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<title>Ogg Vorbis Documentation</title>
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</head>
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<body>
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<div id="xiphlogo">
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<a href="http://www.xiph.org/"><img src="fish_xiph_org.png" alt="Fish Logo and Xiph.Org"/></a>
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</div>
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<h1>Ogg Vorbis stereo-specific channel coupling discussion</h1>
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<h2>Abstract</h2>
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<p>The Vorbis audio CODEC provides a channel coupling
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mechanisms designed to reduce effective bitrate by both eliminating
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interchannel redundancy and eliminating stereo image information
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labeled inaudible or undesirable according to spatial psychoacoustic
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models. This document describes both the mechanical coupling
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mechanisms available within the Vorbis specification, as well as the
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specific stereo coupling models used by the reference
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<tt>libvorbis</tt> codec provided by xiph.org.</p>
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<h2>Mechanisms</h2>
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<p>In encoder release beta 4 and earlier, Vorbis supported multiple
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channel encoding, but the channels were encoded entirely separately
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with no cross-analysis or redundancy elimination between channels.
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This multichannel strategy is very similar to the mp3's <em>dual
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stereo</em> mode and Vorbis uses the same name for its analogous
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uncoupled multichannel modes.</p>
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<p>However, the Vorbis spec provides for, and Vorbis release 1.0 rc1 and
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later implement a coupled channel strategy. Vorbis has two specific
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mechanisms that may be used alone or in conjunction to implement
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channel coupling. The first is <em>channel interleaving</em> via
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residue backend type 2, and the second is <em>square polar
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mapping</em>. These two general mechanisms are particularly well
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suited to coupling due to the structure of Vorbis encoding, as we'll
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explore below, and using both we can implement both totally
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<em>lossless stereo image coupling</em> [bit-for-bit decode-identical
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to uncoupled modes], as well as various lossy models that seek to
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eliminate inaudible or unimportant aspects of the stereo image in
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order to enhance bitrate. The exact coupling implementation is
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generalized to allow the encoder a great deal of flexibility in
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implementation of a stereo or surround model without requiring any
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significant complexity increase over the combinatorially simpler
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mid/side joint stereo of mp3 and other current audio codecs.</p>
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<p>A particular Vorbis bitstream may apply channel coupling directly to
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more than a pair of channels; polar mapping is hierarchical such that
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polar coupling may be extrapolated to an arbitrary number of channels
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and is not restricted to only stereo, quadraphonics, ambisonics or 5.1
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surround. However, the scope of this document restricts itself to the
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stereo coupling case.</p>
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<a name="sqpm"></a>
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<h3>Square Polar Mapping</h3>
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<h4>maximal correlation</h4>
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<p>Recall that the basic structure of a a Vorbis I stream first generates
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from input audio a spectral 'floor' function that serves as an
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MDCT-domain whitening filter. This floor is meant to represent the
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rough envelope of the frequency spectrum, using whatever metric the
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encoder cares to define. This floor is subtracted from the log
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frequency spectrum, effectively normalizing the spectrum by frequency.
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Each input channel is associated with a unique floor function.</p>
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<p>The basic idea behind any stereo coupling is that the left and right
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channels usually correlate. This correlation is even stronger if one
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first accounts for energy differences in any given frequency band
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across left and right; think for example of individual instruments
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mixed into different portions of the stereo image, or a stereo
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recording with a dominant feature not perfectly in the center. The
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floor functions, each specific to a channel, provide the perfect means
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of normalizing left and right energies across the spectrum to maximize
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correlation before coupling. This feature of the Vorbis format is not
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a convenient accident.</p>
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<p>Because we strive to maximally correlate the left and right channels
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and generally succeed in doing so, left and right residue is typically
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nearly identical. We could use channel interleaving (discussed below)
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alone to efficiently remove the redundancy between the left and right
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channels as a side effect of entropy encoding, but a polar
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representation gives benefits when left/right correlation is
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strong.</p>
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<h4>point and diffuse imaging</h4>
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<p>The first advantage of a polar representation is that it effectively
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separates the spatial audio information into a 'point image'
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(magnitude) at a given frequency and located somewhere in the sound
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field, and a 'diffuse image' (angle) that fills a large amount of
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space simultaneously. Even if we preserve only the magnitude (point)
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data, a detailed and carefully chosen floor function in each channel
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provides us with a free, fine-grained, frequency relative intensity
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stereo*. Angle information represents diffuse sound fields, such as
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reverberation that fills the entire space simultaneously.</p>
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<p>*<em>Because the Vorbis model supports a number of different possible
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stereo models and these models may be mixed, we do not use the term
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'intensity stereo' talking about Vorbis; instead we use the terms
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'point stereo', 'phase stereo' and subcategories of each.</em></p>
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<p>The majority of a stereo image is representable by polar magnitude
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alone, as strong sounds tend to be produced at near-point sources;
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even non-diffuse, fast, sharp echoes track very accurately using
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magnitude representation almost alone (for those experimenting with
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Vorbis tuning, this strategy works much better with the precise,
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piecewise control of floor 1; the continuous approximation of floor 0
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results in unstable imaging). Reverberation and diffuse sounds tend
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to contain less energy and be psychoacoustically dominated by the
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point sources embedded in them. Thus, we again tend to concentrate
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more represented energy into a predictably smaller number of numbers.
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Separating representation of point and diffuse imaging also allows us
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to model and manipulate point and diffuse qualities separately.</p>
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<h4>controlling bit leakage and symbol crosstalk</h4>
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<p>Because polar
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representation concentrates represented energy into fewer large
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values, we reduce bit 'leakage' during cascading (multistage VQ
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encoding) as a secondary benefit. A single large, monolithic VQ
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codebook is more efficient than a cascaded book due to entropy
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'crosstalk' among symbols between different stages of a multistage cascade.
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Polar representation is a way of further concentrating entropy into
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predictable locations so that codebook design can take steps to
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improve multistage codebook efficiency. It also allows us to cascade
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various elements of the stereo image independently.</p>
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<h4>eliminating trigonometry and rounding</h4>
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<p>Rounding and computational complexity are potential problems with a
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polar representation. As our encoding process involves quantization,
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mixing a polar representation and quantization makes it potentially
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impossible, depending on implementation, to construct a coupled stereo
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mechanism that results in bit-identical decompressed output compared
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to an uncoupled encoding should the encoder desire it.</p>
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<p>Vorbis uses a mapping that preserves the most useful qualities of
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polar representation, relies only on addition/subtraction (during
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decode; high quality encoding still requires some trig), and makes it
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trivial before or after quantization to represent an angle/magnitude
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through a one-to-one mapping from possible left/right value
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permutations. We do this by basing our polar representation on the
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unit square rather than the unit-circle.</p>
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<p>Given a magnitude and angle, we recover left and right using the
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following function (note that A/B may be left/right or right/left
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depending on the coupling definition used by the encoder):</p>
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<pre>
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if(magnitude>0)
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if(angle>0){
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A=magnitude;
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B=magnitude-angle;
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}else{
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B=magnitude;
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A=magnitude+angle;
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}
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else
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if(angle>0){
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A=magnitude;
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B=magnitude+angle;
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}else{
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B=magnitude;
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A=magnitude-angle;
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}
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}
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</pre>
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<p>The function is antisymmetric for positive and negative magnitudes in
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order to eliminate a redundant value when quantizing. For example, if
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we're quantizing to integer values, we can visualize a magnitude of 5
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and an angle of -2 as follows:</p>
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<p><img src="squarepolar.png" alt="square polar"/></p>
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<p>This representation loses or replicates no values; if the range of A
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and B are integral -5 through 5, the number of possible Cartesian
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permutations is 121. Represented in square polar notation, the
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possible values are:</p>
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<pre>
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0, 0
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-1,-2 -1,-1 -1, 0 -1, 1
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1,-2 1,-1 1, 0 1, 1
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-2,-4 -2,-3 -2,-2 -2,-1 -2, 0 -2, 1 -2, 2 -2, 3
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2,-4 2,-3 ... following the pattern ...
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... 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 5, 7 5, 8 5, 9
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</pre>
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<p>...for a grand total of 121 possible values, the same number as in
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Cartesian representation (note that, for example, <tt>5,-10</tt> is
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the same as <tt>-5,10</tt>, so there's no reason to represent
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both. 2,10 cannot happen, and there's no reason to account for it.)
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It's also obvious that this mapping is exactly reversible.</p>
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<h3>Channel interleaving</h3>
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<p>We can remap and A/B vector using polar mapping into a magnitude/angle
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vector, and it's clear that, in general, this concentrates energy in
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the magnitude vector and reduces the amount of information to encode
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in the angle vector. Encoding these vectors independently with
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residue backend #0 or residue backend #1 will result in bitrate
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savings. However, there are still implicit correlations between the
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magnitude and angle vectors. The most obvious is that the amplitude
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of the angle is bounded by its corresponding magnitude value.</p>
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<p>Entropy coding the results, then, further benefits from the entropy
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model being able to compress magnitude and angle simultaneously. For
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this reason, Vorbis implements residue backend #2 which pre-interleaves
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a number of input vectors (in the stereo case, two, A and B) into a
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single output vector (with the elements in the order of
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A_0, B_0, A_1, B_1, A_2 ... A_n-1, B_n-1) before entropy encoding. Thus
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each vector to be coded by the vector quantization backend consists of
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matching magnitude and angle values.</p>
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<p>The astute reader, at this point, will notice that in the theoretical
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case in which we can use monolithic codebooks of arbitrarily large
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size, we can directly interleave and encode left and right without
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polar mapping; in fact, the polar mapping does not appear to lend any
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benefit whatsoever to the efficiency of the entropy coding. In fact,
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it is perfectly possible and reasonable to build a Vorbis encoder that
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dispenses with polar mapping entirely and merely interleaves the
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channel. Libvorbis based encoders may configure such an encoding and
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it will work as intended.</p>
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<p>However, when we leave the ideal/theoretical domain, we notice that
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polar mapping does give additional practical benefits, as discussed in
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the above section on polar mapping and summarized again here:</p>
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<ul>
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<li>Polar mapping aids in controlling entropy 'leakage' between stages
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of a cascaded codebook.</li>
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<li>Polar mapping separates the stereo image
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into point and diffuse components which may be analyzed and handled
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differently.</li>
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</ul>
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<h2>Stereo Models</h2>
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<h3>Dual Stereo</h3>
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<p>Dual stereo refers to stereo encoding where the channels are entirely
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separate; they are analyzed and encoded as entirely distinct entities.
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This terminology is familiar from mp3.</p>
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<h3>Lossless Stereo</h3>
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<p>Using polar mapping and/or channel interleaving, it's possible to
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couple Vorbis channels losslessly, that is, construct a stereo
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coupling encoding that both saves space but also decodes
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bit-identically to dual stereo. OggEnc 1.0 and later uses this
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mode in all high-bitrate encoding.</p>
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<p>Overall, this stereo mode is overkill; however, it offers a safe
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alternative to users concerned about the slightest possible
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degradation to the stereo image or archival quality audio.</p>
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<h3>Phase Stereo</h3>
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<p>Phase stereo is the least aggressive means of gracefully dropping
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resolution from the stereo image; it affects only diffuse imaging.</p>
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<p>It's often quoted that the human ear is deaf to signal phase above
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about 4kHz; this is nearly true and a passable rule of thumb, but it
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can be demonstrated that even an average user can tell the difference
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between high frequency in-phase and out-of-phase noise. Obviously
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then, the statement is not entirely true. However, it's also the case
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that one must resort to nearly such an extreme demonstration before
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finding the counterexample.</p>
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<p>'Phase stereo' is simply a more aggressive quantization of the polar
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angle vector; above 4kHz it's generally quite safe to quantize noise
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and noisy elements to only a handful of allowed phases, or to thin the
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phase with respect to the magnitude. The phases of high amplitude
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pure tones may or may not be preserved more carefully (they are
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relatively rare and L/R tend to be in phase, so there is generally
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little reason not to spend a few more bits on them)</p>
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<h4>example: eight phase stereo</h4>
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<p>Vorbis may implement phase stereo coupling by preserving the entirety
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of the magnitude vector (essential to fine amplitude and energy
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resolution overall) and quantizing the angle vector to one of only
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four possible values. Given that the magnitude vector may be positive
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or negative, this results in left and right phase having eight
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possible permutation, thus 'eight phase stereo':</p>
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<p><img src="eightphase.png" alt="eight phase"/></p>
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<p>Left and right may be in phase (positive or negative), the most common
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case by far, or out of phase by 90 or 180 degrees.</p>
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<h4>example: four phase stereo</h4>
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<p>Similarly, four phase stereo takes the quantization one step further;
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it allows only in-phase and 180 degree out-out-phase signals:</p>
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<p><img src="fourphase.png" alt="four phase"/></p>
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<h3>example: point stereo</h3>
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<p>Point stereo eliminates the possibility of out-of-phase signal
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entirely. Any diffuse quality to a sound source tends to collapse
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inward to a point somewhere within the stereo image. A practical
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example would be balanced reverberations within a large, live space;
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normally the sound is diffuse and soft, giving a sonic impression of
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volume. In point-stereo, the reverberations would still exist, but
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sound fairly firmly centered within the image (assuming the
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reverberation was centered overall; if the reverberation is stronger
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to the left, then the point of localization in point stereo would be
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to the left). This effect is most noticeable at low and mid
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frequencies and using headphones (which grant perfect stereo
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separation). Point stereo is is a graceful but generally easy to
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detect degradation to the sound quality and is thus used in frequency
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ranges where it is least noticeable.</p>
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<h3>Mixed Stereo</h3>
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<p>Mixed stereo is the simultaneous use of more than one of the above
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stereo encoding models, generally using more aggressive modes in
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higher frequencies, lower amplitudes or 'nearly' in-phase sound.</p>
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<p>It is also the case that near-DC frequencies should be encoded using
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lossless coupling to avoid frame blocking artifacts.</p>
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<h3>Vorbis Stereo Modes</h3>
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<p>Vorbis, as of 1.0, uses lossless stereo and a number of mixed modes
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constructed out of lossless and point stereo. Phase stereo was used
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in the rc2 encoder, but is not currently used for simplicity's sake. It
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will likely be re-added to the stereo model in the future.</p>
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<div id="copyright">
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The Xiph Fish Logo is a
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trademark (™) of Xiph.Org.<br/>
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These pages © 1994 - 2005 Xiph.Org. All rights reserved.
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</div>
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