidth expansion is applied using the same
procedure as in Section 4.2.7.5.7, with
sc_Q16[0] = 65536 - (2<<i)
During round 15, sc_Q16[0] becomes 0 in the above equation, so
a_Q12[k] is set to 0 for all k, guaranteeing a stable filter.
4.2.7.6. Long-Term Prediction (LTP) Parameters
After the normalized LSF indices and, for 20 ms frames, the LSF
interpolation index, voiced frames (see Section 4.2.7.3) include
additional LTP parameters. There is one primary lag index for each
SILK frame, but this is refined to produce a separate lag index per
subframe using a vector quantizer. Each subframe also gets its own
prediction gain coefficient.
4.2.7.6.1. Pitch Lags
The primary lag index is coded either relative to the primary lag of
the prior frame in the same channel or as an absolute index.
Absolute coding is used if and only if
o This is the first SILK frame of its type (LBRR or regular) for
this channel in the current Opus frame,
o The previous SILK frame of the same type (LBRR or regular) for
this channel in the same Opus frame was not coded, or
o That previous SILK frame was coded, but was not voiced (see
Section 4.2.7.3).
With absolute coding, the primary pitch lag may range from 2 ms
(inclusive) up to 18 ms (exclusive), corresponding to pitches from
500 Hz down to 55.6 Hz, respectively. It is comprised of a high part
and a low part, where the decoder first reads the high part using the
32-entry codebook in Table 29 and then the low part using the
codebook corresponding to the current audio bandwidth from Table 30.
The final primary pitch lag is then
lag = lag_high*lag_scale + lag_low + lag_min
where lag_high is the high part, lag_low is the low part, and
lag_scale and lag_min are the values from the "Scale" and "Minimum
Lag" columns of Table 30, respectively.
+-------------------------------------------------------------------+
| PDF |
+-------------------------------------------------------------------+
| {3, 3, 6, 11, 21, 30, 32, 19, 11, 10, 12, 13, 13, 12, 11, 9, 8, |
| 7, 6, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1}/256 |
+-------------------------------------------------------------------+
Table 29: PDF for High Part of Primary Pitch Lag
+------------+------------------------+-------+----------+----------+
| Audio | PDF | Scale | Minimum | Maximum |
| Bandwidth | | | Lag | Lag |
+------------+------------------------+-------+----------+----------+
| NB | {64, 64, 64, 64}/256 | 4 | 16 | 144 |
| | | | | |
| MB | {43, 42, 43, 43, 42, | 6 | 24 | 216 |
| | 43}/256 | | | |
| | | | | |
| WB | {32, 32, 32, 32, 32, | 8 | 32 | 288 |
| | 32, 32, 32}/256 | | | |
+------------+------------------------+-------+----------+----------+
Table 30: PDF for Low Part of Primary Pitch Lag
All frames that do not use absolute coding for the primary lag index
use relative coding instead. The decoder reads a single delta value
using the 21-entry PDF in Table 31. If the resulting value is zero,
it falls back to the absolute coding procedure from the prior
paragraph. Otherwise, the final primary pitch lag is then
lag = previous_lag + (delta_lag_index - 9)
where previous_lag is the primary pitch lag from the most recent
frame in the same channel and delta_lag_index is the value just
decoded. This allows a per-frame change in the pitch lag of -8 to
+11 samples. The decoder does no clamping at this point, so this
value can fall outside the range of 2 ms to 18 ms, and the decoder
must use this unclamped value when using relative coding in the next
SILK frame (if any). However, because an Opus frame can use relative
coding for at most two consecutive SILK frames, integer overflow
should not be an issue.
+-------------------------------------------------------------------+
| PDF |
+-------------------------------------------------------------------+
| {46, 2, 2, 3, 4, 6, 10, 15, 26, 38, 30, 22, 15, 10, 7, 6, 4, 4, |
| 2, 2, 2}/256 |
+-------------------------------------------------------------------+
Table 31: PDF for Primary Pitch Lag Change
After the primary pitch lag, a "pitch contour", stored as a single
entry from one of four small VQ codebooks, gives lag offsets for each
subframe in the current SILK frame. The codebook index is decoded
using one of the PDFs in Table 32 depending on the current frame size
and audio bandwidth. Tables 33 through 36 give the corresponding
offsets to apply to the primary pitch lag for each subframe given the
decoded codebook index.
+-----------+--------+----------+-----------------------------------+
| Audio | SILK | Codebook | PDF |
| Bandwidth | Frame | Size | |
| | Size | | |
+-----------+--------+----------+-----------------------------------+
| NB | 10 ms | 3 | {143, 50, 63}/256 |
| | | | |
| NB | 20 ms | 11 | {68, 12, 21, 17, 19, 22, 30, 24, |
| | | | 17, 16, 10}/256 |
| | | | |
| MB or WB | 10 ms | 12 | {91, 46, 39, 19, 14, 12, 8, 7, 6, |
| | | | 5, 5, 4}/256 |
| | | | |
| MB or WB | 20 ms | 34 | {33, 22, 18, 16, 15, 14, 14, 13, |
| | | | 13, 10, 9, 9, 8, 6, 6, 6, 5, 4, |
| | | | 4, 4, 3, 3, 3, 2, 2, 2, 2, 2, 2, |
| | | | 2, 1, 1, 1, 1}/256 |
+-----------+--------+----------+-----------------------------------+
Table 32: PDFs for Subframe Pitch Contour
+-------+------------------+
| Index | Subframe Offsets |
+-------+------------------+
| 0 | 0 0 |
| | |
| 1 | 1 0 |
| | |
| 2 | 0 1 |
+-------+------------------+
Table 33: Codebook Vectors for Subframe Pitch Contour:
NB, 10 ms Frames
+-------+------------------+
| Index | Subframe Offsets |
+-------+------------------+
| 0 | 0 0 0 0 |
| | |
| 1 | 2 1 0 -1 |
| | |
| 2 | -1 0 1 2 |
| | |
| 3 | -1 0 0 1 |
| | |
| 4 | -1 0 0 0 |
| | |
| 5 | 0 0 0 1 |
| | |
| 6 | 0 0 1 1 |
| | |
| 7 | 1 1 0 0 |
| | |
| 8 | 1 0 0 0 |
| | |
| 9 | 0 0 0 -1 |
| | |
| 10 | 1 0 0 -1 |
+-------+------------------+
Table 34: Codebook Vectors for Subframe Pitch Contour:
NB, 20 ms Frames
+-------+------------------+
| Index | Subframe Offsets |
+-------+------------------+
| 0 | 0 0 |
| | |
| 1 | 0 1 |
| | |
| 2 | 1 0 |
| | |
| 3 | -1 1 |
| | |
| 4 | 1 -1 |
| | |
| 5 | -1 2 |
| | |
| 6 | 2 -1 |
| | |
| 7 | -2 2 |
| | |
| 8 | 2 -2 |
| | |
| 9 | -2 3 |
| | |
| 10 | 3 -2 |
| | |
| 11 | -3 3 |
+-------+------------------+
Table 35: Codebook Vectors for Subframe Pitch Contour: MB or WB,
10 ms Frames
+-------+------------------+
| Index | Subframe Offsets |
+-------+------------------+
| 0 | 0 0 0 0 |
| | |
| 1 | 0 0 1 1 |
| | |
| 2 | 1 1 0 0 |
| | |
| 3 | -1 0 0 0 |
| | |
| 4 | 0 0 0 1 |
| | |
| 5 | 1 0 0 0 |
| | |
| 6 | -1 0 0 1 |
| | |
| 7 | 0 0 0 -1 |
| | |
| 8 | -1 0 1 2 |
| | |
| 9 | 1 0 0 -1 |
| | |
| 10 | -2 -1 1 2 |
| | |
| 11 | 2 1 0 -1 |
| | |
| 12 | -2 0 0 2 |
| | |
| 13 | -2 0 1 3 |
| | |
| 14 | 2 1 -1 -2 |
| | |
| 15 | -3 -1 1 3 |
| | |
| 16 | 2 0 0 -2 |
| | |
| 17 | 3 1 0 -2 |
| | |
| 18 | -3 -1 2 4 |
| | |
| 19 | -4 -1 1 4 |
| | |
| 20 | 3 1 -1 -3 |
| | |
| 21 | -4 -1 2 5 |
| | |
| 22 | 4 2 -1 -3 |
| | |
| 23 | 4 1 -1 -4 |
| | |
| 24 | -5 -1 2 6 |
| | |
| 25 | 5 2 -1 -4 |
| | |
| 26 | -6 -2 2 6 |
| | |
| 27 | -5 -2 2 5 |
| | |
| 28 | 6 2 -1 -5 |
| | |
| 29 | -7 -2 3 8 |
| | |
| 30 | 6 2 -2 -6 |
| | |
| 31 | 5 2 -2 -5 |
| | |
| 32 | 8 3 -2 -7 |
| | |
| 33 | -9 -3 3 9 |
+-------+------------------+
Table 36: Codebook Vectors for Subframe Pitch Contour: MB or WB,
20 ms Frames
The final pitch lag for each subframe is assembled in
silk_decode_pitch() (decode_pitch.c). Let lag be the primary pitch
lag for the current SILK frame, contour_index be index of the VQ
codebook, and lag_cb[contour_index][k] be the corresponding entry of
the codebook from the appropriate table given above for the k'th
subframe. Then the final pitch lag for that subframe is
pitch_lags[k] = clamp(lag_min, lag + lag_cb[contour_index][k],
lag_max)
where lag_min and lag_max are the values from the "Minimum Lag" and
"Maximum Lag" columns of Table 30, respectively.
4.2.7.6.2. LTP Filter Coefficients
SILK uses a separate 5-tap pitch filter for each subframe, selected
from one of three codebooks. The three codebooks each represent
different rate-distortion trade-offs, with average rates of
1.61 bits/subframe, 3.68 bits/subframe, and 4.85 bits/subframe,
respectively.
The importance of the filter coefficients generally depends on two
factors: the periodicity of the signal and relative energy between
the current subframe and the signal from one period earlier. Greater
periodicity and decaying energy both lead to more important filter
coefficients. Thus, they should be coded with lower distortion and
higher rate. These properties are relatively stable over the
duration of a single SILK frame. Hence, all of the subframes in a
SILK frame choose their filter from the same codebook. This is
signaled with an explicitly-coded "periodicity index". This
immediately follows the subframe pitch lags, and is coded using the
3-entry PDF from Table 37.
+------------------+
| PDF |
+------------------+
| {77, 80, 99}/256 |
+------------------+
Table 37: Periodicity Index PDF
The indices of the filters for each subframe follow. They are all
coded using the PDF from Table 38 corresponding to the periodicity
index. Tables 39 through 41 contain the corresponding filter taps as
signed Q7 integers.
+-------------+----------+------------------------------------------+
| Periodicity | Codebook | PDF |
| Index | Size | |
+-------------+----------+------------------------------------------+
| 0 | 8 | {185, 15, 13, 13, 9, 9, 6, 6}/256 |
| | | |
| 1 | 16 | {57, 34, 21, 20, 15, 13, 12, 13, 10, 10, |
| | | 9, 10, 9, 8, 7, 8}/256 |
| | | |
| 2 | 32 | {15, 16, 14, 12, 12, 12, 11, 11, 11, 10, |
| | | 9, 9, 9, 9, 8, 8, 8, 8, 7, 7, 6, 6, 5, |
| | | 4, 5, 4, 4, 4, 3, 4, 3, 2}/256 |
+-------------+----------+------------------------------------------+
Table 38: LTP Filter PDFs
+-------+---------------------+
| Index | Filter Taps (Q7) |
+-------+---------------------+
| 0 | 4 6 24 7 5 |
| | |
| 1 | 0 0 2 0 0 |
| | |
| 2 | 12 28 41 13 -4 |
| | |
| 3 | -9 15 42 25 14 |
| | |
| 4 | 1 -2 62 41 -9 |
| | |
| 5 | -10 37 65 -4 3 |
| | |
| 6 | -6 4 66 7 -8 |
| | |
| 7 | 16 14 38 -3 33 |
+-------+---------------------+
Table 39: Codebook Vectors for LTP Filter, Periodicity Index 0
+-------+---------------------+
| Index | Filter Taps (Q7) |
+-------+---------------------+
| 0 | 13 22 39 23 12 |
| | |
| 1 | -1 36 64 27 -6 |
| | |
| 2 | -7 10 55 43 17 |
| | |
| 3 | 1 1 8 1 1 |
| | |
| 4 | 6 -11 74 53 -9 |
| | |
| 5 | -12 55 76 -12 8 |
| | |
| 6 | -3 3 93 27 -4 |
| | |
| 7 | 26 39 59 3 -8 |
| | |
| 8 | 2 0 77 11 9 |
| | |
| 9 | -8 22 44 -6 7 |
| | |
| 10 | 40 9 26 3 9 |
| | |
| 11 | -7 20 101 -7 4 |
| | |
| 12 | 3 -8 42 26 0 |
| | |
| 13 | -15 33 68 2 23 |
| | |
| 14 | -2 55 46 -2 15 |
| | |
| 15 | 3 -1 21 16 41 |
+-------+---------------------+
Table 40: Codebook Vectors for LTP Filter, Periodicity Index 1
+-------+---------------------+
| Index | Filter Taps (Q7) |
+-------+---------------------+
| 0 | -6 27 61 39 5 |
| | |
| 1 | -11 42 88 4 1 |
| | |
| 2 | -2 60 65 6 -4 |
| | |
| 3 | -1 -5 73 56 1 |
| 4 | -9 19 94 29 -9 |
| | |
| 5 | 0 12 99 6 4 |
| | |
| 6 | 8 -19 102 46 -13 |
| | |
| 7 | 3 2 13 3 2 |
| | |
| 8 | 9 -21 84 72 -18 |
| | |
| 9 | -11 46 104 -22 8 |
| | |
| 10 | 18 38 48 23 0 |
| | |
| 11 | -16 70 83 -21 11 |
| | |
| 12 | 5 -11 117 22 -8 |
| | |
| 13 | -6 23 117 -12 3 |
| | |
| 14 | 3 -8 95 28 4 |
| | |
| 15 | -10 15 77 60 -15 |
| | |
| 16 | -1 4 124 2 -4 |
| | |
| 17 | 3 38 84 24 -25 |
| | |
| 18 | 2 13 42 13 31 |
| | |
| 19 | 21 -4 56 46 -1 |
| | |
| 20 | -1 35 79 -13 19 |
| | |
| 21 | -7 65 88 -9 -14 |
| | |
| 22 | 20 4 81 49 -29 |
| | |
| 23 | 20 0 75 3 -17 |
| | |
| 24 | 5 -9 44 92 -8 |
| | |
| 25 | 1 -3 22 69 31 |
| | |
| 26 | -6 95 41 -12 5 |
| | |
| 27 | 39 67 16 -4 1 |
| | |
| 28 | 0 -6 120 55 -36 |
| | |
| 29 | -13 44 122 4 -24 |
| | |
| 30 | 81 5 11 3 7 |
| | |
| 31 | 2 0 9 10 88 |
+-------+---------------------+
Table 41: Codebook Vectors for LTP Filter, Periodicity Index 2
4.2.7.6.3. LTP Scaling Parameter
An LTP scaling parameter appears after the LTP filter coefficients if
and only if
o This is a voiced frame (see Section 4.2.7.3), and
o Either
* This SILK frame corresponds to the first time interval of the
current Opus frame for its type (LBRR or regular), or
* This is an LBRR frame where the LBRR flags (see Section 4.2.4)
indicate the previous LBRR frame in the same channel is not
coded.
This allows the encoder to trade off the prediction gain between
packets against the recovery time after packet loss. Unlike
absolute-coding for pitch lags, regular SILK frames that are not at
the start of an Opus frame (i.e., that do not correspond to the first
20 ms time interval in Opus frames of 40 or 60 ms) do not include
this field, even if the prior frame was not voiced, or (in the case
of the side channel) not even coded. After an uncoded frame in the
side channel, the LTP buffer (see Section 4.2.7.9.1) is cleared to
zero, and is thus in a known state. In contrast, LBRR frames do
include this field when the prior frame was not coded, since the LTP
buffer contains the output of the PLC, which is non-normative.
If present, the decoder reads a value using the 3-entry PDF in
Table 42. The three possible values represent Q14 scale factors of
15565, 12288, and 8192, respectively (corresponding to approximately
0.95, 0.75, and 0.5). Frames that do not code the scaling parameter
use the default factor of 15565 (approximately 0.95).
+-------------------+
| PDF |
+-------------------+
| {128, 64, 64}/256 |
+-------------------+
Table 42: PDF for LTP Scaling Parameter
4.2.7.7. Linear Congruential Generator (LCG) Seed
As described in Section 4.2.7.8.6, SILK uses a Linear Congruential
Generator (LCG) to inject pseudorandom noise into the quantized
excitation. To ensure synchronization of this process between the
encoder and decoder, each SILK frame stores a 2-bit seed after the
LTP parameters (if any). The encoder may consider the choice of seed
during quantization, and the flexibility of this choice lets it
reduce distortion, helping to pay for the bit cost required to signal
it. The decoder reads the seed using the uniform 4-entry PDF in
Table 43, yielding a value between 0 and 3, inclusive.
+----------------------+
| PDF |
+----------------------+
| {64, 64, 64, 64}/256 |
+----------------------+
Table 43: PDF for LCG Seed
4.2.7.8. Excitation
SILK codes the excitation using a modified version of the Pyramid
Vector Quantizer (PVQ) codebook [PVQ]. The PVQ codebook is designed
for Laplace-distributed values and consists of all sums of K signed,
unit pulses in a vector of dimension N, where two pulses at the same
position are required to have the same sign. Thus, the codebook
includes all integer codevectors y of dimension N that satisfy
N-1
__
\ abs(y[j]) = K
/_
j=0
Unlike regular PVQ, SILK uses a variable-length, rather than fixed-
length, encoding. This encoding is better suited to the more
Gaussian-like distribution of the coefficient magnitudes and the non-
uniform distribution of their signs (caused by the quantization
offset described below). SILK also handles large codebooks by coding
the least significant bits (LSBs) of each coefficient directly. This
adds a small coding efficiency loss, but greatly reduces the
computation time and ROM size required for decoding, as implemented
in silk_decode_pulses() (decode_pulses.c).
SILK fixes the dimension of the codebook to N = 16. The excitation
is made up of a number of "shell blocks", each 16 samples in size.
Table 44 lists the number of shell blocks required for a SILK frame
for each possible audio bandwidth and frame size. 10 ms MB frames
nominally contain 120 samples (10 ms at 12 kHz), which is not a
multiple of 16. This is handled by coding 8 shell blocks (128
samples) and discarding the final 8 samples of the last block. The
decoder contains no special case that prevents an encoder from
placing pulses in these samples, and they must be correctly parsed
from the bitstream if present, but they are otherwise ignored.
+-----------------+------------+------------------------+
| Audio Bandwidth | Frame Size | Number of Shell Blocks |
+-----------------+------------+------------------------+
| NB | 10 ms | 5 |
| | | |
| MB | 10 ms | 8 |
| | | |
| WB | 10 ms | 10 |
| | | |
| NB | 20 ms | 10 |
| | | |
| MB | 20 ms | 15 |
| | | |
| WB | 20 ms | 20 |
+-----------------+------------+------------------------+
Table 44: Number of Shell Blocks Per SILK Frame
4.2.7.8.1. Rate Level
The first symbol in the excitation is a "rate level", which is an
index from 0 to 8, inclusive, coded using the PDF in Table 45
corresponding to the signal type of the current frame (from
Section 4.2.7.3). The rate level selects the PDF used to decode the
number of pulses in the individual shell blocks. It does not
directly convey any information about the bitrate or the number of
pulses itself, but merely changes the probability of the symbols in
Section 4.2.7.8.2. Level 0 provides a more efficient encoding at low
rates generally, and level 8 provides a more efficient encoding at
high rates generally, though the most efficient level for a
particular SILK frame may depend on the exact distribution of the
coded symbols. An encoder should, but is not required to, use the
most efficient rate level.
+----------------------+------------------------------------------+
| Signal Type | PDF |
+----------------------+------------------------------------------+
| Inactive or Unvoiced | {15, 51, 12, 46, 45, 13, 33, 27, 14}/256 |
| | |
| Voiced | {33, 30, 36, 17, 34, 49, 18, 21, 18}/256 |
+----------------------+------------------------------------------+
Table 45: PDFs for the Rate Level
4.2.7.8.2. Pulses per Shell Block
The total number of pulses in each of the shell blocks follows the
rate level. The pulse counts for all of the shell blocks are coded
consecutively, before the content of any of the blocks. Each block
may have anywhere from 0 to 16 pulses, inclusive, coded using the 18-
entry PDF in Table 46 corresponding to the rate level from
Section 4.2.7.8.1. The special value 17 indicates that this block
has one or more additional LSBs to decode for each coefficient. If
the decoder encounters this value, it decodes another value for the
actual pulse count of the block, but uses the PDF corresponding to
the special rate level 9 instead of the normal rate level. This
process repeats until the decoder reads a value less than 17, and it
then sets the number of extra LSBs used to the number of 17's decoded
for that block. If it reads the value 17 ten times, then the next
iteration uses the special rate level 10 instead of 9. The
probability of decoding a 17 when using the PDF for rate level 10 is
zero, ensuring that the number of LSBs for a block will not exceed
10. The cumulative distribution for rate level 10 is just a shifted
version of that for 9 and thus does not require any additional
storage.
+----------+--------------------------------------------------------+
| Rate | PDF |
| Level | |
+----------+--------------------------------------------------------+
| 0 | {131, 74, 25, 8, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
| | 1, 1}/256 |
| | |
| 1 | {58, 93, 60, 23, 7, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
| | 1, 1}/256 |
| | |
| 2 | {43, 51, 46, 33, 24, 16, 11, 8, 6, 3, 3, 3, 2, 1, 1, |
| | 2, 1, 2}/256 |
| | |
| 3 | {17, 52, 71, 57, 31, 12, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
| | 1, 1}/256 |
| | |
| 4 | {6, 21, 41, 53, 49, 35, 21, 11, 6, 3, 2, 2, 1, 1, 1, |
| | 1, 1, 1}/256 |
| | |
| 5 | {7, 14, 22, 28, 29, 28, 25, 20, 17, 13, 11, 9, 7, 5, |
| | 4, 4, 3, 10}/256 |
| | |
| 6 | {2, 5, 14, 29, 42, 46, 41, 31, 19, 11, 6, 3, 2, 1, 1, |
| | 1, 1, 1}/256 |
| | |
| 7 | {1, 2, 4, 10, 19, 29, 35, 37, 34, 28, 20, 14, 8, 5, 4, |
| | 2, 2, 2}/256 |
| | |
| 8 | {1, 2, 2, 5, 9, 14, 20, 24, 27, 28, 26, 23, 20, 15, |
| | 11, 8, 6, 15}/256 |
| | |
| 9 | {1, 1, 1, 6, 27, 58, 56, 39, 25, 14, 10, 6, 3, 3, 2, |
| | 1, 1, 2}/256 |
| | |
| 10 | {2, 1, 6, 27, 58, 56, 39, 25, 14, 10, 6, 3, 3, 2, 1, |
| | 1, 2, 0}/256 |
+----------+--------------------------------------------------------+
Table 46: PDFs for the Pulse Count
4.2.7.8.3. Pulse Location Decoding
The locations of the pulses in each shell block follow the pulse
counts, as decoded by silk_shell_decoder() (shell_coder.c). As with
the pulse counts, these locations are coded for all the shell blocks
before any of the remaining information for each block. Unlike many
other codecs, SILK places no restriction on the distribution of
pulses within a shell block. All of the pulses may be placed in a
single location, or each one in a unique location, or anything in
between.
The location of pulses is coded by recursively partitioning each
block into halves, and coding how many pulses fall on the left side
of the split. All remaining pulses must fall on the right side of
the split. The process then recurses into the left half, and after
that returns, the right half (preorder traversal). The PDF to use is
chosen by the size of the current partition (16, 8, 4, or 2) and the
number of pulses in the partition (1 to 16, inclusive). Tables 47
through 50 list the PDFs used for each partition size and pulse
count. This process skips partitions without any pulses, i.e., where
the initial pulse count from Section 4.2.7.8.2 was zero, or where the
split in the prior level indicated that all of the pulses fell on the
other side. These partitions have nothing to code, so they require
no PDF.
+------------+------------------------------------------------------+
| Pulse | PDF |
| Count | |
+------------+------------------------------------------------------+
| 1 | {126, 130}/256 |
| | |
| 2 | {56, 142, 58}/256 |
| | |
| 3 | {25, 101, 104, 26}/256 |
| | |
| 4 | {12, 60, 108, 64, 12}/256 |
| | |
| 5 | {7, 35, 84, 87, 37, 6}/256 |
| | |
| 6 | {4, 20, 59, 86, 63, 21, 3}/256 |
| | |
| 7 | {3, 12, 38, 72, 75, 42, 12, 2}/256 |
| | |
| 8 | {2, 8, 25, 54, 73, 59, 27, 7, 1}/256 |
| | |
| 9 | {2, 5, 17, 39, 63, 65, 42, 18, 4, 1}/256 |
| | |
| 10 | {1, 4, 12, 28, 49, 63, 54, 30, 11, 3, 1}/256 |
| | |
| 11 | {1, 4, 8, 20, 37, 55, 57, 41, 22, 8, 2, 1}/256 |
| | |
| 12 | {1, 3, 7, 15, 28, 44, 53, 48, 33, 16, 6, 1, 1}/256 |
| | |
| 13 | {1, 2, 6, 12, 21, 35, 47, 48, 40, 25, 12, 5, 1, |
| | 1}/256 |
| | |
| 14 | {1, 1, 4, 10, 17, 27, 37, 47, 43, 33, 21, 9, 4, 1, |
| | 1}/256 |
| | |
| 15 | {1, 1, 1, 8, 14, 22, 33, 40, 43, 38, 28, 16, 8, 1, |
| | 1, 1}/256 |
| | |
| 16 | {1, 1, 1, 1, 13, 18, 27, 36, 41, 41, 34, 24, 14, 1, |
| | 1, 1, 1}/256 |
+------------+------------------------------------------------------+
Table 47: PDFs for Pulse Count Split, 16 Sample Partitions
+------------+------------------------------------------------------+
| Pulse | PDF |
| Count | |
+------------+------------------------------------------------------+
| 1 | {127, 129}/256 |
| | |
| 2 | {53, 149, 54}/256 |
| | |
| 3 | {22, 105, 106, 23}/256 |
| | |
| 4 | {11, 61, 111, 63, 10}/256 |
| | |
| 5 | {6, 35, 86, 88, 36, 5}/256 |
| | |
| 6 | {4, 20, 59, 87, 62, 21, 3}/256 |
| | |
| 7 | {3, 13, 40, 71, 73, 41, 13, 2}/256 |
| | |
| 8 | {3, 9, 27, 53, 70, 56, 28, 9, 1}/256 |
| | |
| 9 | {3, 8, 19, 37, 57, 61, 44, 20, 6, 1}/256 |
| | |
| 10 | {3, 7, 15, 28, 44, 54, 49, 33, 17, 5, 1}/256 |
| | |
| 11 | {1, 7, 13, 22, 34, 46, 48, 38, 28, 14, 4, 1}/256 |
| | |
| 12 | {1, 1, 11, 22, 27, 35, 42, 47, 33, 25, 10, 1, 1}/256 |
| | |
| 13 | {1, 1, 6, 14, 26, 37, 43, 43, 37, 26, 14, 6, 1, |
| | 1}/256 |
| | |
| 14 | {1, 1, 4, 10, 20, 31, 40, 42, 40, 31, 20, 10, 4, 1, |
| | 1}/256 |
| | |
| 15 | {1, 1, 3, 8, 16, 26, 35, 38, 38, 35, 26, 16, 8, 3, |
| | 1, 1}/256 |
| | |
| 16 | {1, 1, 2, 6, 12, 21, 30, 36, 38, 36, 30, 21, 12, 6, |
| | 2, 1, 1}/256 |
+------------+------------------------------------------------------+
Table 48: PDFs for Pulse Count Split, 8 Sample Partitions
+------------+------------------------------------------------------+
| Pulse | PDF |
| Count | |
+------------+------------------------------------------------------+
| 1 | {127, 129}/256 |
| | |
| 2 | {49, 157, 50}/256 |
| | |
| 3 | {20, 107, 109, 20}/256 |
| | |
| 4 | {11, 60, 113, 62, 10}/256 |
| | |
| 5 | {7, 36, 84, 87, 36, 6}/256 |
| | |
| 6 | {6, 24, 57, 82, 60, 23, 4}/256 |
| | |
| 7 | {5, 18, 39, 64, 68, 42, 16, 4}/256 |
| | |
| 8 | {6, 14, 29, 47, 61, 52, 30, 14, 3}/256 |
| | |
| 9 | {1, 15, 23, 35, 51, 50, 40, 30, 10, 1}/256 |
| | |
| 10 | {1, 1, 21, 32, 42, 52, 46, 41, 18, 1, 1}/256 |
| | |
| 11 | {1, 6, 16, 27, 36, 42, 42, 36, 27, 16, 6, 1}/256 |
| | |
| 12 | {1, 5, 12, 21, 31, 38, 40, 38, 31, 21, 12, 5, 1}/256 |
| | |
| 13 | {1, 3, 9, 17, 26, 34, 38, 38, 34, 26, 17, 9, 3, |
| | 1}/256 |
| | |
| 14 | {1, 3, 7, 14, 22, 29, 34, 36, 34, 29, 22, 14, 7, 3, |
| | 1}/256 |
| | |
| 15 | {1, 2, 5, 11, 18, 25, 31, 35, 35, 31, 25, 18, 11, 5, |
| | 2, 1}/256 |
| | |
| 16 | {1, 1, 4, 9, 15, 21, 28, 32, 34, 32, 28, 21, 15, 9, |
| | 4, 1, 1}/256 |
+------------+------------------------------------------------------+
Table 49: PDFs for Pulse Count Split, 4 Sample Partitions
+------------+------------------------------------------------------+
| Pulse | PDF |
| Count | |
+------------+------------------------------------------------------+
| 1 | {128, 128}/256 |
| | |
| 2 | {42, 172, 42}/256 |
| | |
| 3 | {21, 107, 107, 21}/256 |
| | |
| 4 | {12, 60, 112, 61, 11}/256 |
| | |
| 5 | {8, 34, 86, 86, 35, 7}/256 |
| | |
| 6 | {8, 23, 55, 90, 55, 20, 5}/256 |
| | |
| 7 | {5, 15, 38, 72, 72, 36, 15, 3}/256 |
| | |
| 8 | {6, 12, 27, 52, 77, 47, 20, 10, 5}/256 |
| | |
| 9 | {6, 19, 28, 35, 40, 40, 35, 28, 19, 6}/256 |
| | |
| 10 | {4, 14, 22, 31, 37, 40, 37, 31, 22, 14, 4}/256 |
| | |
| 11 | {3, 10, 18, 26, 33, 38, 38, 33, 26, 18, 10, 3}/256 |
| | |
| 12 | {2, 8, 13, 21, 29, 36, 38, 36, 29, 21, 13, 8, 2}/256 |
| | |
| 13 | {1, 5, 10, 17, 25, 32, 38, 38, 32, 25, 17, 10, 5, |
| | 1}/256 |
| | |
| 14 | {1, 4, 7, 13, 21, 29, 35, 36, 35, 29, 21, 13, 7, 4, |
| | 1}/256 |
| | |
| 15 | {1, 2, 5, 10, 17, 25, 32, 36, 36, 32, 25, 17, 10, 5, |
| | 2, 1}/256 |
| | |
| 16 | {1, 2, 4, 7, 13, 21, 28, 34, 36, 34, 28, 21, 13, 7, |
| | 4, 2, 1}/256 |
+------------+------------------------------------------------------+
Table 50: PDFs for Pulse Count Split, 2 Sample Partitions
4.2.7.8.4. LSB Decoding
After the decoder reads the pulse locations for all blocks, it reads
the LSBs (if any) for each block in turn. Inside each block, it
reads all the LSBs for each coefficient in turn, even those where no
pulses were allocated, before proceeding to the next one. For 10 ms
MB frames, it reads LSBs even for the extra 8 samples in the last
block. The LSBs are coded from most significant to least
significant, and they all use the PDF in Table 51.
+----------------+
| PDF |
+----------------+
| {136, 120}/256 |
+----------------+
Table 51: PDF for Excitation LSBs
The number of LSBs read for each coefficient in a block is determined
in Section 4.2.7.8.2. The magnitude of the coefficient is initially
equal to the number of pulses placed at that location in
Section 4.2.7.8.3. As each LSB is decoded, the magnitude is doubled,
and then the value of the LSB added to it, to obtain an updated
magnitude.
4.2.7.8.5. Sign Decoding
After decoding the pulse locations and the LSBs, the decoder knows
the magnitude of each coefficient in the excitation. It then decodes
a sign for all coefficients with a non-zero magnitude, using one of
the PDFs from Table 52. If the value decoded is 0, then the
coefficient magnitude is negated. Otherwise, it remains positive.
The decoder chooses the PDF for the sign based on the signal type and
quantization offset type (from Section 4.2.7.3) and the number of
pulses in the block (from Section 4.2.7.8.2). The number of pulses
in the block does not take into account any LSBs. Most PDFs are
skewed towards negative signs because of the quantization offset, but
the PDFs for zero pulses are highly skewed towards positive signs.
If a block contains many positive coefficients, it is sometimes
beneficial to code it solely using LSBs (i.e., with zero pulses),
since the encoder may be able to save enough bits on the signs to
justify the less efficient coefficient magnitude encoding.
+-------------+-----------------------+-------------+---------------+
| Signal Type | Quantization Offset | Pulse Count | PDF |
| | Type | | |
+-------------+-----------------------+-------------+---------------+
| Inactive | Low | 0 | {2, 254}/256 |
| | | | |
| Inactive | Low | 1 | {207, 49}/256 |
| | | | |
| Inactive | Low | 2 | {189, 67}/256 |
| Inactive | Low | 3 | {179, 77}/256 |
| | | | |
| Inactive | Low | 4 | {174, 82}/256 |
| | | | |
| Inactive | Low | 5 | {163, 93}/256 |
| | | | |
| Inactive | Low | 6 or more | {157, 99}/256 |
| | | | |
| Inactive | High | 0 | {58, 198}/256 |
| | | | |
| Inactive | High | 1 | {245, 11}/256 |
| | | | |
| Inactive | High | 2 | {238, 18}/256 |
| | | | |
| Inactive | High | 3 | {232, 24}/256 |
| | | | |
| Inactive | High | 4 | {225, 31}/256 |
| | | | |
| Inactive | High | 5 | {220, 36}/256 |
| | | | |
| Inactive | High | 6 or more | {211, 45}/256 |
| | | | |
| Unvoiced | Low | 0 | {1, 255}/256 |
| | | | |
| Unvoiced | Low | 1 | {210, 46}/256 |
| | | | |
| Unvoiced | Low | 2 | {190, 66}/256 |
| | | | |
| Unvoiced | Low | 3 | {178, 78}/256 |
| | | | |
| Unvoiced | Low | 4 | {169, 87}/256 |
| | | | |
| Unvoiced | Low | 5 | {162, 94}/256 |
| | | | |
| Unvoiced | Low | 6 or more | {152, |
| | | | 104}/256 |
| | | | |
| Unvoiced | High | 0 | {48, 208}/256 |
| | | | |
| Unvoiced | High | 1 | {242, 14}/256 |
| | | | |
| Unvoiced | High | 2 | {235, 21}/256 |
| | | | |
| Unvoiced | High | 3 | {224, 32}/256 |
| | | | |
| Unvoiced | High | 4 | {214, 42}/256 |
| | | | |
| Unvoiced | High | 5 | {205, 51}/256 |
| Unvoiced | High | 6 or more | {190, 66}/256 |
| | | | |
| Voiced | Low | 0 | {1, 255}/256 |
| | | | |
| Voiced | Low | 1 | {162, 94}/256 |
| | | | |
| Voiced | Low | 2 | {152, |
| | | | 104}/256 |
| | | | |
| Voiced | Low | 3 | {147, |
| | | | 109}/256 |
| | | | |
| Voiced | Low | 4 | {144, |
| | | | 112}/256 |
| | | | |
| Voiced | Low | 5 | {141, |
| | | | 115}/256 |
| | | | |
| Voiced | Low | 6 or more | {138, |
| | | | 118}/256 |
| | | | |
| Voiced | High | 0 | {8, 248}/256 |
| | | | |
| Voiced | High | 1 | {203, 53}/256 |
| | | | |
| Voiced | High | 2 | {187, 69}/256 |
| | | | |
| Voiced | High | 3 | {176, 80}/256 |
| | | | |
| Voiced | High | 4 | {168, 88}/256 |
| | | | |
| Voiced | High | 5 | {161, 95}/256 |
| | | | |
| Voiced | High | 6 or more | {154, |
| | | | 102}/256 |
+-------------+-----------------------+-------------+---------------+
Table 52: PDFs for Excitation Signs
4.2.7.8.6. Reconstructing the Excitation
After the signs have been read, there is enough information to
reconstruct the complete excitation signal. This requires adding a
constant quantization offset to each non-zero sample and then
pseudorandomly inverting and offsetting every sample. The constant
quantization offset varies depending on the signal type and
quantization offset type (see Section 4.2.7.3).
+-------------+--------------------------+--------------------------+
| Signal Type | Quantization Offset Type | Quantization Offset |
| | | (Q23) |
+-------------+--------------------------+--------------------------+
| Inactive | Low | 25 |
| | | |
| Inactive | High | 60 |
| | | |
| Unvoiced | Low | 25 |
| | | |
| Unvoiced | High | 60 |
| | | |
| Voiced | Low | 8 |
| | | |
| Voiced | High | 25 |
+-------------+--------------------------+--------------------------+
Table 53: Excitation Quantization Offsets
Let e_raw[i] be the raw excitation value at position i, with a
magnitude composed of the pulses at that location (see
Section 4.2.7.8.3) combined with any additional LSBs (see
Section 4.2.7.8.4), and with the corresponding sign decoded in
Section 4.2.7.8.5. Additionally, let seed be the current
pseudorandom seed, which is initialized to the value decoded from
Section 4.2.7.7 for the first sample in the current SILK frame, and
updated for each subsequent sample according to the procedure below.
Finally, let offset_Q23 be the quantization offset from Table 53.
Then the following procedure produces the final reconstructed
excitation value, e_Q23[i]:
e_Q23[i] = (e_raw[i] << 8) - sign(e_raw[i])*20 + offset_Q23;
seed = (196314165*seed + 907633515) & 0xFFFFFFFF;
e_Q23[i] = (seed & 0x80000000) ? -e_Q23[i] : e_Q23[i];
seed = (seed + e_raw[i]) & 0xFFFFFFFF;
When e_raw[i] is zero, sign() returns 0 by the definition in
Section 1.1.4, so the factor of 20 does not get added. The final
e_Q23[i] value may require more than 16 bits per sample, but it will
not require more than 23, including the sign.
4.2.7.9. SILK Frame Reconstruction
The remainder of the reconstruction process for the frame does not
need to be bit-exact, as small errors should only introduce
proportionally small distortions. Although the reference
implementation only includes a fixed-point version of the remaining
steps, this section describes them in terms of a floating-point
version for simplicity. This produces a signal with a nominal range
of -1.0 to 1.0.
silk_decode_core() (decode_core.c) contains the code for the main
reconstruction process. It proceeds subframe-by-subframe, since
quantization gains, LTP parameters, and (in 20 ms SILK frames) LPC
coefficients can vary from one to the next.
Let a_Q12[k] be the LPC coefficients for the current subframe. If
this is the first or second subframe of a 20 ms SILK frame and the
LSF interpolation factor, w_Q2 (see Section 4.2.7.5.5), is less than
4, then these correspond to the final LPC coefficients produced by
Section 4.2.7.5.8 from the interpolated LSF coefficients, n1_Q15[k]
(computed in Section 4.2.7.5.5). Otherwise, they correspond to the
final LPC coefficients produced from the uninterpolated LSF
coefficients for the current frame, n2_Q15[k].
Also, let n be the number of samples in a subframe (40 for NB, 60 for
MB, and 80 for WB), s be the index of the current subframe in this
SILK frame (0 or 1 for 10 ms frames, or 0 to 3 for 20 ms frames), and
j be the index of the first sample in the residual corresponding to
the current subframe.
4.2.7.9.1. LTP Synthesis
For unvoiced frames (see Section 4.2.7.3), the LPC residual for i
such that j <= i < (j + n) is simply a normalized copy of the
excitation signal, i.e.,
e_Q23[i]
res[i] = ---------
2.0**23
Voiced SILK frames, on the other hand, pass the excitation through an
LTP filter using the parameters decoded in Section 4.2.7.6 to produce
an LPC residual. The LTP filter requires LPC residual values from
before the current subframe as input. However, since the LPC
coefficients may have changed, it obtains this residual by
"rewhitening" the corresponding output signal using the LPC
coefficients from the current subframe. Let out[i] for i such that
(j - pitch_lags[s] - d_LPC - 2) <= i < j be the fully reconstructed
output signal from the last (pitch_lags[s] + d_LPC + 2) samples of
previous subframes (see Section 4.2.7.9.2), where pitch_lags[s] is
the pitch lag for the current subframe from Section 4.2.7.6.1.
Additionally, let lpc[i] for i such that (j - s*n - d_LPC) <= i < j
be the fully reconstructed output signal from the last (s*n + d_LPC)
samples of previous subframes before clamping (see
Section 4.2.7.9.2). During reconstruction of the first subframe for
this channel after either
o An uncoded regular SILK frame (if this is the side channel), or
o A decoder reset (see Section 4.5.2),
out[i] and lpc[i] are initially cleared to all zeros. If this is the
third or fourth subframe of a 20 ms SILK frame and the LSF
interpolation factor, w_Q2 (see Section 4.2.7.5.5), is less than 4,
then let out_end be set to (j - (s-2)*n) and let LTP_scale_Q14 be set
to 16384. Otherwise, set out_end to (j - s*n) and set LTP_scale_Q14
to the Q14 LTP scaling value from Section 4.2.7.6.3. Then, for i
such that (j - pitch_lags[s] - 2) <= i < out_end, out[i] is
rewhitened into an LPC residual, res[i], via
4.0*LTP_scale_Q14
res[i] = ----------------- * clamp(-1.0,
gain_Q16[s]
d_LPC-1
__ a_Q12[k]
out[i] - \ out[i-k-1] * --------, 1.0)
/_ 4096.0
k=0
This requires storage to buffer up to 306 values of out[i] from
previous subframes. This corresponds to WB with a maximum pitch lag
of 18 ms * 16 kHz samples, plus 16 samples for d_LPC, plus 2 samples
for the width of the LTP filter. Then, for i such that
out_end <= i < j, lpc[i] is rewhitened into an LPC residual, res[i],
via
d_LPC-1
65536.0 __ a_Q12[k]
res[i] = ----------- * (lpc[i] - \ lpc[i-k-1] * --------)
gain_Q16[s] /_ 4096.0
k=0
This requires storage to buffer up to 256 values of lpc[i] from
previous subframes (240 from the current SILK frame and 16 from the
previous SILK frame). This corresponds to WB with up to three
previous subframes in the current SILK frame, plus 16 samples for
d_LPC. The astute reader will notice that, given the definition of
lpc[i] in Section 4.2.7.9.2, the output of this latter equation is
merely a scaled version of the values of res[i] from previous
subframes.
Let e_Q23[i] for j <= i < (j + n) be the excitation for the current
subframe, and b_Q7[k] for 0 <= k < 5 be the coefficients of the LTP
filter taken from the codebook entry in one of Tables 39 through 41
corresponding to the index decoded for the current subframe in
Section 4.2.7.6.2. Then for i such that j <= i < (j + n), the LPC
residual is
4
e_Q23[i] __ b_Q7[k]
res[i] = --------- + \ res[i - pitch_lags[s] + 2 - k] * -------
2.0**23 /_ 128.0
k=0
4.2.7.9.2. LPC Synthesis
LPC synthesis uses the short-term LPC filter to predict the next
output coefficient. For i such that (j - d_LPC) <= i < j, let lpc[i]
be the result of LPC synthesis from the last d_LPC samples of the
previous subframe or zeros in the first subframe for this channel
after either
o An uncoded regular SILK frame (if this is the side channel), or
o A decoder reset (see Section 4.5.2).
Then, for i such that j <= i < (j + n), the result of LPC synthesis
for the current subframe is
d_LPC-1
gain_Q16[i] __ a_Q12[k]
lpc[i] = ----------- * res[i] + \ lpc[i-k-1] * --------
65536.0 /_ 4096.0
k=0
The decoder saves the final d_LPC values, i.e., lpc[i] such that
(j + n - d_LPC) <= i < (j + n), to feed into the LPC synthesis of the
next subframe. This requires storage for up to 16 values of lpc[i]
(for WB frames).
Then, the signal is clamped into the final nominal range:
out[i] = clamp(-1.0, lpc[i], 1.0)
This clamping occurs entirely after the LPC synthesis filter has run.
The decoder saves the unclamped values, lpc[i], to feed into the LPC
filter for the next subframe, but saves the clamped values, out[i],
for rewhitening in voiced frames.
4.2.8. Stereo Unmixing
For stereo streams, after decoding a frame from each channel, the
decoder must convert the mid-side (MS) representation into a left-
right (LR) representation. The function silk_stereo_MS_to_LR
(stereo_MS_to_LR.c) implements this process. In it, the decoder
predicts the side channel using a) a simple low-passed version of the
mid channel, and b) the unfiltered mid channel, using the prediction
weights decoded in Section 4.2.7.1. This simple low-pass filter
imposes a one-sample delay, and the unfiltered mid channel is also
delayed by one sample. In order to allow seamless switching between
stereo and mono, mono streams must also impose the same one-sample
delay. The encoder requires an additional one-sample delay for both
mono and stereo streams, though an encoder may omit the delay for
mono if it knows it will never switch to stereo.
The unmixing process operates in two phases. The first phase lasts
for 8 ms, during which it interpolates the prediction weights from
the previous frame, prev_w0_Q13 and prev_w1_Q13, to the values for
the current frame, w0_Q13 and w1_Q13. The second phase simply uses
these weights for the remainder of the frame.
Let mid[i] and side[i] be the contents of out[i] (from
Section 4.2.7.9.2) for the current mid and side channels,
respectively, and let left[i] and right[i] be the corresponding
stereo output channels. If the side channel is not coded (see
Section 4.2.7.2), then side[i] is set to zero. Also, let j be
defined as in Section 4.2.7.9, n1 be the number of samples in phase 1
(64 for NB, 96 for MB, and 128 for WB), and n2 be the total number of
samples in the frame. Then, for i such that j <= i < (j + n2), the
left and right channel output is
prev_w0_Q13 (w0_Q13 - prev_w0_Q13)
w0 = ----------- + min(i - j, n1)*----------------------
8192.0 8192.0*n1
prev_w1_Q13 (w1_Q13 - prev_w1_Q13)
w1 = ----------- + min(i - j, n1)*----------------------
8192.0 8192.0*n1
mid[i-2] + 2*mid[i-1] + mid[i]
p0 = ------------------------------
4.0
left[i] = clamp(-1.0, (1 + w1)*mid[i-1] + side[i-1] + w0*p0, 1.0)
right[i] = clamp(-1.0, (1 - w1)*mid[i-1] - side[i-1] - w0*p0, 1.0)
These formulas require two samples prior to index j, the start of the
frame, for the mid channel, and one prior sample for the side
channel. For the first frame after a decoder reset, zeros are used
instead.
4.2.9. Resampling
After stereo unmixing (if any), the decoder applies resampling to
convert the decoded SILK output to the sample rate desired by the
application. This is necessary when decoding a Hybrid frame at SWB
or FB sample rates, or whenever the decoder wants the output at a
different sample rate than the internal SILK sampling rate (e.g., to
allow a constant sample rate when the audio bandwidth changes, or to
allow mixing with audio from other applications). The resampler
itself is non-normative, and a decoder can use any method it wants to
perform the resampling.
However, a minimum amount of delay is imposed to allow the resampler
to operate, and this delay is normative, so that the corresponding
delay can be applied to the MDCT layer in the encoder. A decoder is
always free to use a resampler that requires more delay than allowed
for here (e.g., to improve quality), but it must then delay the
output of the MDCT layer by this extra amount. Keeping as much delay
as possible on the encoder side allows an encoder that knows it will
never use any of the SILK or Hybrid modes to skip this delay. By
contrast, if it were all applied by the decoder, then a decoder that
processes audio in fixed-size blocks would be forced to delay the
output of CELT frames just in case of a later switch to a SILK or
Hybrid mode.
Table 54 gives the maximum resampler delay in samples at 48 kHz for
each SILK audio bandwidth. Because the actual output rate may not be
48 kHz, it may not be possible to achieve exactly these delays while
using a whole number of input or output samples. The reference
implementation is able to resample to any of the supported output
sampling rates (8, 12, 16, 24, or 48 kHz) within or near this delay
constraint. Some resampling filters (including those used by the
reference implementation) may add a delay that is not an exact
integer, or is not linear-phase, and so cannot be represented by a
single delay at all frequencies. However, such deviations are
unlikely to be perceptible, and the comparison tool described in
Section 6 is designed to be relatively insensitive to them. The
delays listed here are the ones that should be targeted by the
encoder.
+-----------------+-----------------------+
| Audio Bandwidth | Delay in Milliseconds |
+-----------------+-----------------------+
| NB | 0.538 |
| | |
| MB | 0.692 |
| | |
| WB | 0.706 |
+-----------------+-----------------------+
Table 54: SILK Resampler Delay Allocations
NB is given a smaller decoder delay allocation than MB and WB to
allow a higher-order filter when resampling to 8 kHz in both the
encoder and decoder. This implies that the audio content of two SILK
frames operating at different bandwidths is not perfectly aligned in
time. This is not an issue for any transitions described in
Section 4.5, because they all involve a SILK decoder reset. When the
decoder is reset, any samples remaining in the resampling buffer are
discarded, and the resampler is re-initialized with silence.
4.3. CELT Decoder
The CELT layer of Opus is based on the Modified Discrete Cosine
Transform [MDCT] with partially overlapping windows of 5 to 22.5 ms.
The main principle behind CELT is that the MDCT spectrum is divided
into bands that (roughly) follow the Bark scale, i.e., the scale of
the ear's critical bands [ZWICKER61]. The normal CELT layer uses 21
of those bands, though Opus Custom (see Section 6.2) may use a
different number of bands. In Hybrid mode, the first 17 bands (up to
8 kHz) are not coded. A band can contain as little as one MDCT bin
per channel, and as many as 176 bins per channel, as detailed in
Table 55. In each band, the gain (energy) is coded separately from
the shape of the spectrum. Coding the gain explicitly makes it easy
to preserve the spectral envelope of the signal. The remaining unit-
norm shape vector is encoded using a Pyramid Vector Quantizer
(PVQ) Section 4.3.4.
+--------+--------+------+-------+-------+-------------+------------+
| Frame | 2.5 ms | 5 ms | 10 ms | 20 ms | Start | Stop |
| Size: | | | | | Frequency | Frequency |
+--------+--------+------+-------+-------+-------------+------------+
| Band | Bins: | | | | | |
| | | | | | | |
| 0 | 1 | 2 | 4 | 8 | 0 Hz | 200 Hz |
| | | | | | | |
| 1 | 1 | 2 | 4 | 8 | 200 Hz | 400 Hz |
| | | | | | | |
| 2 | 1 | 2 | 4 | 8 | 400 Hz | 600 Hz |
| | | | | | | |
| 3 | 1 | 2 | 4 | 8 | 600 Hz | 800 Hz |
| | | | | | | |
| 4 | 1 | 2 | 4 | 8 | 800 Hz | 1000 Hz |
| | | | | | | |
| 5 | 1 | 2 | 4 | 8 | 1000 Hz | 1200 Hz |
| | | | | | | |
| 6 | 1 | 2 | 4 | 8 | 1200 Hz | 1400 Hz |
| | | | | | | |
| 7 | 1 | 2 | 4 | 8 | 1400 Hz | 1600 Hz |
| | | | | | | |
| 8 | 2 | 4 | 8 | 16 | 1600 Hz | 2000 Hz |
| | | | | | | |
| 9 | 2 | 4 | 8 | 16 | 2000 Hz | 2400 Hz |
| | | | | | | |
| 10 | 2 | 4 | 8 | 16 | 2400 Hz | 2800 Hz |
| | | | | | | |
| 11 | 2 | 4 | 8 | 16 | 2800 Hz | 3200 Hz |
| | | | | | | |
| 12 | 4 | 8 | 16 | 32 | 3200 Hz | 4000 Hz |
| | | | | | | |
| 13 | 4 | 8 | 16 | 32 | 4000 Hz | 4800 Hz |
| | | | | | | |
| 14 | 4 | 8 | 16 | 32 | 4800 Hz | 5600 Hz |
| | | | | | | |
| 15 | 6 | 12 | 24 | 48 | 5600 Hz | 6800 Hz |
| | | | | | | |
| 16 | 6 | 12 | 24 | 48 | 6800 Hz | 8000 Hz |
| | | | | | | |
| 17 | 8 | 16 | 32 | 64 | 8000 Hz | 9600 Hz |
| | | | | | | |
| 18 | 12 | 24 | 48 | 96 | 9600 Hz | 12000 Hz |
| | | | | | | |
| 19 | 18 | 36 | 72 | 144 | 12000 Hz | 15600 Hz |
| | | | | | | |
| 20 | 22 | 44 | 88 | 176 | 15600 Hz | 20000 Hz |
+--------+--------+------+-------+-------+-------------+------------+
Table 55: MDCT Bins per Channel per Band for Each Frame Size
Transients are notoriously difficult for transform codecs to code.
CELT uses two different strategies for them:
1. Using multiple smaller MDCTs instead of a single large MDCT, and
2. Dynamic time-frequency resolution changes (See Section 4.3.4.5).
To improve quality on highly tonal and periodic signals, CELT
includes a pre-filter/post-filter combination. The pre-filter on the
encoder side attenuates the signal's harmonics. The post-filter on
the decoder side restores the original gain of the harmonics, while
shaping the coding noise to roughly follow the harmonics. Such noise
shaping reduces the perception of the noise.
When coding a stereo signal, three coding methods are available:
o mid-side stereo: encodes the mean and the difference of the left
and right channels,
o intensity stereo: only encodes the mean of the left and right
channels (discards the difference),
o dual stereo: encodes the left and right channels separately.
An overview of the decoder is given in Figure 17.
+---------+
| Coarse |
+->| decoder |----+
| +---------+ |
| |
| +---------+ v
| | Fine | +---+
+->| decoder |->| + |
| +---------+ +---+
| ^ |
+---------+ | | |
| Range | | +----------+ v
| Decoder |-+ | Bit | +------+
+---------+ | |Allocation| | 2**x |
| +----------+ +------+
| | |
| v v +--------+
| +---------+ +---+ +-------+ | pitch |
+->| PVQ |->| * |->| IMDCT |->| post- |--->
| | decoder | +---+ +-------+ | filter |
| +---------+ +--------+
| ^
+--------------------------------------+
Legend: IMDCT = Inverse MDCT
Figure 17: Structure of the CELT decoder
The decoder is based on the following symbols and sets of symbols:
+---------------+---------------------+---------------+
| Symbol(s) | PDF | Condition |
+---------------+---------------------+---------------+
| silence | {32767, 1}/32768 | |
| | | |
| post-filter | {1, 1}/2 | |
| | | |
| octave | uniform (6) | post-filter |
| | | |
| period | raw bits (4+octave) | post-filter |
| | | |
| gain | raw bits (3) | post-filter |
| | | |
| tapset | {2, 1, 1}/4 | post-filter |
| | | |
| transient | {7, 1}/8 | |
| | | |
| intra | {7, 1}/8 | |
| | | |
| coarse energy | Section 4.3.2 | |
| | | |
| tf_change | Section 4.3.1 | |
| | | |
| tf_select | {1, 1}/2 | Section 4.3.1 |
| | | |
| spread | {7, 2, 21, 2}/32 | |
| | | |
| dyn. alloc. | Section 4.3.3 | |
| | | |
| alloc. trim | Table 58 | |
| | | |
| skip | {1, 1}/2 | Section 4.3.3 |
| | | |
| intensity | uniform | Section 4.3.3 |
| | | |
| dual | {1, 1}/2 | |
| | | |
| fine energy | Section 4.3.2 | |
| | | |
| residual | Section 4.3.4 | |
| | | |
| anti-collapse | {1, 1}/2 | Section 4.3.5 |
| | | |
| finalize | Section 4.3.2 | |
+---------------+---------------------+---------------+
Table 56: Order of the Symbols in the CELT Section of the Bitstream
The decoder extracts information from the range-coded bitstream in
the order described in Table 56. In some circumstances, it is
possible for a decoded value to be out of range due to a very small
amount of redundancy in the encoding of large integers by the range
coder. In that case, the decoder should assume there has been an
error in the coding, decoding, or transmission and SHOULD take
measures to conceal the error and/or report to the application that a
problem has occurred. Such out of range errors cannot occur in the
SILK layer.
4.3.1. Transient Decoding
The "transient" flag indicates whether the frame uses a single long
MDCT or several short MDCTs. When it is set, then the MDCT
coefficients represent multiple short MDCTs in the frame. When not
set, the coefficients represent a single long MDCT for the frame.
The flag is encoded in the bitstream with a probability of 1/8. In
addition to the global transient flag is a per-band binary flag to
change the time-frequency (tf) resolution independently in each band.
The change in tf resolution is defined in tf_select_table[][] in
celt.c and depends on the frame size, whether the transient flag is
set, and the value of tf_select. The tf_select flag uses a 1/2
probability, but is only decoded if it can have an impact on the
result knowing the value of all per-band tf_change flags.
4.3.2. Energy Envelope Decoding
It is important to quantize the energy with sufficient resolution
because any energy quantization error cannot be compensated for at a
later stage. Regardless of the resolution used for encoding the
spectral shape of a band, it is perceptually important to preserve
the energy in each band. CELT uses a three-step coarse-fine-fine
strategy for encoding the energy in the base-2 log domain, as
implemented in quant_bands.c.
4.3.2.1. Coarse Energy Decoding
Coarse quantization of the energy uses a fixed resolution of 6 dB
(integer part of base-2 log). To minimize the bitrate, prediction is
applied both in time (using the previous frame) and in frequency
(using the previous bands). The part of the prediction that is based
on the previous frame can be disabled, creating an "intra" frame
where the energy is coded without reference to prior frames. The
decoder first reads the intra flag to determine what prediction is
used. The 2-D z-transform [Z-TRANSFORM] of the prediction filter is
-1 -1
(1 - alpha*z_l )*(1 - z_b )
A(z_l, z_b) = -----------------------------
-1
1 - beta*z_b
where b is the band index and l is the frame index. The prediction
coefficients applied depend on the frame size in use when not using
intra energy and are alpha=0, beta=4915/32768 when using intra
energy. The time-domain prediction is based on the final fine
quantization of the previous frame, while the frequency domain
(within the current frame) prediction is based on coarse quantization
only (because the fine quantization has not been computed yet). The
prediction is clamped internally so that fixed-point implementations
with limited dynamic range always remain in the same state as
floating point implementations. We approximate the ideal probability
distribution of the prediction error using a Laplace distribution
with separate parameters for each frame size in intra- and inter-
frame modes. These parameters are held in the e_prob_model table in
quant_bands.c. The coarse energy decoding is performed by
unquant_coarse_energy() (quant_bands.c). The decoding of the
Laplace-distributed values is implemented in ec_laplace_decode()
(laplace.c).
4.3.2.2. Fine Energy Quantization
The number of bits assigned to fine energy quantization in each band
is determined by the bit allocation computation described in
Section 4.3.3. Let B_i be the number of fine energy bits for band i;
the refinement is an integer f in the range [0,2**B_i-1]. The
mapping between f and the correction applied to the coarse energy is
equal to (f+1/2)/2**B_i - 1/2. Fine energy quantization is
implemented in quant_fine_energy() (quant_bands.c).
When some bits are left "unused" after all other flags have been
decoded, these bits are assigned to a "final" step of fine
allocation. In effect, these bits are used to add one extra fine
energy bit per band per channel. The allocation process determines
two "priorities" for the final fine bits. Any remaining bits are
first assigned only to bands of priority 0, starting from band 0 and
going up. If all bands of priority 0 have received one bit per
channel, then bands of priority 1 are assigned an extra bit per
channel, starting from band 0. If any bits are left after this, they
are left unused. This is implemented in unquant_energy_finalise()
(quant_bands.c).
4.3.3. Bit Allocation
Because the bit allocation drives the decoding of the range-coder
stream, it MUST be recovered exactly so that identical coding
decisions are made in the encoder and decoder. Any deviation from
the reference's resulting bit allocation will result in corrupted
output, though implementers are free to implement the procedure in
any way that produces identical results.
The per-band gain-shape structure of the CELT layer ensures that
using the same number of bits for the spectral shape of a band in
every frame will result in a roughly constant signal-to-noise ratio
in that band. This results in coding noise that has the same
spectral envelope as the signal. The masking curve produced by a
standard psychoacoustic model also closely follows the spectral
envelope of the signal. This structure means that the ideal
allocation is more consistent from frame to frame than it is for
other codecs without an equivalent structure and that a fixed
allocation provides fairly consistent perceptual
performance [VALIN2010].
Many codecs transmit significant amounts of side information to
control the bit allocation within a frame. Often this control is
only indirect, and it must be exercised carefully to achieve the
desired rate constraints. The CELT layer, however, can adapt over a
very wide range of rates, so it has a large number of codebook sizes
to choose from for each band. Explicitly signaling the size of each
of these codebooks would impose considerable overhead, even though
the allocation is relatively static from frame to frame. This is
because all of the information required to compute these codebook
sizes must be derived from a single frame by itself, in order to
retain robustness to packet loss, so the signaling cannot take
advantage of knowledge of the allocation in neighboring frames. This
problem is exacerbated in low-latency (small frame size)
applications, which would include this overhead in every frame.
For this reason, in the MDCT mode, Opus uses a primarily implicit bit
allocation. The available bitstream capacity is known in advance to
both the encoder and decoder without additional signaling, ultimately
from the packet sizes expressed by a higher-level protocol. Using
this information, the codec interpolates an allocation from a hard-
coded table.
While the band-energy structure effectively models intra-band
masking, it ignores the weaker inter-band masking, band-temporal
masking, and other less significant perceptual effects. While these
effects can often be ignored, they can become significant for
particular samples. One mechanism available to encoders would be to
simply increase the overall rate for these frames, but this is not
possible in a constant rate mode and can be fairly inefficient. As a
result three explicitly signaled mechanisms are provided to alter the
implicit allocation:
o Band boost
o Allocation trim
o Band skipping
The first of these mechanisms, band boost, allows an encoder to boost
the allocation in specific bands. The second, allocation trim, works
by biasing the overall allocation towards higher or lower frequency
bands. The third, band skipping, selects which low-precision high
frequency bands will be allocated no shape bits at all.
In stereo mode, there are two additional parameters potentially coded
as part of the allocation procedure: a parameter to allow the
selective elimination of allocation for the 'side' (i.e., intensity
stereo) in jointly coded bands, and a flag to deactivate joint coding
(i.e., dual stereo). These values are not signaled if they would be
meaningless in the overall context of the allocation.
Because every signaled adjustment increases overhead and
implementation complexity, none were included speculatively: the
reference encoder makes use of all of these mechanisms. While the
decision logic in the reference was found to be effective enough to
justify the overhead and complexity, further analysis techniques may
be discovered that increase the effectiveness of these parameters.
As with other signaled parameters, an encoder is free to choose the
values in any manner, but, unless a technique is known to deliver
superior perceptual results, the methods used by the reference
implementation should be used.
The allocation process consists of the following steps: determining
the per-band maximum allocation vector, decoding the boosts, decoding
the tilt, determining the remaining capacity of the frame, searching
the mode table for the entry nearest but not exceeding the available
space (subject to the tilt, boosts, band maximums, and band
minimums), linear interpolation, reallocation of unused bits with
concurrent skip decoding, determination of the fine-energy vs. shape
split, and final reallocation. This process results in a per-band
shape allocation (in 1/8th-bit units), a per-band fine-energy
allocation (in 1 bit per channel units), a set of band priorities for
controlling the use of remaining bits at the end of the frame, and a
remaining balance of unallocated space, which is usually zero except
at very high rates.
The "static" bit allocation (in 1/8 bits) for a quality q, excluding
the minimums, maximums, tilt and boosts, is equal to
channels*N*alloc[band][q]<<LM>>2, where alloc[][] is given in
Table 57 and LM=log2(frame_size/120). The allocation is obtained by
linearly interpolating between two values of q (in steps of 1/64) to
find the highest allocation that does not exceed the number of bits
remaining.
Rows indicate the MDCT bands, columns are the different quality (q)
parameters. The units are 1/32 bit per MDCT bin.
+---+----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+---+----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 0 | 90 | 110 | 118 | 126 | 134 | 144 | 152 | 162 | 172 | 200 |
| | | | | | | | | | | |
| 0 | 80 | 100 | 110 | 119 | 127 | 137 | 145 | 155 | 165 | 200 |
| | | | | | | | | | | |
| 0 | 75 | 90 | 103 | 112 | 120 | 130 | 138 | 148 | 158 | 200 |
| | | | | | | | | | | |
| 0 | 69 | 84 | 93 | 104 | 114 | 124 | 132 | 142 | 152 | 200 |
| | | | | | | | | | | |
| 0 | 63 | 78 | 86 | 95 | 103 | 113 | 123 | 133 | 143 | 200 |
| | | | | | | | | | | |
| 0 | 56 | 71 | 80 | 89 | 97 | 107 | 117 | 127 | 137 | 200 |
| | | | | | | | | | | |
| 0 | 49 | 65 | 75 | 83 | 91 | 101 | 111 | 121 | 131 | 200 |
| | | | | | | | | | | |
| 0 | 40 | 58 | 70 | 78 | 85 | 95 | 105 | 115 | 125 | 200 |
| | | | | | | | | | | |
| 0 | 34 | 51 | 65 | 72 | 78 | 88 | 98 | 108 | 118 | 198 |
| | | | | | | | | | | |
| 0 | 29 | 45 | 59 | 66 | 72 | 82 | 92 | 102 | 112 | 193 |
| | | | | | | | | | | |
| 0 | 20 | 39 | 53 | 60 | 66 | 76 | 86 | 96 | 106 | 188 |
| | | | | | | | | | | |
| 0 | 18 | 32 | 47 | 54 | 60 | 70 | 80 | 90 | 100 | 183 |
| | | | | | | | | | | |
| 0 | 10 | 26 | 40 | 47 | 54 | 64 | 74 | 84 | 94 | 178 |
| | | | | | | | | | | |
| 0 | 0 | 20 | 31 | 39 | 47 | 57 | 67 | 77 | 87 | 173 |
| | | | | | | | | | | |
| 0 | 0 | 12 | 23 | 32 | 41 | 51 | 61 | 71 | 81 | 168 |
| | | | | | | | | | | |
| 0 | 0 | 0 | 15 | 25 | 35 | 45 | 55 | 65 | 75 | 163 |
| | | | | | | | | | | |
| 0 | 0 | 0 | 4 | 17 | 29 | 39 | 49 | 59 | 69 | 158 |
| | | | | | | | | | | |
| 0 | 0 | 0 | 0 | 12 | 23 | 33 | 43 | 53 | 63 | 153 |
| | | | | | | | | | | |
| 0 | 0 | 0 | 0 | 1 | 16 | 26 | 36 | 46 | 56 | 148 |
| | | | | | | | | | | |
| 0 | 0 | 0 | 0 | 0 | 10 | 15 | 20 | 30 | 45 | 129 |
| | | | | | | | | | | |
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 20 | 104 |
+---+----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
Table 57: CELT Static Allocation Table
The maximum allocation vector is an approximation of the maximum
space that can be used by each band for a given mode. The value is
approximate because the shape encoding is variable rate (due to
entropy coding of splitting parameters). Setting the maximum too low
reduces the maximum achievable quality in a band while setting it too
high may result in waste: bitstream capacity available at the end of
the frame that cannot be put to any use. The maximums specified by
the codec reflect the average maximum. In the reference
implementation, the maximums in bits/sample are precomputed in a
static table (see cache_caps50[] in static_modes_float.h) for each
band, for each value of LM, and for both mono and stereo.
Implementations are expected to simply use the same table data, but
the procedure for generating this table is included in rate.c as part
of compute_pulse_cache().
To convert the values in cache.caps into the actual maximums: first,
set nbBands to the maximum number of bands for this mode, and stereo
to zero if stereo is not in use and one otherwise. For each band,
set N to the number of MDCT bins covered by the band (for one
channel), set LM to the shift value for the frame size. Then, set i
to nbBands*(2*LM+stereo). Next, set the maximum for the band to the
i-th index of cache.caps + 64 and multiply by the number of channels
in the current frame (one or two) and by N, then divide the result by
4 using integer division. The resulting vector will be called cap[].
The elements fit in signed 16-bit integers but do not fit in 8 bits.
This procedure is implemented in the reference in the function
init_caps() in celt.c.
The band boosts are represented by a series of binary symbols that
are entropy coded with very low probability. Each band can
potentially be boosted multiple times, subject to the frame actually
having enough room to obey the boost and having enough room to code
the boost symbol. The default coding cost for a boost starts out at
six bits (probability p=1/64), but subsequent boosts in a band cost
only a single bit and every time a band is boosted the initial cost
is reduced (down to a minimum of two bits, or p=1/4). Since the
initial cost of coding a boost is 6 bits, the coding cost of the
boost symbols when completely unused is 0.48 bits/frame for a 21 band
mode (21*-log2(1-1/2**6)).
To decode the band boosts: First, set 'dynalloc_logp' to 6, the
initial amount of storage required to signal a boost in bits,
'total_bits' to the size of the frame in 8th bits, 'total_boost' to
zero, and 'tell' to the total number of 8th bits decoded so far. For
each band from the coding start (0 normally, but 17 in Hybrid mode)
to the coding end (which changes depending on the signaled
bandwidth), the boost quanta in units of 1/8 bit is calculated as
quanta = min(8*N, max(48, N)). This represents a boost step size of
six bits, subject to a lower limit of 1/8th bit/sample and an upper
limit of 1 bit/sample. Set 'boost' to zero and 'dynalloc_loop_logp'
to dynalloc_logp. While dynalloc_loop_log (the current worst case
symbol cost) in 8th bits plus tell is less than total_bits plus
total_boost and boost is less than cap[] for this band: Decode a bit
from the bitstream with dynalloc_loop_logp as the cost of a one and
update tell to reflect the current used capacity. If the decoded
value is zero break the loop. Otherwise, add quanta to boost and
total_boost, subtract quanta from total_bits, and set
dynalloc_loop_log to 1. When the loop finishes 'boost' contains the
bit allocation boost for this band. If boost is non-zero and
dynalloc_logp is greater than 2, decrease dynalloc_logp. Once this
process has been executed on all bands, the band boosts have been
decoded. This procedure is implemented around line 2474 of celt.c.
At very low rates, it is possible that there won't be enough
available space to execute the inner loop even once. In these cases,
band boost is not possible, but its overhead is completely
eliminated. Because of the high cost of band boost when activated, a
reasonable encoder should not be using it at very low rates. The
reference implements its dynalloc decision logic around line 1304 of
celt.c.
The allocation trim is an integer value from 0-10. The default value
of 5 indicates no trim. The trim parameter is entropy coded in order
to lower the coding cost of less extreme adjustments. Values lower
than 5 bias the allocation towards lower frequencies and values above
5 bias it towards higher frequencies. Like other signaled
parameters, signaling of the trim is gated so that it is not included
if there is insufficient space available in the bitstream. To decode
the trim, first set the trim value to 5, then if and only if the
count of decoded 8th bits so far (ec_tell_frac) plus 48 (6 bits) is
less than or equal to the total frame size in 8th bits minus
total_boost (a product of the above band boost procedure), decode the
trim value using the PDF in Table 58.
+--------------------------------------------+
| PDF |
+--------------------------------------------+
| {2, 2, 5, 10, 22, 46, 22, 10, 5, 2, 2}/128 |
+--------------------------------------------+
Table 58: PDF for the Trim
For 10 ms and 20 ms frames using short blocks and that have at least
LM+2 bits left prior to the allocation process, one anti-collapse bit
is reserved in the allocation process so it can be decoded later.
Following the anti-collapse reservation, one bit is reserved for skip
if available.
For stereo frames, bits are reserved for intensity stereo and for
dual stereo. Intensity stereo requires ilog2(end-start) bits. Those
bits are reserved if there are enough bits left. Following this, one
bit is reserved for dual stereo if available.
The allocation computation begins by setting up some initial
conditions. 'total' is set to the remaining available 8th bits,
computed by taking the size of the coded frame times 8 and
subtracting ec_tell_frac(). From this value, one (8th bit) is
subtracted to ensure that the resulting allocation will be
conservative. 'anti_collapse_rsv' is set to 8 (8th bits) if and only
if the frame is a transient, LM is greater than 1, and total is
greater than or equal to (LM+2) * 8. Total is then decremented by
anti_collapse_rsv and clamped to be equal to or greater than zero.
'skip_rsv' is set to 8 (8th bits) if total is greater than 8,
otherwise it is zero. Total is then decremented by skip_rsv. This
reserves space for the final skipping flag.
If the current frame is stereo, intensity_rsv is set to the
conservative log2 in 8th bits of the number of coded bands for this
frame (given by the table LOG2_FRAC_TABLE in rate.c). If
intensity_rsv is greater than total, then intensity_rsv is set to
zero. Otherwise, total is decremented by intensity_rsv, and if total
is still greater than 8, dual_stereo_rsv is set to 8 and total is
decremented by dual_stereo_rsv.
The allocation process then computes a vector representing the hard
minimum amounts allocation any band will receive for shape. This
minimum is higher than the technical limit of the PVQ process, but
very low rate allocations produce an excessively sparse spectrum and
these bands are better served by having no allocation at all. For
each coded band, set thresh[band] to 24 times the number of MDCT bins
in the band and divide by 16. If 8 times the number of channels is
greater, use that instead. This sets the minimum allocation to one
bit per channel or 48 128th bits per MDCT bin, whichever is greater.
The band-size dependent part of this value is not scaled by the
channel count, because at the very low rates where this limit is
applicable there will usually be no bits allocated to the side.
The previously decoded allocation trim is used to derive a vector of
per-band adjustments, 'trim_offsets[]'. For each coded band take the
alloc_trim and subtract 5 and LM. Then, multiply the result by the
number of channels, the number of MDCT bins in the shortest frame
size for this mode, the number of remaining bands, 2**LM, and 8.
Next, divide this value by 64. Finally, if the number of MDCT bins
in the band per channel is only one, 8 times the number of channels
is subtracted in order to diminish the allocation by one bit, because
width 1 bands receive greater benefit from the coarse energy coding.
4.3.4. Shape Decoding
In each band, the normalized "shape" is encoded using Pyramid Vector
Quantizer.
In the simplest case, the number of bits allocated in Section 4.3.3
is converted to a number of pulses as described by Section 4.3.4.1.
Knowing the number of pulses and the number of samples in the band,
the decoder calculates the size of the codebook as detailed in
Section 4.3.4.2. The size is used to decode an unsigned integer
(uniform probability model), which is the codeword index. This index
is converted into the corresponding vector as explained in
Section 4.3.4.2. This vector is then scaled to unit norm.
4.3.4.1. Bits to Pulses
Although the allocation is performed in 1/8th bit units, the
quantization requires an integer number of pulses K. To do this, the
encoder searches for the value of K that produces the number of bits
nearest to the allocated value (rounding down if exactly halfway
between two values), not to exceed the total number of bits
available. For efficiency reasons, the search is performed against a
precomputed allocation table that only permits some K values for each
N. The number of codebook entries can be computed as explained in
Section 4.3.4.2. The difference between the number of bits allocated
and the number of bits used is accumulated to a "balance"
(initialized to zero) that helps adjust the allocation for the next
bands. One third of the balance is applied to the bit allocation of
each band to help achieve the target allocation. The only exceptions
are the band before the last and the last band, for which half the
balance and the whole balance are applied, respectively.
4.3.4.2. PVQ Decoding
Decoding of PVQ vectors is implemented in decode_pulses() (cwrs.c).
The unique codeword index is decoded as a uniformly distributed
integer value between 0 and V(N,K)-1, where V(N,K) is the number of
possible combinations of K pulses in N samples. The index is then
converted to a vector in the same way specified in [PVQ]. The
indexing is based on the calculation of V(N,K) (denoted N(L,K) in
[PVQ]).
The number of combinations can be computed recursively as V(N,K) =
V(N-1,K) + V(N,K-1) + V(N-1,K-1), with V(N,0) = 1 and V(0,K) = 0, K
!= 0. There are many different ways to compute V(N,K), including
precomputed tables and direct use of the recursive formulation. The
reference implementation applies the recursive formulation one line
(or column) at a time to save on memory use, along with an alternate,
univariate recurrence to initialize an arbitrary line, and direct
polynomial solutions for small N. All of these methods are
equivalent, and have different trade-offs in speed, memory usage, and
code size. Implementations MAY use any methods they like, as long as
they are equivalent to the mathematical definition.
The decoded vector X is recovered as follows. Let i be the index
decoded with the procedure in Section 4.1.5 with ft = V(N,K), so that
0 <= i < V(N,K). Let k = K. Then, for j = 0 to (N - 1), inclusive,
do:
1. Let p = (V(N-j-1,k) + V(N-j,k))/2.
2. If i < p, then let sgn = 1, else let sgn = -1 and set i = i - p.
3. Let k0 = k and set p = p - V(N-j-1,k).
4. While p > i, set k = k - 1 and p = p - V(N-j-1,k).
5. Set X[j] = sgn*(k0 - k) and i = i - p.
The decoded vector X is then normalized such that its L2-norm equals
one.
4.3.4.3. Spreading
The normalized vector decoded in Section 4.3.4.2 is then rotated for
the purpose of avoiding tonal artifacts. The rotation gain is equal
to
g_r = N / (N + f_r*K)
where N is the number of dimensions, K is the number of pulses, and
f_r depends on the value of the "spread" parameter in the bitstream.
+--------------+------------------------+
| Spread value | f_r |
+--------------+------------------------+
| 0 | infinite (no rotation) |
| | |
| 1 | 15 |
| | |
| 2 | 10 |
| | |
| 3 | 5 |
+--------------+------------------------+
Table 59: Spreading Values
The rotation angle is then calculated as
2
pi * g_r
theta = ----------
4
A 2-D rotation R(i,j) between points x_i and x_j is defined as:
x_i' = cos(theta)*x_i + sin(theta)*x_j
x_j' = -sin(theta)*x_i + cos(theta)*x_j
An N-D rotation is then achieved by applying a series of 2-D
rotations back and forth, in the following order: R(x_1, x_2), R(x_2,
x_3), ..., R(x_N-2, X_N-1), R(x_N-1, X_N), R(x_N-2, X_N-1), ...,
R(x_1, x_2).
If the decoded vector represents more than one time block, then this
spreading process is applied separately on each time block. Also, if
each block represents 8 samples or more, then another N-D rotation,
by (pi/2-theta), is applied _before_ the rotation described above.
This extra rotation is applied in an interleaved manner with a stride
equal to round(sqrt(N/nb_blocks)), i.e., it is applied independently
for each set of sample S_k = {stride*n + k}, n=0..N/stride-1.
4.3.4.4. Split Decoding
To avoid the need for multi-precision calculations when decoding PVQ
codevectors, the maximum size allowed for codebooks is 32 bits. When
larger codebooks are needed, the vector is instead split in two sub-
vectors of size N/2. A quantized gain parameter with precision
derived from the current allocation is entropy coded to represent the
relative gains of each side of the split, and the entire decoding
process is recursively applied. Multiple levels of splitting may be
applied up to a limit of LM+1 splits. The same recursive mechanism
is applied for the joint coding of stereo audio.
4.3.4.5. Time-Frequency Change
The time-frequency (TF) parameters are used to control the time-
frequency resolution trade-off in each coded band. For each band,
there are two possible TF choices. For the first band coded, the PDF
is {3, 1}/4 for frames marked as transient and {15, 1}/16 for the
other frames. For subsequent bands, the TF choice is coded relative
to the previous TF choice with probability {15, 1}/16 for transient
frames and {31, 1}/32 otherwise. The mapping between the decoded TF
choices and the adjustment in TF resolution is shown in the tables
below.
+-----------------+---+----+
| Frame size (ms) | 0 | 1 |
+-----------------+---+----+
| 2.5 | 0 | -1 |
| | | |
| 5 | 0 | -1 |
| | | |
| 10 | 0 | -2 |
| | | |
| 20 | 0 | -2 |
+-----------------+---+----+
Table 60: TF Adjustments for Non-transient Frames and tf_select=0
+-----------------+---+----+
| Frame size (ms) | 0 | 1 |
+-----------------+---+----+
| 2.5 | 0 | -1 |
| | | |
| 5 | 0 | -2 |
| | | |
| 10 | 0 | -3 |
| | | |
| 20 | 0 | -3 |
+-----------------+---+----+
Table 61: TF Adjustments for Non-transient Frames and tf_select=1
+-----------------+---+----+
| Frame size (ms) | 0 | 1 |
+-----------------+---+----+
| 2.5 | 0 | -1 |
| | | |
| 5 | 1 | 0 |
| | | |
| 10 | 2 | 0 |
| | | |
| 20 | 3 | 0 |
+-----------------+---+----+
Table 62: TF Adjustments for Transient Frames and tf_select=0
+-----------------+---+----+
| Frame size (ms) | 0 | 1 |
+-----------------+---+----+
| 2.5 | 0 | -1 |
| | | |
| 5 | 1 | -1 |
| | | |
| 10 | 1 | -1 |
| | | |
| 20 | 1 | -1 |
+-----------------+---+----+
Table 63: TF Adjustments for Transient Frames and tf_select=1
A negative TF adjustment means that the temporal resolution is
increased, while a positive TF adjustment means that the frequency
resolution is increased. Changes in TF resolution are implemented
using the Hadamard transform [HADAMARD]. To increase the time
resolution by N, N "levels" of the Hadamard transform are applied to
the decoded vector for each interleaved MDCT vector. To increase the
frequency resolution (assumes a transient frame), then N levels of
the Hadamard transform are applied _across_ the interleaved MDCT
vector. In the case of increased time resolution, the decoder uses
the "sequency order" because the input vector is sorted in time.
4.3.5. Anti-collapse Processing
The anti-collapse feature is designed to avoid the situation where
the use of multiple short MDCTs causes the energy in one or more of
the MDCTs to be zero for some bands, causing unpleasant artifacts.
When the frame has the transient bit set, an anti-collapse bit is
decoded. When anti-collapse is set, the energy in each small MDCT is
prevented from collapsing to zero. For each band of each MDCT where
a collapse is detected, a pseudo-random signal is inserted with an
energy corresponding to the minimum energy over the two previous
frames. A renormalization step is then required to ensure that the
anti-collapse step did not alter the energy preservation property.
4.3.6. Denormalization
Just as each band was normalized in the encoder, the last step of the
decoder before the inverse MDCT is to denormalize the bands. Each
decoded normalized band is multiplied by the square root of the
decoded energy. This is done by denormalise_bands() (bands.c).
4.3.7. Inverse MDCT
The inverse MDCT implementation has no special characteristics. The
input is N frequency-domain samples and the output is 2*N time-domain
samples, while scaling by 1/2. A "low-overlap" window reduces the
algorithmic delay. It is derived from a basic (full-overlap) 240-
sample version of the window used by the Vorbis codec:
2
/ /pi /pi n + 1/2\ \ \
W(n) = |sin|-- * sin|-- * -------| | |
\ \2 \2 L / / /
The low-overlap window is created by zero-padding the basic window
and inserting ones in the middle, such that the resulting window
still satisfies power complementarity [PRINCEN86]. The IMDCT and
windowing are performed by mdct_backward (mdct.c).
4.3.7.1. Post-Filter
The output of the inverse MDCT (after weighted overlap-add) is sent
to the post-filter. Although the post-filter is applied at the end,
the post-filter parameters are encoded at the beginning, just after
the silence flag. The post-filter can be switched on or off using
one bit (logp=1). If the post-filter is enabled, then the octave is
decoded as an integer value between 0 and 6 of uniform probability.
Once the octave is known, the fine pitch within the octave is decoded
using 4+octave raw bits. The final pitch period is equal to
(16<<octave)+fine_pitch-1 so it is bounded between 15 and 1022,
inclusively. Next, the gain is decoded as three raw bits and is
equal to G=3*(int_gain+1)/32. The set of post-filter taps is decoded
last, using a pdf equal to {2, 1, 1}/4. Tapset zero corresponds to
the filter coefficients g0 = 0.3066406250, g1 = 0.2170410156, g2 =
0.1296386719. Tapset one corresponds to the filter coefficients g0 =
0.4638671875, g1 = 0.2680664062, g2 = 0, and tapset two uses filter
coefficients g0 = 0.7998046875, g1 = 0.1000976562, g2 = 0.
The post-filter response is thus computed as:
y(n) = x(n) + G*(g0*y(n-T) + g1*(y(n-T+1)+y(n-T+1))
+ g2*(y(n-T+2)+y(n-T+2)))
During a transition between different gains, a smooth transition is
calculated using the square of the MDCT window. It is important that
values of y(n) be interpolated one at a time such that the past value
of y(n) used is interpolated.
4.3.7.2. De-emphasis
After the post-filter, the signal is de-emphasized using the inverse
of the pre-emphasis filter used in the encoder:
1 1
---- = ---------------
A(z) -1
1 - alpha_p*z
where alpha_p=0.8500061035.
4.4. Packet Loss Concealment (PLC)
Packet Loss Concealment (PLC) is an optional decoder-side feature
that SHOULD be included when receiving from an unreliable channel.
Because PLC is not part of the bitstream, there are many acceptable
ways to implement PLC with different complexity/quality trade-offs.
The PLC in the reference implementation depends on the mode of last
packet received. In CELT mode, the PLC finds a periodicity in the
decoded signal and repeats the windowed waveform using the pitch
offset. The windowed waveform is overlapped in such a way as to
preserve the time-domain aliasing cancellation with the previous
frame and the next frame. This is implemented in celt_decode_lost()
(mdct.c). In SILK mode, the PLC uses LPC extrapolation from the
previous frame, implemented in silk_PLC() (PLC.c).
4.4.1. Clock Drift Compensation
Clock drift refers to the gradual desynchronization of two endpoints
whose sample clocks run at different frequencies while they are
streaming live audio. Differences in clock frequencies are generally
attributable to manufacturing variation in the endpoints' clock
hardware. For long-lived streams, the time difference between sender
and receiver can grow without bound.
When the sender's clock runs slower than the receiver's, the effect
is similar to packet loss: too few packets are received. The
receiver can distinguish between drift and loss if the transport
provides packet timestamps. A receiver for live streams SHOULD
conceal the effects of drift, and it MAY do so by invoking the PLC.
When the sender's clock runs faster than the receiver's, too many
packets will be received. The receiver MAY respond by skipping any
packet (i.e., not submitting the packet for decoding). This is
likely to produce a less severe artifact than if the frame were
dropped after decoding.
A decoder MAY employ a more sophisticated drift compensation method.
For example, the NetEQ component [GOOGLE-NETEQ] of the Google WebRTC
codebase [GOOGLE-WEBRTC] compensates for drift by adding or removing
one period when the signal is highly periodic. The reference
implementation of Opus allows a caller to learn whether the current
frame's signal is highly periodic, and if so what the period is,
using the OPUS_GET_PITCH() request.
4.5. Configuration Switching
Switching between the Opus coding modes, audio bandwidths, and
channel counts requires careful consideration to avoid audible
glitches. Switching between any two configurations of the CELT-only
mode, any two configurations of the Hybrid mode, or from WB SILK to
Hybrid mode does not require any special treatment in the decoder, as
the MDCT overlap will smooth the transition. Switching from Hybrid
mode to WB SILK requires adding in the final contents of the CELT
overlap buffer to the first SILK-only packet. This can be done by
decoding a 2.5 ms silence frame with the CELT decoder using the
channel count of the SILK-only packet (and any choice of audio
bandwidth), which will correctly handle the cases when the channel
count changes as well.
When changing the channel count for SILK-only or Hybrid packets, the
encoder can avoid glitches by smoothly varying the stereo width of
the input signal before or after the transition, and it SHOULD do so.
However, other transitions between SILK-only packets or between NB or
MB SILK and Hybrid packets may cause glitches, because neither the
LSF coefficients nor the LTP, LPC, stereo unmixing, and resampler
buffers are available at the new sample rate. These switches SHOULD
be delayed by the encoder until quiet periods or transients, where
the inevitable glitches will be less audible. Additionally, the
bitstream MAY include redundant side information ("redundancy"), in
the form of additional CELT frames embedded in each of the Opus
frames around the transition.
The other transitions that cannot be easily handled are those where
the lower frequencies switch between the SILK LP-based model and the
CELT MDCT model. However, an encoder may not have an opportunity to
delay such a switch to a convenient point. For example, if the
content switches from speech to music, and the encoder does not have
enough latency in its analysis to detect this in advance, there may
be no convenient silence period during which to make the transition
for quite some time. To avoid or reduce glitches during these
problematic mode transitions, and between audio bandwidth changes in
the SILK-only modes, transitions MAY include redundant side
information ("redundancy"), in the form of an additional CELT frame
embedded in the Opus frame.
A transition between coding the lower frequencies with the LP model
and the MDCT model or a transition that involves changing the SILK
bandwidth is only normatively specified when it includes redundancy.
For those without redundancy, it is RECOMMENDED that the decoder use
a concealment technique (e.g., make use of a PLC algorithm) to "fill
in" the gap or discontinuity caused by the mode transition.
Therefore, PLC MUST NOT be applied during any normative transition,
i.e., when
o A packet includes redundancy for this transition (as described
below),
o The transition is between any WB SILK packet and any Hybrid
packet, or vice versa,
o The transition is between any two Hybrid mode packets, or
o The transition is between any two CELT mode packets,
unless there is actual packet loss.
4.5.1. Transition Side Information (Redundancy)
Transitions with side information include an extra 5 ms "redundant"
CELT frame within the Opus frame. This frame is designed to fill in
the gap or discontinuity in the different layers without requiring
the decoder to conceal it. For transitions from CELT-only to SILK-
only or Hybrid, the redundant frame is inserted in the first Opus
frame after the transition (i.e., the first SILK-only or Hybrid
frame). For transitions from SILK-only or Hybrid to CELT-only, the
redundant frame is inserted in the last Opus frame before the
transition (i.e., the last SILK-only or Hybrid frame).
4.5.1.1. Redundancy Flag
The presence of redundancy is signaled in all SILK-only and Hybrid
frames, not just those involved in a mode transition. This allows
the frames to be decoded correctly even if an adjacent frame is lost.
For SILK-only frames, this signaling is implicit, based on the size
of the Opus frame and the number of bits consumed decoding the SILK
portion of it. After decoding the SILK portion of the Opus frame,
the decoder uses ec_tell() (see Section 4.1.6.1) to check if there
are at least 17 bits remaining. If so, then the frame contains
redundancy.
For Hybrid frames, this signaling is explicit. After decoding the
SILK portion of the Opus frame, the decoder uses ec_tell() (see
Section 4.1.6.1) to ensure there are at least 37 bits remaining. If
so, it reads a symbol with the PDF in Table 64, and if the value is
1, then the frame contains redundancy. Otherwise (if there were
fewer than 37 bits left or the value was 0), the frame does not
contain redundancy.
+----------------+
| PDF |
+----------------+
| {4095, 1}/4096 |
+----------------+
Table 64: Redundancy Flag PDF
4.5.1.2. Redundancy Position Flag
Since the current frame is a SILK-only or a Hybrid frame, it must be
at least 10 ms. Therefore, it needs an additional flag to indicate
whether the redundant 5 ms CELT frame should be mixed into the
beginning of the current frame, or the end. After determining that a
frame contains redundancy, the decoder reads a 1 bit symbol with a
uniform PDF (Table 65).
+----------+
| PDF |
+----------+
| {1, 1}/2 |
+----------+
Table 65: Redundancy Position PDF
If the value is zero, this is the first frame in the transition, and
the redundancy belongs at the end. If the value is one, this is the
second frame in the transition, and the redundancy belongs at the
beginning. There is no way to specify that an Opus frame contains
separate redundant CELT frames at both the beginning and the end.
4.5.1.3. Redundancy Size
Unlike the CELT portion of a Hybrid frame, the redundant CELT frame
does not use the same entropy coder state as the rest of the Opus
frame, because this would break the CELT bit allocation mechanism in
Hybrid frames. Thus, a redundant CELT frame always starts and ends
on a byte boundary, even in SILK-only frames, where this is not
strictly necessary.
For SILK-only frames, the number of bytes in the redundant CELT frame
is simply the number of whole bytes remaining, which must be at least
2, due to the space check in Section 4.5.1.1. For Hybrid frames, the
number of bytes is equal to 2, plus a decoded unsigned integer less
than 256 (see Section 4.1.5). This may be more than the number of
whole bytes remaining in the Opus frame, in which case the frame is
invalid. However, a decoder is not required to ignore the entire
frame, as this may be the result of a bit error that desynchronized
the range coder. There may still be useful data before the error,
and a decoder MAY keep any audio decoded so far instead of invoking
the PLC, but it is RECOMMENDED that the decoder stop decoding and
discard the rest of the current Opus frame.
It would have been possible to avoid these invalid states in the
design of Opus by limiting the range of the explicit length decoded
from Hybrid frames by the actual number of whole bytes remaining.
However, this would require an encoder to determine the rate
allocation for the MDCT layer up front, before it began encoding that
layer. By allowing some invalid sizes, the encoder is able to defer
that decision until much later. When encoding Hybrid frames that do
not include redundancy, the encoder must still decide up front if it
wishes to use the minimum 37 bits required to trigger encoding of the
redundancy flag, but this is a much looser restriction.
After determining the size of the redundant CELT frame, the decoder
reduces the size of the buffer currently in use by the range coder by
that amount. The MDCT layer reads any raw bits from the end of this
reduced buffer, and all calculations of the number of bits remaining
in the buffer must be done using this new, reduced size, rather than
the original size of the Opus frame.
4.5.1.4. Decoding the Redundancy
The redundant frame is decoded like any other CELT-only frame, with
the exception that it does not contain a TOC byte. The frame size is
fixed at 5 ms, the channel count is set to that of the current frame,
and the audio bandwidth is also set to that of the current frame,
with the exception that for MB SILK frames, it is set to WB.
If the redundancy belongs at the beginning (in a CELT-only to SILK-
only or Hybrid transition), the final reconstructed output uses the
first 2.5 ms of audio output by the decoder for the redundant frame
as is, discarding the corresponding output from the SILK-only or
Hybrid portion of the frame. The remaining 2.5 ms is cross-lapped
with the decoded SILK/Hybrid signal using the CELT's power-
complementary MDCT window to ensure a smooth transition.
If the redundancy belongs at the end (in a SILK-only or Hybrid to
CELT-only transition), only the second half (2.5 ms) of the audio
output by the decoder for the redundant frame is used. In that case,
the second half of the redundant frame is cross-lapped with the end
of the SILK/Hybrid signal, again using CELT's power-complementary
MDCT window to ensure a smooth transition.
4.5.2. State Reset
When a transition occurs, the state of the SILK or the CELT decoder
(or both) may need to be reset before decoding a frame in the new
mode. This avoids reusing "out of date" memory, which may not have
been updated in some time or may not be in a well-defined state due
to, e.g., PLC. The SILK state is reset before every SILK-only or
Hybrid frame where the previous frame was CELT-only. The CELT state
is reset every time the operating mode changes and the new mode is
either Hybrid or CELT-only, except when the transition uses
redundancy as described above. When switching from SILK-only or
Hybrid to CELT-only with redundancy, the CELT state is reset before
decoding the redundant CELT frame embedded in the SILK-only or Hybrid
frame, but it is not reset before decoding the following CELT-only
frame. When switching from CELT-only mode to SILK-only or Hybrid
mode with redundancy, the CELT decoder is not reset for decoding the
redundant CELT frame.
4.5.3. Summary of Transitions
Figure 18 illustrates all of the normative transitions involving a
mode change, an audio bandwidth change, or both. Each one uses an S,
H, or C to represent an Opus frame in the corresponding mode. In
addition, an R indicates the presence of redundancy in the Opus frame
with which it is cross-lapped. Its location in the first or last
5 ms is assumed to correspond to whether it is the frame before or
after the transition. Other uses of redundancy are non-normative.
Finally, a c indicates the contents of the CELT overlap buffer after
the previously decoded frame (i.e., as extracted by decoding a
silence frame).
SILK to SILK with Redundancy: S -> S -> S
&
!R -> R
&
;S -> S -> S
NB or MB SILK to Hybrid with Redundancy: S -> S -> S
&
!R ->;H -> H -> H
WB SILK to Hybrid: S -> S -> S ->!H -> H -> H
SILK to CELT with Redundancy: S -> S -> S
&
!R -> C -> C -> C
Hybrid to NB or MB SILK with Redundancy: H -> H -> H
&
!R -> R
&
;S -> S -> S
Hybrid to WB SILK: H -> H -> H -> c
\ +
> S -> S -> S
Hybrid to CELT with Redundancy: H -> H -> H
&
!R -> C -> C -> C
CELT to SILK with Redundancy: C -> C -> C -> R
&
;S -> S -> S
CELT to Hybrid with Redundancy: C -> C -> C -> R
&
|H -> H -> H
Key:
S SILK-only frame ; SILK decoder reset
H Hybrid frame | CELT and SILK decoder resets
C CELT-only frame ! CELT decoder reset
c CELT overlap + Direct mixing
R Redundant CELT frame & Windowed cross-lap
Figure 18: Normative Transitions
The first two and the last two Opus frames in each example are
illustrative, i.e., there is no requirement that a stream remain in
the same configuration for three consecutive frames before or after a
switch.
The behavior of transitions without redundancy where PLC is allowed
is non-normative. An encoder might still wish to use these
transitions if, for example, it doesn't want to add the extra bitrate
required for redundancy or if it makes a decision to switch after it
has already transmitted the frame that would have had to contain the
redundancy. Figure 19 illustrates the recommended cross-lapping and
decoder resets for these transitions.
SILK to SILK (audio bandwidth change): S -> S -> S ;S -> S -> S
NB or MB SILK to Hybrid: S -> S -> S |H -> H -> H
SILK to CELT without Redundancy: S -> S -> S -> P
&
!C -> C -> C
Hybrid to NB or MB SILK: H -> H -> H -> c
+
;S -> S -> S
Hybrid to CELT without Redundancy: H -> H -> H -> P
&
!C -> C -> C
CELT to SILK without Redundancy: C -> C -> C -> P
&
;S -> S -> S
CELT to Hybrid without Redundancy: C -> C -> C -> P
&
|H -> H -> H
Key:
S SILK-only frame ; SILK decoder reset
H Hybrid frame | CELT and SILK decoder resets
C CELT-only frame ! CELT decoder reset
c CELT overlap + Direct mixing
P Packet Loss Concealment & Windowed cross-lap
Figure 19: Recommended Non-Normative Transitions
Encoders SHOULD NOT use other transitions, e.g., those that involve
redundancy in ways not illustrated in Figure 18.
5. Opus Encoder
Just like the decoder, the Opus encoder also normally consists of two
main blocks: the SILK encoder and the CELT encoder. However, unlike
the case of the decoder, a valid (though potentially suboptimal) Opus
encoder is not required to support all modes and may thus only
include a SILK encoder module or a CELT encoder module. The output
bitstream of the Opus encoding contains bits from the SILK and CELT
encoders, though these are not separable due to the use of a range
coder. A block diagram of the encoder is illustrated below.
+------------+ +---------+
| Sample | | SILK |------+
+->| Rate |--->| Encoder | V
+-----------+ | | Conversion | | | +---------+
| Optional | | +------------+ +---------+ | Range |
->| High-pass |--+ | Encoder |---->
| Filter | | +--------------+ +---------+ | | Bit-
+-----------+ | | Delay | | CELT | +---------+ stream
+->| Compensation |->| Encoder | ^
| | | |------+
+--------------+ +---------+
Figure 20: Opus Encoder
For a normal encoder where both the SILK and the CELT modules are
included, an optimal encoder should select which coding mode to use
at run-time depending on the conditions. In the reference
implementation, the frame size is selected by the application, but
the other configuration parameters (number of channels, bandwidth,
mode) are automatically selected (unless explicitly overridden by the
application) depending on the following:
o Requested bitrate
o Input sampling rate
o Type of signal (speech vs. music)
o Frame size in use
The type of signal currently needs to be provided by the application
(though it can be changed in real-time). An Opus encoder
implementation could also do automatic detection, but since Opus is
an interactive codec, such an implementation would likely have to
either delay the signal (for non-interactive applications) or delay
the mode switching decisions (for interactive applications).
When the encoder is configured for voice over IP applications, the
input signal is filtered by a high-pass filter to remove the lowest
part of the spectrum that contains little speech energy and may
contain background noise. This is a second order Auto Regressive
Moving Average (i.e., with poles and zeros) filter with a cut-off
frequency around 50 Hz. In the future, a music detector may also be
used to lower the cut-off frequency when the input signal is detected
to be music rather than speech.
5.1. Range Encoder
The range coder acts as the bit-packer for Opus. It is used in three
different ways: to encode
o Entropy-coded symbols with a fixed probability model using
ec_encode() (entenc.c),
o Integers from 0 to (2**M - 1) using ec_enc_uint() or ec_enc_bits()
(entenc.c),
o Integers from 0 to (ft - 1) (where ft is not a power of two) using
ec_enc_uint() (entenc.c).
The range encoder maintains an internal state vector composed of the
four-tuple (val, rng, rem, ext) representing the low end of the
current range, the size of the current range, a single buffered
output byte, and a count of additional carry-propagating output
bytes. Both val and rng are 32-bit unsigned integer values, rem is a
byte value or less than 255 or the special value -1, and ext is an
unsigned integer with at least 11 bits. This state vector is
initialized at the start of each frame to the value
(0, 2**31, -1, 0). After encoding a sequence of symbols, the value
of rng in the encoder should exactly match the value of rng in the
decoder after decoding the same sequence of symbols. This is a
powerful tool for detecting errors in either an encoder or decoder
implementation. The value of val, on the other hand, represents
different things in the encoder and decoder, and is not expected to
match.
The decoder has no analog for rem and ext. These are used to perform
carry propagation in the renormalization loop below. Each iteration
of this loop produces 9 bits of output, consisting of 8 data bits and
a carry flag. The encoder cannot determine the final value of the
output bytes until it propagates these carry flags. Therefore, the
reference implementation buffers a single non-propagating output byte
(i.e., one less than 255) in rem and keeps a count of additional
propagating (i.e., 255) output bytes in ext. An implementation may
choose to use any mathematically equivalent scheme to perform carry
propagation.
5.1.1. Encoding Symbols
The main encoding function is ec_encode() (entenc.c), which encodes
symbol k in the current context using the same three-tuple
(fl[k], fh[k], ft) as the decoder to describe the range of the symbol
(see Section 4.1).
ec_encode() updates the state of the encoder as follows. If fl[k] is
greater than zero, then
rng
val = val + rng - --- * (ft - fl)
ft
rng
rng = --- * (fh - fl)
ft
Otherwise, val is unchanged and
rng
rng = rng - --- * (fh - fl)
ft
The divisions here are integer division.
5.1.1.1. Renormalization
After this update, the range is normalized using a procedure very
similar to that of Section 4.1.2.1, implemented by ec_enc_normalize()
(entenc.c). The following process is repeated until rng > 2**23.
First, the top 9 bits of val, (val>>23), are sent to the carry
buffer, described in Section 5.1.1.2. Then, the encoder sets
val = (val<<8) & 0x7FFFFFFF
rng = rng<<8
5.1.1.2. Carry Propagation and Output Buffering
The function ec_enc_carry_out() (entenc.c) implements carry
propagation and output buffering. It takes, as input, a 9-bit
unsigned value, c, consisting of 8 data bits and an additional carry
bit. If c is equal to the value 255, then ext is simply incremented,
and no other state updates are performed. Otherwise, let b = (c>>8)
be the carry bit. Then,
o If the buffered byte rem contains a value other than -1, the
encoder outputs the byte (rem + b). Otherwise, if rem is -1, no
byte is output.
o If ext is non-zero, then the encoder outputs ext bytes -- all with
a value of 0 if b is set, or 255 if b is unset -- and sets ext to
0.
o rem is set to the 8 data bits:
rem = c & 255
5.1.2. Alternate Encoding Methods
The reference implementation uses three additional encoding methods
that are exactly equivalent to the above, but make assumptions and
simplifications that allow for a more efficient implementation.
5.1.2.1. ec_encode_bin()
The first is ec_encode_bin() (entenc.c), defined using the parameter
ftb instead of ft. It is mathematically equivalent to calling
ec_encode() with ft = (1<<ftb), but it avoids using division.
5.1.2.2. ec_enc_bit_logp()
The next is ec_enc_bit_logp() (entenc.c), which encodes a single
binary symbol. The context is described by a single parameter, logp,
which is the absolute value of the base-2 logarithm of the
probability of a "1". It is mathematically equivalent to calling
ec_encode() with the 3-tuple (fl[k] = 0, fh[k] = (1<<logp) - 1,
ft = (1<<logp)) if k is 0 and with (fl[k] = (1<<logp) - 1,
fh[k] = ft = (1<<logp)) if k is 1. The implementation requires no
multiplications or divisions.
5.1.2.3. ec_enc_icdf()
The last is ec_enc_icdf() (entenc.c), which encodes a single binary
symbol with a table-based context of up to 8 bits. This uses the
same icdf table as ec_dec_icdf() from Section 4.1.3.3. The function
is mathematically equivalent to calling ec_encode() with
fl[k] = (1<<ftb) - icdf[k-1] (or 0 if k == 0), fh[k] = (1<<ftb) -
icdf[k], and ft = (1<<ftb). This only saves a few arithmetic
operations over ec_encode_bin(), but it allows the encoder to use the
same icdf tables as the decoder.
5.1.3. Encoding Raw Bits
The raw bits used by the CELT layer are packed at the end of the
buffer using ec_enc_bits() (entenc.c). Because the raw bits may
continue into the last byte output by the range coder if there is
room in the low-order bits, the encoder must be prepared to merge
these values into a single byte. The procedure in Section 5.1.5 does
this in a way that ensures both the range coded data and the raw bits
can be decoded successfully.
5.1.4. Encoding Uniformly Distributed Integers
The function ec_enc_uint() (entenc.c) encodes one of ft equiprobable
symbols in the range 0 to (ft - 1), inclusive, each with a frequency
of 1, where ft may be as large as (2**32 - 1). Like the decoder (see
Section 4.1.5), it splits up the value into a range coded symbol
representing up to 8 of the high bits, and, if necessary, raw bits
representing the remainder of the value.
ec_enc_uint() takes a two-tuple (t, ft), where t is the unsigned
integer to be encoded, 0 <= t < ft, and ft is not necessarily a power
of two. Let ftb = ilog(ft - 1), i.e., the number of bits required to
store (ft - 1) in two's complement notation. If ftb is 8 or less,
then t is encoded directly using ec_encode() with the three-tuple (t,
t + 1, ft).
If ftb is greater than 8, then the top 8 bits of t are encoded using
the three-tuple (t>>(ftb - 8), (t>>(ftb - 8)) + 1,
((ft - 1)>>(ftb - 8)) + 1), and the remaining bits,
(t & ((1<<(ftb - 8)) - 1), are encoded as raw bits with
ec_enc_bits().
5.1.5. Finalizing the Stream
After all symbols are encoded, the stream must be finalized by
outputting a value inside the current range. Let end be the unsigned
integer in the interval [val, val + rng) with the largest number of
trailing zero bits, b, such that (end + (1<<b) - 1) is also in the
interval [val, val + rng). This choice of end allows the maximum
number of trailing bits to be set to arbitrary values while still
ensuring the range coded part of the buffer can be decoded correctly.
Then, while end is not zero, the top 9 bits of end, i.e., (end>>23),
are passed to the carry buffer in accordance with the procedure in
Section 5.1.1.2, and end is updated via
end = (end<<8) & 0x7FFFFFFF
Finally, if the buffered output byte, rem, is neither zero nor the
special value -1, or the carry count, ext, is greater than zero, then
9 zero bits are sent to the carry buffer to flush it to the output
buffer. When outputting the final byte from the range coder, if it
would overlap any raw bits already packed into the end of the output
buffer, they should be ORed into the same byte. The bit allocation
routines in the CELT layer should ensure that this can be done
without corrupting the range coder data so long as end is chosen as
described above. If there is any space between the end of the range
coder data and the end of the raw bits, it is padded with zero bits.
This entire process is implemented by ec_enc_done() (entenc.c).
5.1.6. Current Bit Usage
The bit allocation routines in Opus need to be able to determine a
conservative upper bound on the number of bits that have been used to
encode the current frame thus far. This drives allocation decisions
and ensures that the range coder and raw bits will not overflow the
output buffer. This is computed in the reference implementation to
whole-bit precision by the function ec_tell() (entcode.h) and to
fractional 1/8th bit precision by the function ec_tell_frac()
(entcode.c). Like all operations in the range coder, it must be
implemented in a bit-exact manner, and it must produce exactly the
same value returned by the same functions in the decoder after
decoding the same symbols.
5.2. SILK Encoder
In many respects, the SILK encoder mirrors the SILK decoder described
in Section 4.2. Details such as the quantization and range coder
tables can be found there, while this section describes the high-
level design choices that were made. The diagram below shows the
basic modules of the SILK encoder.
+----------+ +--------+ +---------+
| Sample | | Stereo | | SILK |
------>| Rate |--->| Mixing |--->| Core |---------->
Input |Conversion| | | | Encoder | Bitstream
+----------+ +--------+ +---------+
Figure 21: SILK Encoder
5.2.1. Sample Rate Conversion
The input signal's sampling rate is adjusted by a sample rate
conversion module so that it matches the SILK internal sampling rate.
The input to the sample rate converter is delayed by a number of
samples depending on the sample rate ratio, such that the overall
delay is constant for all input and output sample rates.
5.2.2. Stereo Mixing
The stereo mixer is only used for stereo input signals. It converts
a stereo left-right signal into an adaptive mid-side representation.
The first step is to compute non-adaptive mid-side signals as half
the sum and difference between left and right signals. The side
signal is then minimized in energy by subtracting a prediction of it
based on the mid signal. This prediction works well when the left
and right signals exhibit linear dependency, for instance, for an
amplitude-panned input signal. Like in the decoder, the prediction
coefficients are linearly interpolated during the first 8 ms of the
frame. The mid signal is always encoded, whereas the residual side
signal is only encoded if it has sufficient energy compared to the
mid signal's energy. If it has not, the "mid_only_flag" is set
without encoding the side signal.
The predictor coefficients are coded regardless of whether the side
signal is encoded. For each frame, two predictor coefficients are
computed, one that predicts between low-passed mid and side channels,
and one that predicts between high-passed mid and side channels. The
low-pass filter is a simple three-tap filter and creates a delay of
one sample. The high-pass filtered signal is the difference between
the mid signal delayed by one sample and the low-passed signal.
Instead of explicitly computing the high-passed signal, it is
computationally more efficient to transform the prediction
coefficients before applying them to the filtered mid signal, as
follows:
pred(n) = LP(n) * w0 + HP(n) * w1
= LP(n) * w0 + (mid(n-1) - LP(n)) * w1
= LP(n) * (w0 - w1) + mid(n-1) * w1
where w0 and w1 are the low-pass and high-pass prediction
coefficients, mid(n-1) is the mid signal delayed by one sample, LP(n)
and HP(n) are the low-passed and high-passed signals and pred(n) is
the prediction signal that is subtracted from the side signal.
5.2.3. SILK Core Encoder
What follows is a description of the core encoder and its components.
For simplicity, the core encoder is referred to simply as the encoder
in the remainder of this section. An overview of the encoder is
given in Figure 22.
+---+
+--------------------------------->| |
+---------+ | +---------+ | |
|Voice | | |LTP |12 | |
+-->|Activity |--+ +----->|Scaling |-----------+---->| |
| |Detection|3 | | |Control |<--+ | | |
| +---------+ | | +---------+ | | | |
| | | +---------+ | | | |
| | | |Gains | | | | |
| | | +-->|Processor|---|---+---|---->| R |
| | | | | |11 | | | | a |
| \/ | | +---------+ | | | | n |
| +---------+ | | +---------+ | | | | g |
| |Pitch | | | |LSF | | | | | e |
| +->|Analysis |---+ | |Quantizer|---|---|---|---->| |
| | | |4 | | | |8 | | | | E |-->
| | +---------+ | | +---------+ | | | | n | 2
| | | | 9/\ 10| | | | | c |
| | | | | \/ | | | | o |
| | +---------+ | | +----------+ | | | | d |
| | |Noise | +--|-->|Prediction|--+---|---|---->| e |
| +->|Shaping |---|--+ |Analysis |7 | | | | r |
| | |Analysis |5 | | | | | | | | |
| | +---------+ | | +----------+ | | | | |
| | | | /\ | | | | |
| | +----------|--|--------+ | | | | |
| | | \/ \/ \/ \/ \/ | |
| | | +----------+ +------------+ | |
| | | | | |Noise | | |
-+-------+-----+----->|Pre-filter|--------->|Shaping |-->| |
1 | | 6 |Quantization|13 | |
+----------+ +------------+ +---+
1: Input speech signal
2: Range encoded bitstream
3: Voice activity estimate
4: Pitch lags (per 5 ms) and voicing decision (per 20 ms)
5: Noise shaping quantization coefficients
- Short-term synthesis and analysis
noise shaping coefficients (per 5 ms)
- Long-term synthesis and analysis noise
shaping coefficients (per 5 ms and for voiced speech only)
- Noise shaping tilt (per 5 ms)
- Quantizer gain/step size (per 5 ms)
6: Input signal filtered with analysis noise shaping filters
7: Short- and Long-Term Prediction coefficients
LTP (per 5 ms) and LPC (per 20 ms)
8: LSF quantization indices
9: LSF coefficients
10: Quantized LSF coefficients
11: Processed gains, and synthesis noise shape coefficients
12: LTP state scaling coefficient. Controlling error
propagation / prediction gain trade-off
13: Quantized signal
Figure 22: SILK Core Encoder
5.2.3.1. Voice Activity Detection
The input signal is processed by a Voice Activity Detection (VAD)
algorithm to produce a measure of voice activity, spectral tilt, and
signal-to-noise estimates for each frame. The VAD uses a sequence of
half-band filterbanks to split the signal into four subbands:
0...Fs/16, Fs/16...Fs/8, Fs/8...Fs/4, and Fs/4...Fs/2, where Fs is
the sampling frequency (8, 12, 16, or 24 kHz). The lowest subband,
from 0 - Fs/16, is high-pass filtered with a first-order moving
average (MA) filter (with transfer function H(z) = 1-z**(-1)) to
reduce the energy at the lowest frequencies. For each frame, the
signal energy per subband is computed. In each subband, a noise
level estimator tracks the background noise level and a Signal-to-
Noise Ratio (SNR) value is computed as the logarithm of the ratio of
energy-to-noise level. Using these intermediate variables, the
following parameters are calculated for use in other SILK modules:
o Average SNR. The average of the subband SNR values.
o Smoothed subband SNRs. Temporally smoothed subband SNR values.
o Speech activity level. Based on the average SNR and a weighted
average of the subband energies.
o Spectral tilt. A weighted average of the subband SNRs, with
positive weights for the low subbands and negative weights for the
high subbands.
5.2.3.2. Pitch Analysis
The input signal is processed by the open loop pitch estimator shown
in Figure 23.
+--------+ +----------+
|2 x Down| |Time- |
+->|sampling|->|Correlator| |
| | | | | |4
| +--------+ +----------+ \/
| | 2 +-------+
| | +-->|Speech |5
+---------+ +--------+ | \/ | |Type |->
|LPC | |Down | | +----------+ | |
+->|Analysis | +->|sample |-+------------->|Time- | +-------+
| | | | |to 8 kHz| |Correlator|----------->
| +---------+ | +--------+ |__________| 6
| | | |3
| \/ | \/
| +---------+ | +----------+
| |Whitening| | |Time- |
-+->|Filter |-+--------------------------->|Correlator|----------->
1 | | | | 7
+---------+ +----------+
1: Input signal
2: Lag candidates from stage 1
3: Lag candidates from stage 2
4: Correlation threshold
5: Voiced/unvoiced flag
6: Pitch correlation
7: Pitch lags
Figure 23: Block Diagram of the Pitch Estimator
The pitch analysis finds a binary voiced/unvoiced classification,
and, for frames classified as voiced, four pitch lags per frame --
one for each 5 ms subframe -- and a pitch correlation indicating the
periodicity of the signal. The input is first whitened using a
Linear Prediction (LP) whitening filter, where the coefficients are
computed through standard Linear Predictive Coding (LPC) analysis.
The order of the whitening filter is 16 for best results, but is
reduced to 12 for medium complexity and 8 for low complexity modes.
The whitened signal is analyzed to find pitch lags for which the time
correlation is high. The analysis consists of three stages for
reducing the complexity:
o In the first stage, the whitened signal is downsampled to 4 kHz
(from 8 kHz), and the current frame is correlated to a signal
delayed by a range of lags, starting from a shortest lag
corresponding to 500 Hz, to a longest lag corresponding to 56 Hz.
o The second stage operates on an 8 kHz signal (downsampled from 12,
16, or 24 kHz) and measures time correlations only near the lags
corresponding to those that had sufficiently high correlations in
the first stage. The resulting correlations are adjusted for a
small bias towards short lags to avoid ending up with a multiple
of the true pitch lag. The highest adjusted correlation is
compared to a threshold depending on:
* Whether the previous frame was classified as voiced.
* The speech activity level.
* The spectral tilt.
If the threshold is exceeded, the current frame is classified as
voiced and the lag with the highest adjusted correlation is stored
for a final pitch analysis of the highest precision in the third
stage.
o The last stage operates directly on the whitened input signal to
compute time correlations for each of the four subframes
independently in a narrow range around the lag with highest
correlation from the second stage.
5.2.3.3. Noise Shaping Analysis
The noise shaping analysis finds gains and filter coefficients used
in the pre-filter and noise shaping quantizer. These parameters are
chosen such that they will fulfill several requirements:
o Balancing quantization noise and bitrate. The quantization gains
determine the step size between reconstruction levels of the
excitation signal. Therefore, increasing the quantization gain
amplifies quantization noise, but also reduces the bitrate by
lowering the entropy of the quantization indices.
o Spectral shaping of the quantization noise; the noise shaping
quantizer is capable of reducing quantization noise in some parts
of the spectrum at the cost of increased noise in other parts
without substantially changing the bitrate. By shaping the noise
such that it follows the signal spectrum, it becomes less audible.
In practice, best results are obtained by making the shape of the
noise spectrum slightly flatter than the signal spectrum.
o De-emphasizing spectral valleys; by using different coefficients
in the analysis and synthesis part of the pre-filter and noise
shaping quantizer, the levels of the spectral valleys can be
decreased relative to the levels of the spectral peaks such as
speech formants and harmonics. This reduces the entropy of the
signal, which is the difference between the coded signal and the
quantization noise, thus lowering the bitrate.
o Matching the levels of the decoded speech formants to the levels
of the original speech formants; an adjustment gain and a first
order tilt coefficient are computed to compensate for the effect
of the noise shaping quantization on the level and spectral tilt.
/ \ ___
| // \\
| // \\ ____
|_// \\___// \\ ____
| / ___ \ / \\ // \\
P |/ / \ \_/ \\_____// \\
o | / \ ____ \ / \\
w | / \___/ \ \___/ ____ \\___ 1
e |/ \ / \ \
r | \_____/ \ \__ 2
| \
| \___ 3
|
+---------------------------------------->
Frequency
1: Input signal spectrum
2: De-emphasized and level matched spectrum
3: Quantization noise spectrum
Figure 24: Noise Shaping and Spectral De-emphasis Illustration
Figure 24 shows an example of an input signal spectrum (1). After
de-emphasis and level matching, the spectrum has deeper valleys (2).
The quantization noise spectrum (3) more or less follows the input
signal spectrum, while having slightly less pronounced peaks. The
entropy, which provides a lower bound on the bitrate for encoding the
excitation signal, is proportional to the area between the de-
emphasized spectrum (2) and the quantization noise spectrum (3).
Without de-emphasis, the entropy is proportional to the area between
input spectrum (1) and quantization noise (3) -- clearly higher.
The transformation from input signal to de-emphasized signal can be
described as a filtering operation with a filter
-1 Wana(z)
H(z) = G * ( 1 - c_tilt * z ) * -------
Wsyn(z)
having an adjustment gain G, a first order tilt adjustment filter
with tilt coefficient c_tilt, and where
16 d
__ -k -L __ -k
Wana(z) = (1 - \ a_ana(k) * z )*(1 - z * \ b_ana(k) * z )
/_ /_
k=1 k=-d
is the analysis part of the de-emphasis filter, consisting of the
short-term shaping filter with coefficients a_ana(k) and the long-
term shaping filter with coefficients b_ana(k) and pitch lag L. The
parameter d determines the number of long-term shaping filter taps.
Similarly, but without the tilt adjustment, the synthesis part can be
written as
16 d
__ -k -L __ -k
Wsyn(z) = (1 - \ a_syn(k) * z )*(1 - z * \ b_syn(k) * z )
/_ /_
k=1 k=-d
All noise shaping parameters are computed and applied per subframe of
5 ms. First, an LPC analysis is performed on a windowed signal block
of 15 ms. The signal block has a look-ahead of 5 ms relative to the
current subframe, and the window is an asymmetric sine window. The
LPC analysis is done with the autocorrelation method, with an order
of between 8, in lowest-complexity mode, and 16, for best quality.
Optionally, the LPC analysis and noise shaping filters are warped by
replacing the delay elements by first-order allpass filters. This
increases the frequency resolution at low frequencies and reduces it
at high ones, which better matches the human auditory system and
improves quality. The warped analysis and filtering comes at a cost
in complexity and is therefore only done in higher complexity modes.
The quantization gain is found by taking the square root of the
residual energy from the LPC analysis and multiplying it by a value
inversely proportional to the coding quality control parameter and
the pitch correlation.
Next, the two sets of short-term noise shaping coefficients a_ana(k)
and a_syn(k) are obtained by applying different amounts of bandwidth
expansion to the coefficients found in the LPC analysis. This
bandwidth expansion moves the roots of the LPC polynomial towards the
origin, using the formulas
k
a_ana(k) = a(k)*g_ana and
k
a_syn(k) = a(k)*g_syn
where a(k) is the k'th LPC coefficient, and the bandwidth expansion
factors g_ana and g_syn are calculated as
g_ana = 0.95 - 0.01*C and
g_syn = 0.95 + 0.01*C
where C is the coding quality control parameter between 0 and 1.
Applying more bandwidth expansion to the analysis part than to the
synthesis part gives the desired de-emphasis of spectral valleys in
between formants.
The long-term shaping is applied only during voiced frames. It uses
a three-tap filter, described by
b_ana = F_ana * [0.25, 0.5, 0.25] and
b_syn = F_syn * [0.25, 0.5, 0.25].
For unvoiced frames, these coefficients are set to 0. The
multiplication factors F_ana and F_syn are chosen between 0 and 1,
depending on the coding quality control parameter, as well as the
calculated pitch correlation and smoothed subband SNR of the lowest
subband. By having F_ana less than F_syn, the pitch harmonics are
emphasized relative to the valleys in between the harmonics.
The tilt coefficient c_tilt is for unvoiced frames chosen as
c_tilt = 0.25
and as
c_tilt = 0.25 + 0.2625 * V
for voiced frames, where V is the voice activity level between 0 and
1.
The adjustment gain G serves to correct any level mismatch between
the original and decoded signals that might arise from the noise
shaping and de-emphasis. This gain is computed as the ratio of the
prediction gain of the short-term analysis and synthesis filter
coefficients. The prediction gain of an LPC synthesis filter is the
square root of the output energy when the filter is excited by a
unit-energy impulse on the input. An efficient way to compute the
prediction gain is by first computing the reflection coefficients
from the LPC coefficients through the step-down algorithm, and
extracting the prediction gain from the reflection coefficients as
K
___ 2 -0.5
predGain = ( | | 1 - (r_k) )
k=1
where r_k is the k'th reflection coefficient.
Initial values for the quantization gains are computed as the square
root of the residual energy of the LPC analysis, adjusted by the
coding quality control parameter. These quantization gains are later
adjusted based on the results of the prediction analysis.
5.2.3.4. Prediction Analysis
The prediction analysis is performed in one of two ways depending on
how the pitch estimator classified the frame. The processing for
voiced and unvoiced speech is described in Section 5.2.3.4.1 and
Section 5.2.3.4.2, respectively. Inputs to this function include the
pre-whitened signal from the pitch estimator (see Section 5.2.3.2).
5.2.3.4.1. Voiced Speech
For a frame of voiced speech, the pitch pulses will remain dominant
in the pre-whitened input signal. Further whitening is desirable as
it leads to higher quality at the same available bitrate. To achieve
this, a Long-Term Prediction (LTP) analysis is carried out to
estimate the coefficients of a fifth-order LTP filter for each of
four subframes. The LTP coefficients are quantized using the method
described in Section 5.2.3.6, and the quantized LTP coefficients are
used to compute the LTP residual signal. This LTP residual signal is
the input to an LPC analysis where the LPC coefficients are estimated
using Burg's method [BURG], such that the residual energy is
minimized. The estimated LPC coefficients are converted to a Line
Spectral Frequency (LSF) vector and quantized as described in
Section 5.2.3.5. After quantization, the quantized LSF vector is
converted back to LPC coefficients using the full procedure in
Section 4.2.7.5. By using quantized LTP coefficients and LPC
coefficients derived from the quantized LSF coefficients, the encoder
remains fully synchronized with the decoder. The quantized LPC and
LTP coefficients are also used to filter the input signal and measure
residual energy for each of the four subframes.
5.2.3.4.2. Unvoiced Speech
For a speech signal that has been classified as unvoiced, there is no
need for LTP filtering, as it has already been determined that the
pre-whitened input signal is not periodic enough within the allowed
pitch period range for LTP analysis to be worth the cost in terms of
complexity and bitrate. The pre-whitened input signal is therefore
discarded, and, instead, the input signal is used for LPC analysis
using Burg's method. The resulting LPC coefficients are converted to
an LSF vector and quantized as described in the following section.
They are then transformed back to obtain quantized LPC coefficients,
which are then used to filter the input signal and measure residual
energy for each of the four subframes.
5.2.3.4.2.1. Burg's Method
The main purpose of linear prediction in SILK is to reduce the
bitrate by minimizing the residual energy. At least at high
bitrates, perceptual aspects are handled independently by the noise
shaping filter. Burg's method is used because it provides higher
prediction gain than the autocorrelation method and, unlike the
covariance method, produces stable filters (assuming numerical errors
don't spoil that). SILK's implementation of Burg's method is also
computationally faster than the autocovariance method. The
implementation of Burg's method differs from traditional
implementations in two aspects. The first difference is that it
operates on autocorrelations, similar to the Schur algorithm [SCHUR],
but with a simple update to the autocorrelations after finding each
reflection coefficient to make the result identical to Burg's method.
This brings down the complexity of Burg's method to near that of the
autocorrelation method. The second difference is that the signal in
each subframe is scaled by the inverse of the residual quantization
step size. Subframes with a small quantization step size will, on
average, spend more bits for a given amount of residual energy than
subframes with a large step size. Without scaling, Burg's method
minimizes the total residual energy in all subframes, which doesn't
necessarily minimize the total number of bits needed for coding the
quantized residual. The residual energy of the scaled subframes is a
better measure for that number of bits.
5.2.3.5. LSF Quantization
Unlike many other speech codecs, SILK uses variable bitrate coding
for the LSFs. This improves the average rate-distortion (R-D) trade-
off and reduces outliers. The variable bitrate coding minimizes a
linear combination of the weighted quantization errors and the
bitrate. The weights for the quantization errors are the Inverse
Harmonic Mean Weighting (IHMW) function proposed by Laroia et al.
(see [LAROIA-ICASSP]). These weights are referred to here as Laroia
weights.
The LSF quantizer consists of two stages. The first stage is an
(unweighted) vector quantizer (VQ), with a codebook size of 32
vectors. The quantization errors for the codebook vector are sorted,
and for the N best vectors a second stage quantizer is run. By
varying the number N, a trade-off is made between R-D performance and
computational efficiency. For each of the N codebook vectors, the
Laroia weights corresponding to that vector (and not to the input
vector) are calculated. Then, the residual between the input LSF
vector and the codebook vector is scaled by the square roots of these
Laroia weights. This scaling partially normalizes error sensitivity
for the residual vector so that a uniform quantizer with fixed step
sizes can be used in the second stage without too much performance
loss. Additionally, by scaling with Laroia weights determined from
the first-stage codebook vector, the process can be reversed in the
decoder.
The second stage uses predictive delayed decision scalar
quantization. The quantization error is weighted by Laroia weights
determined from the LSF input vector. The predictor multiplies the
previous quantized residual value by a prediction coefficient that
depends on the vector index from the first stage VQ and on the
location in the LSF vector. The prediction is subtracted from the
LSF residual value before quantizing the result and is added back
afterwards. This subtraction can be interpreted as shifting the
quantization levels of the scalar quantizer, and as a result the
quantization error of each value depends on the quantization decision
of the previous value. This dependency is exploited by the delayed
decision mechanism to search for a quantization sequency with best
R-D performance with a Viterbi-like algorithm [VITERBI]. The
quantizer processes the residual LSF vector in reverse order (i.e.,
it starts with the highest residual LSF value). This is done because
the prediction works slightly better in the reverse direction.
The quantization index of the first stage is entropy coded. The
quantization sequence from the second stage is also entropy coded,
where for each element the probability table is chosen depending on
the vector index from the first stage and the location of that
element in the LSF vector.
5.2.3.5.1. LSF Stabilization
If the input is stable, finding the best candidate usually results in
a quantized vector that is also stable. Because of the two-stage
approach, however, it is possible that the best quantization
candidate is unstable. The encoder applies the same stabilization
procedure applied by the decoder (see Section 4.2.7.5.4) to ensure
the LSF parameters are within their valid range, increasingly sorted,
and have minimum distances between each other and the border values.
5.2.3.6. LTP Quantization
For voiced frames, the prediction analysis described in
Section 5.2.3.4.1 resulted in four sets (one set per subframe) of
five LTP coefficients, plus four weighting matrices. The LTP
coefficients for each subframe are quantized using entropy
constrained vector quantization. A total of three vector codebooks
are available for quantization, with different rate-distortion trade-
offs. The three codebooks have 10, 20, and 40 vectors and average
rates of about 3, 4, and 5 bits per vector, respectively.
Consequently, the first codebook has larger average quantization
distortion at a lower rate, whereas the last codebook has smaller
average quantization distortion at a higher rate. Given the
weighting matrix W_ltp and LTP vector b, the weighted rate-distortion
measure for a codebook vector cb_i with rate r_i is give by
RD = u * (b - cb_i)' * W_ltp * (b - cb_i) + r_i
where u is a fixed, heuristically determined parameter balancing the
distortion and rate. Which codebook gives the best performance for a
given LTP vector depends on the weighting matrix for that LTP vector.
For example, for a low valued W_ltp, it is advantageous to use the
codebook with 10 vectors as it has a lower average rate. For a large
W_ltp, on the other hand, it is often better to use the codebook with
40 vectors, as it is more likely to contain the best codebook vector.
The weighting matrix W_ltp depends mostly on two aspects of the input
signal. The first is the periodicity of the signal; the more
periodic, the larger W_ltp. The second is the change in signal
energy in the current subframe, relative to the signal one pitch lag
earlier. A decaying energy leads to a larger W_ltp than an
increasing energy. Both aspects fluctuate relatively slowly, which
causes the W_ltp matrices for different subframes of one frame often
to be similar. Because of this, one of the three codebooks typically
gives good performance for all subframes. Therefore, the codebook
search for the subframe LTP vectors is constrained to only allow
codebook vectors to be chosen from the same codebook, resulting in a
rate reduction.
To find the best codebook, each of the three vector codebooks is used
to quantize all subframe LTP vectors and produce a combined weighted
rate-distortion measure for each vector codebook. The vector
codebook with the lowest combined rate-distortion over all subframes
is chosen. The quantized LTP vectors are used in the noise shaping
quantizer, and the index of the codebook plus the four indices for
the four subframe codebook vectors are passed on to the range
encoder.
5.2.3.7. Pre-filter
In the pre-filter, the input signal is filtered using the spectral
valley de-emphasis filter coefficients from the noise shaping
analysis (see Section 5.2.3.3). By applying only the noise shaping
analysis filter to the input signal, it provides the input to the
noise shaping quantizer.
5.2.3.8. Noise Shaping Quantizer
The noise shaping quantizer independently shapes the signal and
coding noise spectra to obtain a perceptually higher quality at the
same bitrate.
The pre-filter output signal is multiplied with a compensation gain G
computed in the noise shaping analysis. Then, the output of a
synthesis shaping filter is added, and the output of a prediction
filter is subtracted to create a residual signal. The residual
signal is multiplied by the inverse quantized quantization gain from
the noise shaping analysis and input to a scalar quantizer. The
quantization indices of the scalar quantizer represent a signal of
pulses that is input to the pyramid range encoder. The scalar
quantizer also outputs a quantization signal, which is multiplied by
the quantized quantization gain from the noise shaping analysis to
create an excitation signal. The output of the prediction filter is
added to the excitation signal to form the quantized output signal
y(n). The quantized output signal y(n) is input to the synthesis
shaping and prediction filters.
Optionally, the noise shaping quantizer operates in a delayed
decision mode. In this mode, it uses a Viterbi algorithm to keep
track of multiple rounding choices in the quantizer and select the
best one after a delay of 32 samples. This improves the rate/
distortion performance of the quantizer.
5.2.3.9. Constant Bitrate Mode
SILK was designed to run in variable bitrate (VBR) mode. However,
the reference implementation also has a constant bitrate (CBR) mode
for SILK. In CBR mode, SILK will attempt to encode each packet with
no more than the allowed number of bits. The Opus wrapper code then
pads the bitstream if any unused bits are left in SILK mode, or it
encodes the high band with the remaining number of bits in Hybrid
mode. The number of payload bits is adjusted by changing the
quantization gains and the rate/distortion trade-off in the noise
shaping quantizer, in an iterative loop around the noise shaping
quantizer and entropy coding. Compared to the SILK VBR mode, the CBR
mode has lower audio quality at a given average bitrate and has
higher computational complexity.
5.3. CELT Encoder
Most of the aspects of the CELT encoder can be directly derived from
the description of the decoder. For example, the filters and
rotations in the encoder are simply the inverse of the operation
performed by the decoder. Similarly, the quantizers generally
optimize for the mean square error (because noise shaping is part of
the bitstream itself), so no special search is required. For this
reason, only the less straightforward aspects of the encoder are
described here.
5.3.1. Pitch Pre-filter
The pitch pre-filter is applied after the pre-emphasis. It is
applied in such a way as to be the inverse of the decoder's post-
filter. The main non-obvious aspect of the pre-filter is the
selection of the pitch period. The pitch search should be optimized
for the following criteria:
o continuity: it is important that the pitch period does not change
abruptly between frames; and
o avoidance of pitch multiples: when the period used is a multiple
of the real period (lower frequency fundamental), the post-filter
loses most of its ability to reduce noise
5.3.2. Bands and Normalization
The MDCT output is divided into bands that are designed to match the
ear's critical bands for the smallest (2.5 ms) frame size. The
larger frame sizes use integer multiples of the 2.5 ms layout. For
each band, the encoder computes the energy that will later be
encoded. Each band is then normalized by the square root of the
*unquantized* energy, such that each band now forms a unit vector X.
The energy and the normalization are computed by
compute_band_energies() and normalise_bands() (bands.c),
respectively.
5.3.3. Energy Envelope Quantization
Energy quantization (both coarse and fine) can be easily understood
from the decoding process. For all useful bitrates, the coarse
quantizer always chooses the quantized log energy value that
minimizes the error for each band. Only at very low rate does the
encoder allow larger errors to minimize the rate and avoid using more
bits than are available. When the available CPU requirements allow
it, it is best to try encoding the coarse energy both with and
without inter-frame prediction such that the best prediction mode can
be selected. The optimal mode depends on the coding rate, the
available bitrate, and the current rate of packet loss.
The fine energy quantizer always chooses the quantized log energy
value that minimizes the error for each band because the rate of the
fine quantization depends only on the bit allocation and not on the
values that are coded.
5.3.4. Bit Allocation
The encoder must use exactly the same bit allocation process as used
by the decoder and described in Section 4.3.3. The three mechanisms
that can be used by the encoder to adjust the bitrate on a frame-by-
frame basis are band boost, allocation trim, and band skipping.
5.3.4.1. Band Boost
The reference encoder makes a decision to boost a band when the
energy of that band is significantly higher than that of the
neighboring bands. Let E_j be the log-energy of band j, we define
D_j = 2*E_j - E_j-1 - E_j+1
The allocation of band j is boosted once if D_j > t1 and twice if D_j
> t2. For LM>=1, t1=2 and t2=4, while for LM<1, t1=3 and t2=5.
5.3.4.2. Allocation Trim
The allocation trim is a value between 0 and 10 (inclusively) that
controls the allocation balance between the low and high frequencies.
The encoder starts with a safe "default" of 5 and deviates from that
default in two different ways. First, the trim can deviate by +/- 2
depending on the spectral tilt of the input signal. For signals with
more low frequencies, the trim is increased by up to 2, while for
signals with more high frequencies, the trim is decreased by up to 2.
For stereo inputs, the trim value can be decreased by up to 4 when
the inter-channel correlation at low frequency (first 8 bands) is
high.
5.3.4.3. Band Skipping
The encoder uses band skipping to ensure that the shape of the bands
is only coded if there is at least 1/2 bit per sample available for
the PVQ. If not, then no bit is allocated and folding is used
instead. To ensure continuity in the allocation, some amount of
hysteresis is added to the process, such that a band that received
PVQ bits in the previous frame only needs 7/16 bit/sample to be coded
for the current frame, while a band that did not receive PVQ bits in
the previous frames needs at least 9/16 bit/sample to be coded.
5.3.5. Stereo Decisions
Because CELT applies mid-side stereo coupling in the normalized
domain, it does not suffer from important stereo image problems even
when the two channels are completely uncorrelated. For this reason,
it is always safe to use stereo coupling on any audio frame. That
being said, there are some frames for which dual (independent) stereo
is still more efficient. This decision is made by comparing the
estimated entropy with and without coupling over the first 13 bands,
taking into account the fact that all bands with more than two MDCT
bins require one extra degree of freedom when coded in mid-side. Let
L1_ms and L1_lr be the L1-norm of the mid-side vector and the L1-norm
of the left-right vector, respectively. The decision to use mid-side
is made if and only if
L1_ms L1_lr
-------- < -----
bins + E bins
where bins is the number of MDCT bins in the first 13 bands and E is
the number of extra degrees of freedom for mid-side coding. For
LM>1, E=13, otherwise E=5.
The reference encoder decides on the intensity stereo threshold based
on the bitrate alone. After taking into account the frame size by
subtracting 80 bits per frame for coarse energy, the first band using
intensity coding is as follows:
+------------------+------------+
| bitrate (kbit/s) | start band |
+------------------+------------+
| <35 | 8 |
| | |
| 35-50 | 12 |
| | |
| 50-68 | 16 |
| | |
| 84-84 | 18 |
| | |
| 84-102 | 19 |
| | |
| 102-130 | 20 |
| | |
| >130 | disabled |
+------------------+------------+
Table 66: Thresholds for Intensity Stereo
5.3.6. Time-Frequency Decision
The choice of time-frequency resolution used in Section 4.3.4.5 is
based on R-D optimization. The distortion is the L1-norm (sum of
absolute values) of each band after each TF resolution under
consideration. The L1 norm is used because it represents the entropy
for a Laplacian source. The number of bits required to code a change
in TF resolution between two bands is higher than the cost of having
those two bands use the same resolution, which is what requires the
R-D optimization. The optimal decision is computed using the Viterbi
algorithm. See tf_analysis() in celt/celt.c.
5.3.7. Spreading Values Decision
The choice of the spreading value in Table 59 has an impact on the
nature of the coding noise introduced by CELT. The larger the f_r
value, the lower the impact of the rotation, and the more tonal the
coding noise. The more tonal the signal, the more tonal the noise
should be, so the CELT encoder determines the optimal value for f_r
by estimating how tonal the signal is. The tonality estimate is
based on discrete pdf (4-bin histogram) of each band. Bands that
have a large number of small values are considered more tonal and a
decision is made by combining all bands with more than 8 samples.
See spreading_decision() in celt/bands.c.
5.3.8. Spherical Vector Quantization
CELT uses a Pyramid Vector Quantizer (PVQ) [PVQ] for quantizing the
details of the spectrum in each band that have not been predicted by
the pitch predictor. The PVQ codebook consists of all sums of K
signed pulses in a vector of N samples, where two pulses at the same
position are required to have the same sign. Thus, the codebook
includes all integer codevectors y of N dimensions that satisfy
sum(abs(y(j))) = K.
In bands where there are sufficient bits allocated, PVQ is used to
encode the unit vector that results from the normalization in
Section 5.3.2 directly. Given a PVQ codevector y, the unit vector X
is obtained as X = y/||y||, where ||.|| denotes the L2 norm.
5.3.8.1. PVQ Search
The search for the best codevector y is performed by alg_quant()
(vq.c). There are several possible approaches to the search, with a
trade-off between quality and complexity. The method used in the
reference implementation computes an initial codeword y1 by
projecting the normalized spectrum X onto the codebook pyramid of K-1
pulses:
y0 = truncate_towards_zero( (K-1) * X / sum(abs(X)))
Depending on N, K and the input data, the initial codeword y0 may
contain from 0 to K-1 non-zero values. All the remaining pulses,
with the exception of the last one, are found iteratively with a
greedy search that minimizes the normalized correlation between y and
X:
T
J = -X * y / ||y||
The search described above is considered to be a good trade-off
between quality and computational cost. However, there are other
possible ways to search the PVQ codebook and the implementers MAY use
any other search methods. See alg_quant() in celt/vq.c.
5.3.8.2. PVQ Encoding
The vector to encode, X, is converted into an index i such that
0 <= i < V(N,K) as follows. Let i = 0 and k = 0. Then, for
j = (N - 1) down to 0, inclusive, do:
1. If k > 0, set i = i + (V(N-j-1,k-1) + V(N-j,k-1))/2.
2. Set k = k + abs(X[j]).
3. If X[j] < 0, set i = i + (V(N-j-1,k) + V(N-j,k))/2.
The index i is then encoded using the procedure in Section 5.1.4 with
ft = V(N,K).
6. Conformance
It is our intention to allow the greatest possible choice of freedom
in implementing the specification. For this reason, outside of the
exceptions noted in this section, conformance is defined through the
reference implementation of the decoder provided in Appendix A.
Although this document includes a prose description of the codec,
should the description contradict the source code of the reference
implementation, the latter shall take precedence.
Compliance with this specification means that, in addition to
following the normative keywords in this document, a decoder's output
MUST also be within the thresholds specified by the opus_compare.c
tool (included with the code) when compared to the reference
implementation for each of the test vectors provided (see
Appendix A.4) and for each output sampling rate and channel count
supported. In addition, a compliant decoder implementation MUST have
the same final range decoder state as that of the reference decoder.
It is therefore RECOMMENDED that the decoder implement the same
functional behavior as the reference. A decoder implementation is
not required to support all output sampling rates or all output
channel counts.
6.1. Testing
Using the reference code provided in Appendix A, a test vector can be
decoded with
opus_demo -d <rate> <channels> testvectorX.bit testX.out
where <rate> is the sampling rate and can be 8000, 12000, 16000,
24000, or 48000, and <channels> is 1 for mono or 2 for stereo.
If the range decoder state is incorrect for one of the frames, the
decoder will exit with "Error: Range coder state mismatch between
encoder and decoder". If the decoder succeeds, then the output can
be compared with the "reference" output with
opus_compare -s -r <rate> testvectorX.dec testX.out
for stereo or
opus_compare -r <rate> testvectorX.dec testX.out
for mono.
In addition to indicating whether the test vector comparison passes,
the opus_compare tool outputs an "Opus quality metric" that indicates
how well the tested decoder matches the reference implementation. A
quality of 0 corresponds to the passing threshold, while a quality of
100 is the highest possible value and means that the output of the
tested decoder is identical to the reference implementation. The
passing threshold (quality 0) was calibrated in such a way that it
corresponds to additive white noise with a 48 dB SNR (similar to what
can be obtained on a cassette deck). It is still possible for an
implementation to sound very good with such a low quality measure
(e.g., if the deviation is due to inaudible phase distortion), but
unless this is verified by listening tests, it is RECOMMENDED that
implementations achieve a quality above 90 for 48 kHz decoding. For
other sampling rates, it is normal for the quality metric to be lower
(typically, as low as 50 even for a good implementation) because of
harmless mismatch with the delay and phase of the internal sampling
rate conversion.
On POSIX environments, the run_vectors.sh script can be used to
verify all test vectors. This can be done with
run_vectors.sh <exec path> <vector path> <rate>
where <exec path> is the directory where the opus_demo and
opus_compare executables are built and <vector path> is the directory
containing the test vectors.
6.2. Opus Custom
Opus Custom is an OPTIONAL part of the specification that is defined
to handle special sample rates and frame rates that are not supported
by the main Opus specification. Use of Opus Custom is discouraged
for all but very special applications for which a frame size
different from 2.5, 5, 10, or 20 ms is needed (for either complexity
or latency reasons). Because Opus Custom is optional, streams
encoded using Opus Custom cannot be expected to be decodable by all
Opus implementations. Also, because no in-band mechanism exists for
specifying the sampling rate and frame size of Opus Custom streams,
out-of-band signaling is required. In Opus Custom operation, only
the CELT layer is available, using the opus_custom_* function calls
in opus_custom.h.
7. Security Considerations
Like any other audio codec, Opus should not be used with insecure
ciphers or cipher-modes that are vulnerable to known plaintext
attacks. In addition to the zeros used in Opus padding, digital
silence frames generate predictable compressed results and the TOC
byte may have an easily predictable value.
Implementations of the Opus codec need to take appropriate security
considerations into account, as outlined in [DOS]. It is extremely
important for the decoder to be robust against malicious payloads.
Malicious payloads must not cause the decoder to overrun its
allocated memory or to take an excessive amount of resources to
decode. Although problems in encoders are typically rarer, the same
applies to the encoder. Malicious audio streams must not cause the
encoder to misbehave because this would allow an attacker to attack
transcoding gateways.
The reference implementation contains no known buffer overflow or
cases where a specially crafted packet or audio segment could cause a
significant increase in CPU load. However, on certain CPU
architectures where denormalized floating-point operations are much
slower than normal floating-point operations, it is possible for some
audio content (e.g., silence or near silence) to cause an increase in
CPU load. Denormals can be introduced by reordering operations in
the compiler and depend on the target architecture, so it is
difficult to guarantee that an implementation avoids them. For
architectures on which denormals are problematic, adding very small
floating-point offsets to the affected signals to prevent significant
numbers of denormalized operations is RECOMMENDED. Alternatively, it
is often possible to configure the hardware to treat denormals as
zero (DAZ). No such issue exists for the fixed-point reference
implementation.
The reference implementation was validated in the following
conditions:
1. Sending the decoder valid packets generated by the reference
encoder and verifying that the decoder's final range coder state
matches that of the encoder.
2. Sending the decoder packets generated by the reference encoder
and then subjected to random corruption.
3. Sending the decoder random packets.
4. Sending the decoder packets generated by a version of the
reference encoder modified to make random coding decisions
(internal fuzzing), including mode switching, and verifying that
the range coder final states match.
In all of the conditions above, both the encoder and the decoder were
run inside the Valgrind [VALGRIND] memory debugger, which tracks
reads and writes to invalid memory regions as well as the use of
uninitialized memory. There were no errors reported on any of the
tested conditions.
8. Acknowledgements
Thanks to all other developers, including Henrik Astrom, Jon
Bergenheim, Raymond Chen, Soren Skak Jensen, Gregory Maxwell,
Christopher Montgomery, and Karsten Vandborg Sorensen. We would also
like to thank Igor Dyakonov, Hoang Thi Minh Nguyet, Christian Hoene,
Gian-Carlo Pascutto, and Jan Skoglund for their help with testing of
the Opus codec. Thanks to Andrew D'Addesio, Elwyn Davies, Ralph
Giles, John Ridges, Ben Schwartz, Kat Walsh, Mark Warner, Keith Yan,
and many others on the Opus and CELT mailing lists for their bug
reports and feedback. At last, the authors would like to thank
Robert Sparks, Cullen Jennings, and Jonathan Rosenberg for their
support throughout the standardization process.
9. References
9.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
9.2. Informative References
[BURG] Burg, J., "Maximum Entropy Spectral Analysis", Proceedings
of the 37th Annual International SEG Meeting, Vol.
6, 1975.
[CELT] Valin, JM., Terriberry, T., Maxwell, G., and C.
Montgomery, "Constrained-Energy Lapped Transform (CELT)
Codec", Work in Progress, July 2010.
[CODING-THESIS]
Pasco, R., "Source coding algorithms for fast data
compression", Ph.D. thesis Dept. of Electrical
Engineering, Stanford University, May 1976.
[DOS] Handley, M., Rescorla, E., and IAB, "Internet Denial-of-
Service Considerations", RFC 4732, December 2006.
[FFT] Wikipedia, "Fast Fourier Transform",
<http://en.wikipedia.org/w/
index.php?title=Fast_Fourier_transform&oldid=508004516>.
[GOOGLE-NETEQ]
"Google NetEQ code", <http://code.google.com/p/webrtc/
source/browse/trunk/src/modules/audio_coding/NetEQ/main/
source/?r=583>.
[GOOGLE-WEBRTC]
"Google WebRTC code", <http://code.google.com/p/webrtc/>.
[HADAMARD] Wikipedia, "Hadamard Transform", <http://en.wikipedia.org/
w/index.php?title=Hadamard_transform&oldid=508252957>.
[KABAL86] Kabal, P. and R. Ramachandran, "The Computation of Line
Spectral Frequencies Using Chebyshev Polynomials", IEEE
Trans. Acoustics, Speech, Signal Processing, Vol. 34, no.
6, pp. 1419-1426, December 1986.
[LAROIA-ICASSP]
Laroia, R., Phamdo, N., and N. Farvardin, "Robust and
Efficient Quantization of Speech LSP Parameters Using
Structured Vector Quantization", ICASSP-1991, Proc. IEEE
Int. Conf. Acoust., Speech, Signal Processing, pp. 641-
644, October 1991.
[LPC] Wikipedia, "Linear Prediction", <http://en.wikipedia.org/
w/index.php?title=Linear_prediction&oldid=497201278>.
[MARTIN79] Martin, G., "Range encoding: An algorithm for removing
redundancy from a digitised message", Proc. Institution of
Electronic and Radio Engineers International Conference on
Video and Data Recording, 1979.
[MATROSKA-WEBSITE]
"Matroska website", <http://matroska.org/>.
[MDCT] Wikipedia, "Modified Discrete Cosine Transform", <http://
en.wikipedia.org/w/
index.php?title=Modified_discrete_cosine_
transform&oldid=490295438>.
[OPUS-GIT] "Opus Git Repository", <https://git.xiph.org/opus.git>.
[OPUS-WEBSITE]
"Opus website", <http://opus-codec.org/>.
[PRINCEN86]
Princen, J. and A. Bradley, "Analysis/Synthesis Filter
Bank Design Based on Time Domain Aliasing Cancellation",
IEEE Trans. Acoustics, Speech, and Siginal Processing,
ASSP-34 (5), pp. 1153-1161, October, 1986.
[PVQ] Fischer, T., "A Pyramid Vector Quantizer", IEEE Trans. on
Information Theory, Vol. 32, pp. 568-583, July 1986.
[RANGE-CODING]
Wikipedia, "Range Coding", <http://en.wikipedia.org/w/
index.php?title=Range_encoding&oldid=509582757>.
[REQUIREMENTS]
Valin, JM. and K. Vos, "Requirements for an Internet Audio
Codec", RFC 6366, August 2011.
[RFC3533] Pfeiffer, S., "The Ogg Encapsulation Format Version 0",
RFC 3533, May 2003.
[RFC3550] Schulzrinne, H., Casner, S., Frederick, R., and V.
Jacobson, "RTP: A Transport Protocol for Real-Time
Applications", STD 64, RFC 3550, July 2003.
[SCHUR] Le Roux, J. and C. Gueguen, "A fixed point computation of
partial correlation coefficients", ICASSP-1977, Proc. IEEE
Int. Conf. Acoustics, Speech, and Signal Processing, pp.
257-259, June 1977.
[SILK] Vos, K., Jensen, S., and K. Sorensen, "SILK Speech Codec",
Work in Progress, September 2010.
[SPECTRAL-PAIRS]
Wikipedia, "Line Spectral Pairs", <http://
en.wikipedia.org/w/
index.php?title=Line_spectral_pairs&oldid=365426016>.
[SRTP-VBR] Perkins, C. and JM. Valin, "Guidelines for the Use of
Variable Bit Rate Audio with Secure RTP", RFC 6562,
March 2012.
[VALGRIND] "Valgrind website", <http://valgrind.org/>.
[VALIN2010]
Valin, JM., Terriberry, T., Montgomery, C., and G.
Maxwell, "A High-Quality Speech and Audio Codec With Less
Than 10 ms Delay", IEEE Trans. on Audio, Speech, and
Language Processing, Vol. 18, No. 1, pp. 58-67 2010.
[VECTORS-PROC]
"Opus Testvectors (proceedings)", <http://www.ietf.org/
proceedings/83/slides/slides-83-codec-0.gz>.
[VECTORS-WEBSITE]
"Opus Testvectors (website)",
<http://opus-codec.org/testvectors/>.
[VITERBI] Wikipedia, "Viterbi Algorithm", <http://en.wikipedia.org/
w/index.php?title=Viterbi_algorithm&oldid=508835871>.
[VORBIS-WEBSITE]
"Vorbis website", <http://xiph.org/vorbis/>.
[WHITENING]
Wikipedia, "White Noise", <http://en.wikipedia.org/w/
index.php?title=White_noise&oldid=497791998>.
[Z-TRANSFORM]
Wikipedia, "Z-transform", <http://en.wikipedia.org/w/
index.php?title=Z-transform&oldid=508392884>.
[ZWICKER61]
Zwicker, E., "Subdivision of the Audible Frequency Range
into Critical Bands", The Journal of the Acoustical
Society of America, Vol. 33, No 2 pp. 248, February 1961.
Appendix A. Reference Implementation
This appendix contains the complete source code for the reference
implementation of the Opus codec written in C. By default, this
implementation relies on floating-point arithmetic, but it can be
compiled to use only fixed-point arithmetic by defining the
FIXED_POINT macro. The normative behavior is defined as the output
using the floating-point configuration. Information on building and
using the reference implementation is available in the README file.
The implementation can be compiled with either a C89 or a C99
compiler. It is reasonably optimized for most platforms such that
only architecture-specific optimizations are likely to be useful.
The Fast Fourier Transform (FFT) [FFT] used is a slightly modified
version of the KISS-FFT library, but it is easy to substitute any
other FFT library.
While the reference implementation does not rely on any _undefined
behavior_ as defined by C89 or C99, it relies on common
_implementation-defined behavior_ for two's complement architectures:
o Right shifts of negative values are consistent with two's
complement arithmetic, so that a>>b is equivalent to
floor(a/(2**b)),
o For conversion to a signed integer of N bits, the value is reduced
modulo 2**N to be within range of the type,
o The result of integer division of a negative value is truncated
towards zero, and
o The compiler provides a 64-bit integer type (a C99 requirement
which is supported by most C89 compilers).
In its current form, the reference implementation also requires the
following architectural characteristics to obtain acceptable
performance:
o Two's complement arithmetic,
o At least a 16 bit by 16 bit integer multiplier (32-bit result),
and
o At least a 32-bit adder/accumulator.
A.1. Extracting the Source
The complete source code can be extracted from this document, by
running the following command line:
o cat rfc6716.txt | grep '^\ \ \ ###' | sed -e 's/...###//' | base64
--decode > opus-rfc6716.tar.gz
o tar xzvf opus-rfc6716.tar.gz
o cd opus-rfc6716
o make
On systems where the provided Makefile does not work, the following
command line may be used to compile the source code:
o cc -O2 -g -o opus_demo src/opus_demo.c `cat *.mk | grep -v fixed |
sed -e 's/.*=//' -e 's/\\\\//'` -DOPUS_BUILD -Iinclude -Icelt
-Isilk -Isilk/float -DUSE_ALLOCA -Drestrict= -lm
On systems where the base64 utility is not present, the following
commands can be used instead:
o cat rfc6716.txt | grep '^\ \ \ ###' | sed -e 's/...###//' >
opus.b64
o openssl base64 -d -in opus.b64 > opus-rfc6716.tar.gz
The SHA1 hash of the opus-rfc6716.tar.gz file is
86a927223e73d2476646a1b933fcd3fffb6ecc8c.
A.2. Up-to-Date Implementation
As of the time of publication of this memo, an up-to-date
implementation conforming to this RFC is available in a Git
repository [OPUS-GIT]. Releases and other resources are available at
[OPUS-WEBSITE]. However, although that implementation is expected to
remain conformant with the RFC, it is the code in this document that
shall remain normative.
A.3. Base64-Encoded Source Code
###H4sIAEeqNVACA+xde3PixrLfv/kUfXarEvDF2ODHZrNJajHIWCe8LgJ7t+65pSOL
###AXRWSEQPe52c891v98xISEI8vMZ7kyqTikHSdE93T0/Pr+ehdRehf+hNzPO31fOj
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A.4. Test Vectors
Because of size constraints, the Opus test vectors are not
distributed in this document. They are available in the proceedings
of the 83rd IETF meeting (Paris) [VECTORS-PROC] and from the Opus
codec website at [VECTORS-WEBSITE]. These test vectors were created
specifically to exercise all aspects of the decoder. Therefore, the
audio quality of the decoded output is significantly lower than what
Opus can achieve in normal operation.
The SHA1 hash of the files in the test vector package are
e49b2862ceec7324790ed8019eb9744596d5be01 testvector01.bit
b809795ae1bcd606049d76de4ad24236257135e0 testvector02.bit
e0c4ecaeab44d35a2f5b6575cd996848e5ee2acc testvector03.bit
a0f870cbe14ebb71fa9066ef3ee96e59c9a75187 testvector04.bit
9b3d92b48b965dfe9edf7b8a85edd4309f8cf7c8 testvector05.bit
28e66769ab17e17f72875283c14b19690cbc4e57 testvector06.bit
bacf467be3215fc7ec288f29e2477de1192947a6 testvector07.bit
ddbe08b688bbf934071f3893cd0030ce48dba12f testvector08.bit
3932d9d61944dab1201645b8eeaad595d5705ecb testvector09.bit
521eb2a1e0cc9c31b8b740673307c2d3b10c1900 testvector10.bit
6bc8f3146fcb96450c901b16c3d464ccdf4d5d96 testvector11.bit
338c3f1b4b97226bc60bc41038becbc6de06b28f testvector12.bit
a20a2122d42de644f94445e20185358559623a1f testvector01.dec
48ac1ff1995250a756e1e17bd32acefa8cd2b820 testvector02.dec
d15567e919db2d0e818727092c0af8dd9df23c95 testvector03.dec
1249dd28f5bd1e39a66fd6d99449dca7a8316342 testvector04.dec
93eee37e5d26a456d2c24483060132ff7eae2143 testvector05.dec
a294fc17e3157768c46c5ec0f2116de0d2c37ee2 testvector06.dec
2bf550e2f072e0941438db3f338fe99444385848 testvector07.dec
2695c1f2d1f9748ea0bf07249c70fd7b87f61680 testvector08.dec
12862add5d53a9d2a7079340a542a2f039b992bb testvector09.dec
a081252bb2b1a902fdc500530891f47e2a373d84 testvector10.dec
dfd0f844f2a42df506934fac2100a3c03beec711 testvector11.dec
8c16b2a1fb60e3550ba165068f9d7341357fdb63 testvector12.dec
Appendix B. Self-Delimiting Framing
To use the internal framing described in Section 3, the decoder must
know the total length of the Opus packet, in bytes. This section
describes a simple variation of that framing that can be used when
the total length of the packet is not known. Nothing in the encoding
of the packet itself allows a decoder to distinguish between the
regular, undelimited framing and the self-delimiting framing
described in this appendix. Which one is used and where must be
established by context at the transport layer. It is RECOMMENDED
that a transport layer choose exactly one framing scheme, rather than
allowing an encoder to signal which one it wants to use.
For example, although a regular Opus stream does not support more
than two channels, a multi-channel Opus stream may be formed from
several one- and two-channel streams. To pack an Opus packet from
each of these streams together in a single packet at the transport
layer, one could use the self-delimiting framing for all but the last
stream, and then the regular, undelimited framing for the last one.
Reverting to the undelimited framing for the last stream saves
overhead (because the total size of the transport-layer packet will
still be known), and ensures that a "multi-channel" stream that only
has a single Opus stream uses the same framing as a regular Opus
stream does. This avoids the need for signaling to distinguish these
two cases.
The self-delimiting framing is identical to the regular, undelimited
framing from Section 3, except that each Opus packet contains one
extra length field, encoded using the same one- or two-byte scheme
from Section 3.2.1. This extra length immediately precedes the
compressed data of the first Opus frame in the packet, and is
interpreted in the various modes as follows:
o Code 0 packets: It is the length of the single Opus frame (see
Figure 25).
o Code 1 packets: It is the length used for both of the Opus frames
(see Figure 26).
o Code 2 packets: It is the length of the second Opus frame (see
Figure 27).
o CBR Code 3 packets: It is the length used for all of the Opus
frames (see Figure 28).
o VBR Code 3 packets: It is the length of the last Opus frame (see
Figure 29).
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| config |s|0|0| N1 (1-2 bytes): |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |
| Compressed frame 1 (N1 bytes)... :
: |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 25: A Self-Delimited Code 0 Packet
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| config |s|0|1| N1 (1-2 bytes): |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ :
| Compressed frame 1 (N1 bytes)... |
: +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ :
| Compressed frame 2 (N1 bytes)... |
: +-+-+-+-+-+-+-+-+
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 26: A Self-Delimited Code 1 Packet
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| config |s|1|0| N1 (1-2 bytes): N2 (1-2 bytes : |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ :
| Compressed frame 1 (N1 bytes)... |
: +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |
| Compressed frame 2 (N2 bytes)... :
: |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 27: A Self-Delimited Code 2 Packet
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| config |s|1|1|0|p| M | Pad len (Opt) : N1 (1-2 bytes):
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 1 (N1 bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 2 (N1 bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: ... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame M (N1 bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: Opus Padding (Optional)... |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 28: A Self-Delimited CBR Code 3 Packet
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| config |s|1|1|1|p| M | Padding length (Optional) :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: N1 (1-2 bytes): ... : N[M-1] | N[M] :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 1 (N1 bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame 2 (N2 bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: ... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
: Compressed frame M (N[M] bytes)... :
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
: Opus Padding (Optional)... |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 29: A Self-Delimited VBR Code 3 Packet
Authors' Addresses
Jean-Marc Valin
Mozilla Corporation
650 Castro Street
Mountain View, CA 94041
USA
Phone: +1 650 903-0800
EMail: jmvalin@jmvalin.ca
Koen Vos
Skype Technologies S.A.
Soder Malarstrand 43
Stockholm, 11825
SE
Phone: +46 73 085 7619
EMail: koenvos74@gmail.com
Timothy B. Terriberry
Mozilla Corporation
650 Castro Street
Mountain View, CA 94041
USA
Phone: +1 650 903-0800
EMail: tterriberry@mozilla.com