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\section{Introduction and Description} \label{vorbis:spec:intro}

\subsection{Overview}

This document provides a high level description of the Vorbis codec's

construction.  A bit-by-bit specification appears beginning in

\xref{vorbis:spec:codec}.

The later sections assume a high-level

understanding of the Vorbis decode process, which is

provided here.

\subsubsection{Application}

Vorbis is a general purpose perceptual audio CODEC intended to allow

maximum encoder flexibility, thus allowing it to scale competitively

over an exceptionally wide range of bitrates.  At the high

quality/bitrate end of the scale (CD or DAT rate stereo, 16/24 bits)

it is in the same league as MPEG-2 and MPC.  Similarly, the 1.0

encoder can encode high-quality CD and DAT rate stereo at below 48kbps

without resampling to a lower rate.  Vorbis is also intended for

lower and higher sample rates (from 8kHz telephony to 192kHz digital

masters) and a range of channel representations (monaural,

polyphonic, stereo, quadraphonic, 5.1, ambisonic, or up to 255

discrete channels).

\subsubsection{Classification}

Vorbis I is a forward-adaptive monolithic transform CODEC based on the

Modified Discrete Cosine Transform.  The codec is structured to allow

addition of a hybrid wavelet filterbank in Vorbis II to offer better

transient response and reproduction using a transform better suited to

localized time events.

\subsubsection{Assumptions}

The Vorbis CODEC design assumes a complex, psychoacoustically-aware

encoder and simple, low-complexity decoder. Vorbis decode is

computationally simpler than mp3, although it does require more

working memory as Vorbis has no static probability model; the vector

codebooks used in the first stage of decoding from the bitstream are

packed in their entirety into the Vorbis bitstream headers. In

packed form, these codebooks occupy only a few kilobytes; the extent

to which they are pre-decoded into a cache is the dominant factor in

decoder memory usage.

Vorbis provides none of its own framing, synchronization or protection

against errors; it is solely a method of accepting input audio,

dividing it into individual frames and compressing these frames into

raw, unformatted 'packets'. The decoder then accepts these raw

packets in sequence, decodes them, synthesizes audio frames from

them, and reassembles the frames into a facsimile of the original

audio stream. Vorbis is a free-form variable bit rate (VBR) codec and packets have no

minimum size, maximum size, or fixed/expected size.  Packets

are designed that they may be truncated (or padded) and remain

decodable; this is not to be considered an error condition and is used

extensively in bitrate management in peeling.  Both the transport

mechanism and decoder must allow that a packet may be any size, or

end before or after packet decode expects.

Vorbis packets are thus intended to be used with a transport mechanism

that provides free-form framing, sync, positioning and error correction

in accordance with these design assumptions, such as Ogg (for file

transport) or RTP (for network multicast).  For purposes of a few

examples in this document, we will assume that Vorbis is to be

embedded in an Ogg stream specifically, although this is by no means a

requirement or fundamental assumption in the Vorbis design.

The specification for embedding Vorbis into

an Ogg transport stream is in \xref{vorbis:over:ogg}.

\subsubsection{Codec Setup and Probability Model}

Vorbis' heritage is as a research CODEC and its current design

reflects a desire to allow multiple decades of continuous encoder

improvement before running out of room within the codec specification.

For these reasons, configurable aspects of codec setup intentionally

lean toward the extreme of forward adaptive.

The single most controversial design decision in Vorbis (and the most

unusual for a Vorbis developer to keep in mind) is that the entire

probability model of the codec, the Huffman and VQ codebooks, is

packed into the bitstream header along with extensive CODEC setup

parameters (often several hundred fields).  This makes it impossible,

as it would be with MPEG audio layers, to embed a simple frame type

flag in each audio packet, or begin decode at any frame in the stream

without having previously fetched the codec setup header.

\begin{note}

Vorbis \emph{can} initiate decode at any arbitrary packet within a

bitstream so long as the codec has been initialized/setup with the

setup headers.

\end{note}

Thus, Vorbis headers are both required for decode to begin and

relatively large as bitstream headers go.  The header size is

unbounded, although for streaming a rule-of-thumb of 4kB or less is

recommended (and Xiph.Org's Vorbis encoder follows this suggestion).

Our own design work indicates the primary liability of the

required header is in mindshare; it is an unusual design and thus

causes some amount of complaint among engineers as this runs against

current design trends (and also points out limitations in some

existing software/interface designs, such as Windows' ACM codec

framework).  However, we find that it does not fundamentally limit

Vorbis' suitable application space.

\subsubsection{Format Specification}

The Vorbis format is well-defined by its decode specification; any

encoder that produces packets that are correctly decoded by the

reference Vorbis decoder described below may be considered a proper

Vorbis encoder.  A decoder must faithfully and completely implement

the specification defined below (except where noted) to be considered

a proper Vorbis decoder.

\subsubsection{Hardware Profile}

Although Vorbis decode is computationally simple, it may still run

into specific limitations of an embedded design.  For this reason,

embedded designs are allowed to deviate in limited ways from the

`full' decode specification yet still be certified compliant.  These

optional omissions are labelled in the spec where relevant.

\subsection{Decoder Configuration}

Decoder setup consists of configuration of multiple, self-contained

component abstractions that perform specific functions in the decode

pipeline.  Each different component instance of a specific type is

semantically interchangeable; decoder configuration consists both of

internal component configuration, as well as arrangement of specific

instances into a decode pipeline.  Componentry arrangement is roughly

as follows:

\begin{center}

\includegraphics[width=\textwidth]{components}

\captionof{figure}{decoder pipeline configuration}

\end{center}

\subsubsection{Global Config}

Global codec configuration consists of a few audio related fields

(sample rate, channels), Vorbis version (always '0' in Vorbis I),

bitrate hints, and the lists of component instances.  All other

configuration is in the context of specific components.

\subsubsection{Mode}

Each Vorbis frame is coded according to a master 'mode'.  A bitstream

may use one or many modes.

The mode mechanism is used to encode a frame according to one of

multiple possible methods with the intention of choosing a method best

suited to that frame.  Different modes are, e.g. how frame size

is changed from frame to frame. The mode number of a frame serves as a

top level configuration switch for all other specific aspects of frame

decode.

A 'mode' configuration consists of a frame size setting, window type

(always 0, the Vorbis window, in Vorbis I), transform type (always

type 0, the MDCT, in Vorbis I) and a mapping number.  The mapping

number specifies which mapping configuration instance to use for

low-level packet decode and synthesis.

\subsubsection{Mapping}

A mapping contains a channel coupling description and a list of

'submaps' that bundle sets of channel vectors together for grouped

encoding and decoding. These submaps are not references to external

components; the submap list is internal and specific to a mapping.

A 'submap' is a configuration/grouping that applies to a subset of

floor and residue vectors within a mapping.  The submap functions as a

last layer of indirection such that specific special floor or residue

settings can be applied not only to all the vectors in a given mode,

but also specific vectors in a specific mode.  Each submap specifies

the proper floor and residue instance number to use for decoding that

submap's spectral floor and spectral residue vectors.

As an example:

Assume a Vorbis stream that contains six channels in the standard 5.1

format.  The sixth channel, as is normal in 5.1, is bass only.

Therefore it would be wasteful to encode a full-spectrum version of it

as with the other channels.  The submapping mechanism can be used to

apply a full range floor and residue encoding to channels 0 through 4,

and a bass-only representation to the bass channel, thus saving space.

In this example, channels 0-4 belong to submap 0 (which indicates use

of a full-range floor) and channel 5 belongs to submap 1, which uses a

bass-only representation.

\subsubsection{Floor}

Vorbis encodes a spectral 'floor' vector for each PCM channel.  This

vector is a low-resolution representation of the audio spectrum for

the given channel in the current frame, generally used akin to a

whitening filter.  It is named a 'floor' because the Xiph.Org

reference encoder has historically used it as a unit-baseline for

spectral resolution.

A floor encoding may be of two types.  Floor 0 uses a packed LSP

representation on a dB amplitude scale and Bark frequency scale.

Floor 1 represents the curve as a piecewise linear interpolated

representation on a dB amplitude scale and linear frequency scale.

The two floors are semantically interchangeable in

encoding/decoding. However, floor type 1 provides more stable

inter-frame behavior, and so is the preferred choice in all

coupled-stereo and high bitrate modes.  Floor 1 is also considerably

less expensive to decode than floor 0.

Floor 0 is not to be considered deprecated, but it is of limited

modern use.  No known Vorbis encoder past Xiph.Org's own beta 4 makes

use of floor 0.

The values coded/decoded by a floor are both compactly formatted and

make use of entropy coding to save space.  For this reason, a floor

configuration generally refers to multiple codebooks in the codebook

component list.  Entropy coding is thus provided as an abstraction,

and each floor instance may choose from any and all available

codebooks when coding/decoding.

\subsubsection{Residue}

The spectral residue is the fine structure of the audio spectrum

once the floor curve has been subtracted out.  In simplest terms, it

is coded in the bitstream using cascaded (multi-pass) vector

quantization according to one of three specific packing/coding

algorithms numbered 0 through 2.  The packing algorithm details are

configured by residue instance.  As with the floor components, the

final VQ/entropy encoding is provided by external codebook instances

and each residue instance may choose from any and all available

codebooks.

\subsubsection{Codebooks}

Codebooks are a self-contained abstraction that perform entropy

decoding and, optionally, use the entropy-decoded integer value as an

offset into an index of output value vectors, returning the indicated

vector of values.

The entropy coding in a Vorbis I codebook is provided by a standard

Huffman binary tree representation.  This tree is tightly packed using

one of several methods, depending on whether codeword lengths are

ordered or unordered, or the tree is sparse.

The codebook vector index is similarly packed according to index

characteristic.  Most commonly, the vector index is encoded as a

single list of values of possible values that are then permuted into

a list of n-dimensional rows (lattice VQ).

\subsection{High-level Decode Process}

\subsubsection{Decode Setup}

Before decoding can begin, a decoder must initialize using the

bitstream headers matching the stream to be decoded.  Vorbis uses

three header packets; all are required, in-order, by this

specification. Once set up, decode may begin at any audio packet

belonging to the Vorbis stream. In Vorbis I, all packets after the

three initial headers are audio packets.

The header packets are, in order, the identification

header, the comments header, and the setup header.

\paragraph{Identification Header}

The identification header identifies the bitstream as Vorbis, Vorbis

version, and the simple audio characteristics of the stream such as

sample rate and number of channels.

\paragraph{Comment Header}

The comment header includes user text comments (``tags'') and a vendor

string for the application/library that produced the bitstream.  The

encoding and proper use of the comment header is described in \xref{vorbis:spec:comment}.

\paragraph{Setup Header}

The setup header includes extensive CODEC setup information as well as

the complete VQ and Huffman codebooks needed for decode.

\subsubsection{Decode Procedure}

The decoding and synthesis procedure for all audio packets is

fundamentally the same.

\begin{enumerate}

\item decode packet type flag

\item decode mode number

\item decode window shape (long windows only)

\item decode floor

\item decode residue into residue vectors

\item inverse channel coupling of residue vectors

\item generate floor curve from decoded floor data

\item compute dot product of floor and residue, producing audio spectrum vector

\item inverse monolithic transform of audio spectrum vector, always an MDCT in Vorbis I

\item overlap/add left-hand output of transform with right-hand output of previous frame

\item store right hand-data from transform of current frame for future lapping

\item if not first frame, return results of overlap/add as audio result of current frame

\end{enumerate}

Note that clever rearrangement of the synthesis arithmetic is

possible; as an example, one can take advantage of symmetries in the

MDCT to store the right-hand transform data of a partial MDCT for a

50\% inter-frame buffer space savings, and then complete the transform

later before overlap/add with the next frame.  This optimization

produces entirely equivalent output and is naturally perfectly legal.

The decoder must be \emph{entirely mathematically equivalent} to the

specification, it need not be a literal semantic implementation.

\paragraph{Packet type decode}

Vorbis I uses four packet types. The first three packet types mark each

of the three Vorbis headers described above. The fourth packet type

marks an audio packet. All other packet types are reserved; packets

marked with a reserved type should be ignored.

Following the three header packets, all packets in a Vorbis I stream

are audio.  The first step of audio packet decode is to read and

verify the packet type; \emph{a non-audio packet when audio is expected

indicates stream corruption or a non-compliant stream. The decoder

must ignore the packet and not attempt decoding it to

audio}.

\paragraph{Mode decode}

Vorbis allows an encoder to set up multiple, numbered packet 'modes',

as described earlier, all of which may be used in a given Vorbis

stream. The mode is encoded as an integer used as a direct offset into

the mode instance index.

\paragraph{Window shape decode (long windows only)} \label{vorbis:spec:window}

Vorbis frames may be one of two PCM sample sizes specified during

codec setup.  In Vorbis I, legal frame sizes are powers of two from 64

to 8192 samples.  Aside from coupling, Vorbis handles channels as

independent vectors and these frame sizes are in samples per channel.

Vorbis uses an overlapping transform, namely the MDCT, to blend one

frame into the next, avoiding most inter-frame block boundary

artifacts.  The MDCT output of one frame is windowed according to MDCT

requirements, overlapped 50\% with the output of the previous frame and

added.  The window shape assures seamless reconstruction.

This is easy to visualize in the case of equal sized-windows:

\begin{center}

\includegraphics[width=\textwidth]{window1}

\captionof{figure}{overlap of two equal-sized windows}

\end{center}

And slightly more complex in the case of overlapping unequal sized

windows:

\begin{center}

\includegraphics[width=\textwidth]{window2}

\captionof{figure}{overlap of a long and a short window}

\end{center}

In the unequal-sized window case, the window shape of the long window

must be modified for seamless lapping as above.  It is possible to

correctly infer window shape to be applied to the current window from

knowing the sizes of the current, previous and next window.  It is

legal for a decoder to use this method. However, in the case of a long

window (short windows require no modification), Vorbis also codes two

flag bits to specify pre- and post- window shape.  Although not

strictly necessary for function, this minor redundancy allows a packet

to be fully decoded to the point of lapping entirely independently of

any other packet, allowing easier abstraction of decode layers as well

as allowing a greater level of easy parallelism in encode and

decode.

A description of valid window functions for use with an inverse MDCT

can be found in \cite{Sporer/Brandenburg/Edler}.  Vorbis windows

all use the slope function

\[ y = \sin(.5*\pi \, \sin^2((x+.5)/n*\pi)) . \]

\paragraph{floor decode}

Each floor is encoded/decoded in channel order, however each floor

belongs to a 'submap' that specifies which floor configuration to

use.  All floors are decoded before residue decode begins.

\paragraph{residue decode}

Although the number of residue vectors equals the number of channels,

channel coupling may mean that the raw residue vectors extracted

during decode do not map directly to specific channels.  When channel

coupling is in use, some vectors will correspond to coupled magnitude

or angle.  The coupling relationships are described in the codec setup

and may differ from frame to frame, due to different mode numbers.

Vorbis codes residue vectors in groups by submap; the coding is done

in submap order from submap 0 through n-1.  This differs from floors

which are coded using a configuration provided by submap number, but

are coded individually in channel order.

\paragraph{inverse channel coupling}

A detailed discussion of stereo in the Vorbis codec can be found in

the document \href{stereo.html}{Stereo Channel Coupling in the

Vorbis CODEC}.  Vorbis is not limited to only stereo coupling, but

the stereo document also gives a good overview of the generic coupling

mechanism.

Vorbis coupling applies to pairs of residue vectors at a time;

decoupling is done in-place a pair at a time in the order and using

the vectors specified in the current mapping configuration.  The

decoupling operation is the same for all pairs, converting square

polar representation (where one vector is magnitude and the second

angle) back to Cartesian representation.

After decoupling, in order, each pair of vectors on the coupling list,

the resulting residue vectors represent the fine spectral detail

of each output channel.

\paragraph{generate floor curve}

The decoder may choose to generate the floor curve at any appropriate

time.  It is reasonable to generate the output curve when the floor

data is decoded from the raw packet, or it can be generated after

inverse coupling and applied to the spectral residue directly,

combining generation and the dot product into one step and eliminating

some working space.

Both floor 0 and floor 1 generate a linear-range, linear-domain output

vector to be multiplied (dot product) by the linear-range,

linear-domain spectral residue.

\paragraph{compute floor/residue dot product}

This step is straightforward; for each output channel, the decoder

multiplies the floor curve and residue vectors element by element,

producing the finished audio spectrum of each channel.

% TODO/FIXME: The following two paragraphs have identical twins

%   in section 4 (under "dot product")

One point is worth mentioning about this dot product; a common mistake

in a fixed point implementation might be to assume that a 32 bit

fixed-point representation for floor and residue and direct

multiplication of the vectors is sufficient for acceptable spectral

depth in all cases because it happens to mostly work with the current

Xiph.Org reference encoder.

However, floor vector values can span \~{}140dB (\~{}24 bits unsigned), and

the audio spectrum vector should represent a minimum of 120dB (\~{}21

bits with sign), even when output is to a 16 bit PCM device.  For the

residue vector to represent full scale if the floor is nailed to

$-140$dB, it must be able to span 0 to $+140$dB.  For the residue vector

to reach full scale if the floor is nailed at 0dB, it must be able to

represent $-140$dB to $+0$dB.  Thus, in order to handle full range

dynamics, a residue vector may span $-140$dB to $+140$dB entirely within

spec.  A 280dB range is approximately 48 bits with sign; thus the

residue vector must be able to represent a 48 bit range and the dot

product must be able to handle an effective 48 bit times 24 bit

multiplication.  This range may be achieved using large (64 bit or

larger) integers, or implementing a movable binary point

representation.

\paragraph{inverse monolithic transform (MDCT)}

The audio spectrum is converted back into time domain PCM audio via an

inverse Modified Discrete Cosine Transform (MDCT).  A detailed

description of the MDCT is available in \cite{Sporer/Brandenburg/Edler}.

Note that the PCM produced directly from the MDCT is not yet finished

audio; it must be lapped with surrounding frames using an appropriate

window (such as the Vorbis window) before the MDCT can be considered

orthogonal.

\paragraph{overlap/add data}

Windowed MDCT output is overlapped and added with the right hand data

of the previous window such that the 3/4 point of the previous window

is aligned with the 1/4 point of the current window (as illustrated in

the window overlap diagram). At this point, the audio data between the

center of the previous frame and the center of the current frame is

now finished and ready to be returned.

\paragraph{cache right hand data}

The decoder must cache the right hand portion of the current frame to

be lapped with the left hand portion of the next frame.

\paragraph{return finished audio data}

The overlapped portion produced from overlapping the previous and

current frame data is finished data to be returned by the decoder.

This data spans from the center of the previous window to the center

of the current window.  In the case of same-sized windows, the amount

of data to return is one-half block consisting of and only of the

overlapped portions. When overlapping a short and long window, much of

the returned range is not actually overlap.  This does not damage

transform orthogonality.  Pay attention however to returning the

correct data range; the amount of data to be returned is:

\begin{Verbatim}[commandchars=\\\{\}]

window\_blocksize(previous\_window)/4+window\_blocksize(current\_window)/4

\end{Verbatim}

from the center of the previous window to the center of the current

window.

Data is not returned from the first frame; it must be used to 'prime'

the decode engine.  The encoder accounts for this priming when

calculating PCM offsets; after the first frame, the proper PCM output

offset is '0' (as no data has been returned yet).