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| 70 | <a href="https://xiph.org/"><img src="fish_xiph_org.png" alt="Fish Logo and Xiph.Org"/></a>
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| 71 | </div>
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| 72 |
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| 73 | <h1>Ogg Vorbis stereo-specific channel coupling discussion</h1>
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| 74 |
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| 75 | <h2>Abstract</h2>
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| 76 |
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| 77 | <p>The Vorbis audio CODEC provides a channel coupling
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| 78 | mechanisms designed to reduce effective bitrate by both eliminating
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| 79 | interchannel redundancy and eliminating stereo image information
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| 80 | labeled inaudible or undesirable according to spatial psychoacoustic
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| 81 | models. This document describes both the mechanical coupling
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| 82 | mechanisms available within the Vorbis specification, as well as the
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| 83 | specific stereo coupling models used by the reference
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| 84 | <tt>libvorbis</tt> codec provided by xiph.org.</p>
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| 85 |
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| 86 | <h2>Mechanisms</h2>
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| 87 |
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| 88 | <p>In encoder release beta 4 and earlier, Vorbis supported multiple
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| 89 | channel encoding, but the channels were encoded entirely separately
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| 90 | with no cross-analysis or redundancy elimination between channels.
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| 91 | This multichannel strategy is very similar to the mp3's <em>dual
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| 92 | stereo</em> mode and Vorbis uses the same name for its analogous
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| 93 | uncoupled multichannel modes.</p>
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| 94 |
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| 95 | <p>However, the Vorbis spec provides for, and Vorbis release 1.0 rc1 and
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| 96 | later implement a coupled channel strategy. Vorbis has two specific
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| 97 | mechanisms that may be used alone or in conjunction to implement
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| 98 | channel coupling. The first is <em>channel interleaving</em> via
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| 99 | residue backend type 2, and the second is <em>square polar
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| 100 | mapping</em>. These two general mechanisms are particularly well
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| 101 | suited to coupling due to the structure of Vorbis encoding, as we'll
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| 102 | explore below, and using both we can implement both totally
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| 103 | <em>lossless stereo image coupling</em> [bit-for-bit decode-identical
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| 104 | to uncoupled modes], as well as various lossy models that seek to
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| 105 | eliminate inaudible or unimportant aspects of the stereo image in
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| 106 | order to enhance bitrate. The exact coupling implementation is
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| 107 | generalized to allow the encoder a great deal of flexibility in
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| 108 | implementation of a stereo or surround model without requiring any
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| 109 | significant complexity increase over the combinatorially simpler
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| 110 | mid/side joint stereo of mp3 and other current audio codecs.</p>
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| 111 |
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| 112 | <p>A particular Vorbis bitstream may apply channel coupling directly to
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| 113 | more than a pair of channels; polar mapping is hierarchical such that
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| 114 | polar coupling may be extrapolated to an arbitrary number of channels
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| 115 | and is not restricted to only stereo, quadraphonics, ambisonics or 5.1
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| 116 | surround. However, the scope of this document restricts itself to the
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| 117 | stereo coupling case.</p>
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| 118 |
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| 119 | <a name="sqpm"></a>
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| 120 | <h3>Square Polar Mapping</h3>
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| 121 |
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| 122 | <h4>maximal correlation</h4>
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| 123 |
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| 124 | <p>Recall that the basic structure of a a Vorbis I stream first generates
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| 125 | from input audio a spectral 'floor' function that serves as an
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| 126 | MDCT-domain whitening filter. This floor is meant to represent the
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| 127 | rough envelope of the frequency spectrum, using whatever metric the
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| 128 | encoder cares to define. This floor is subtracted from the log
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| 129 | frequency spectrum, effectively normalizing the spectrum by frequency.
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| 130 | Each input channel is associated with a unique floor function.</p>
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| 131 |
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| 132 | <p>The basic idea behind any stereo coupling is that the left and right
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| 133 | channels usually correlate. This correlation is even stronger if one
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| 134 | first accounts for energy differences in any given frequency band
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| 135 | across left and right; think for example of individual instruments
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| 136 | mixed into different portions of the stereo image, or a stereo
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| 137 | recording with a dominant feature not perfectly in the center. The
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| 138 | floor functions, each specific to a channel, provide the perfect means
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| 139 | of normalizing left and right energies across the spectrum to maximize
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| 140 | correlation before coupling. This feature of the Vorbis format is not
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| 141 | a convenient accident.</p>
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| 142 |
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| 143 | <p>Because we strive to maximally correlate the left and right channels
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| 144 | and generally succeed in doing so, left and right residue is typically
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| 145 | nearly identical. We could use channel interleaving (discussed below)
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| 146 | alone to efficiently remove the redundancy between the left and right
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| 147 | channels as a side effect of entropy encoding, but a polar
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| 148 | representation gives benefits when left/right correlation is
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| 149 | strong.</p>
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| 150 |
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| 151 | <h4>point and diffuse imaging</h4>
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| 152 |
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| 153 | <p>The first advantage of a polar representation is that it effectively
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| 154 | separates the spatial audio information into a 'point image'
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| 155 | (magnitude) at a given frequency and located somewhere in the sound
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| 156 | field, and a 'diffuse image' (angle) that fills a large amount of
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| 157 | space simultaneously. Even if we preserve only the magnitude (point)
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| 158 | data, a detailed and carefully chosen floor function in each channel
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| 159 | provides us with a free, fine-grained, frequency relative intensity
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| 160 | stereo*. Angle information represents diffuse sound fields, such as
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| 161 | reverberation that fills the entire space simultaneously.</p>
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| 162 |
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| 163 | <p>*<em>Because the Vorbis model supports a number of different possible
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| 164 | stereo models and these models may be mixed, we do not use the term
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| 165 | 'intensity stereo' talking about Vorbis; instead we use the terms
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| 166 | 'point stereo', 'phase stereo' and subcategories of each.</em></p>
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| 167 |
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| 168 | <p>The majority of a stereo image is representable by polar magnitude
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| 169 | alone, as strong sounds tend to be produced at near-point sources;
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| 170 | even non-diffuse, fast, sharp echoes track very accurately using
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| 171 | magnitude representation almost alone (for those experimenting with
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| 172 | Vorbis tuning, this strategy works much better with the precise,
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| 173 | piecewise control of floor 1; the continuous approximation of floor 0
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| 174 | results in unstable imaging). Reverberation and diffuse sounds tend
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| 175 | to contain less energy and be psychoacoustically dominated by the
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| 176 | point sources embedded in them. Thus, we again tend to concentrate
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| 177 | more represented energy into a predictably smaller number of numbers.
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| 178 | Separating representation of point and diffuse imaging also allows us
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| 179 | to model and manipulate point and diffuse qualities separately.</p>
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| 180 |
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| 181 | <h4>controlling bit leakage and symbol crosstalk</h4>
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| 182 |
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| 183 | <p>Because polar
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| 184 | representation concentrates represented energy into fewer large
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| 185 | values, we reduce bit 'leakage' during cascading (multistage VQ
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| 186 | encoding) as a secondary benefit. A single large, monolithic VQ
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| 187 | codebook is more efficient than a cascaded book due to entropy
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| 188 | 'crosstalk' among symbols between different stages of a multistage cascade.
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| 189 | Polar representation is a way of further concentrating entropy into
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| 190 | predictable locations so that codebook design can take steps to
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| 191 | improve multistage codebook efficiency. It also allows us to cascade
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| 192 | various elements of the stereo image independently.</p>
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| 193 |
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| 194 | <h4>eliminating trigonometry and rounding</h4>
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| 195 |
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| 196 | <p>Rounding and computational complexity are potential problems with a
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| 197 | polar representation. As our encoding process involves quantization,
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| 198 | mixing a polar representation and quantization makes it potentially
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| 199 | impossible, depending on implementation, to construct a coupled stereo
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| 200 | mechanism that results in bit-identical decompressed output compared
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| 201 | to an uncoupled encoding should the encoder desire it.</p>
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| 202 |
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| 203 | <p>Vorbis uses a mapping that preserves the most useful qualities of
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| 204 | polar representation, relies only on addition/subtraction (during
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| 205 | decode; high quality encoding still requires some trig), and makes it
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| 206 | trivial before or after quantization to represent an angle/magnitude
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| 207 | through a one-to-one mapping from possible left/right value
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| 208 | permutations. We do this by basing our polar representation on the
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| 209 | unit square rather than the unit-circle.</p>
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| 210 |
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| 211 | <p>Given a magnitude and angle, we recover left and right using the
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| 212 | following function (note that A/B may be left/right or right/left
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| 213 | depending on the coupling definition used by the encoder):</p>
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| 214 |
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| 215 | <pre>
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| 216 | if(magnitude>0)
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| 217 | if(angle>0){
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| 218 | A=magnitude;
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| 219 | B=magnitude-angle;
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| 220 | }else{
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| 221 | B=magnitude;
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| 222 | A=magnitude+angle;
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| 223 | }
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| 224 | else
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| 225 | if(angle>0){
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| 226 | A=magnitude;
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| 227 | B=magnitude+angle;
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| 228 | }else{
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| 229 | B=magnitude;
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| 230 | A=magnitude-angle;
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| 231 | }
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| 232 | }
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| 233 | </pre>
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| 234 |
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| 235 | <p>The function is antisymmetric for positive and negative magnitudes in
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| 236 | order to eliminate a redundant value when quantizing. For example, if
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| 237 | we're quantizing to integer values, we can visualize a magnitude of 5
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| 238 | and an angle of -2 as follows:</p>
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| 239 |
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| 240 | <p><img src="squarepolar.png" alt="square polar"/></p>
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| 241 |
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| 242 | <p>This representation loses or replicates no values; if the range of A
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| 243 | and B are integral -5 through 5, the number of possible Cartesian
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| 244 | permutations is 121. Represented in square polar notation, the
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| 245 | possible values are:</p>
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| 246 |
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| 247 | <pre>
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| 248 | 0, 0
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| 249 |
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| 250 | -1,-2 -1,-1 -1, 0 -1, 1
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| 251 |
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| 252 | 1,-2 1,-1 1, 0 1, 1
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| 253 |
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| 254 | -2,-4 -2,-3 -2,-2 -2,-1 -2, 0 -2, 1 -2, 2 -2, 3
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| 255 |
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| 256 | 2,-4 2,-3 ... following the pattern ...
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| 257 |
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| 258 | ... 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 5, 7 5, 8 5, 9
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| 259 |
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| 260 | </pre>
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| 261 |
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| 262 | <p>...for a grand total of 121 possible values, the same number as in
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| 263 | Cartesian representation (note that, for example, <tt>5,-10</tt> is
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| 264 | the same as <tt>-5,10</tt>, so there's no reason to represent
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| 265 | both. 2,10 cannot happen, and there's no reason to account for it.)
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| 266 | It's also obvious that this mapping is exactly reversible.</p>
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| 267 |
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| 268 | <h3>Channel interleaving</h3>
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| 269 |
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| 270 | <p>We can remap and A/B vector using polar mapping into a magnitude/angle
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| 271 | vector, and it's clear that, in general, this concentrates energy in
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| 272 | the magnitude vector and reduces the amount of information to encode
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| 273 | in the angle vector. Encoding these vectors independently with
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| 274 | residue backend #0 or residue backend #1 will result in bitrate
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| 275 | savings. However, there are still implicit correlations between the
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| 276 | magnitude and angle vectors. The most obvious is that the amplitude
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| 277 | of the angle is bounded by its corresponding magnitude value.</p>
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| 278 |
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| 279 | <p>Entropy coding the results, then, further benefits from the entropy
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| 280 | model being able to compress magnitude and angle simultaneously. For
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| 281 | this reason, Vorbis implements residue backend #2 which pre-interleaves
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| 282 | a number of input vectors (in the stereo case, two, A and B) into a
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| 283 | single output vector (with the elements in the order of
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| 284 | A_0, B_0, A_1, B_1, A_2 ... A_n-1, B_n-1) before entropy encoding. Thus
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| 285 | each vector to be coded by the vector quantization backend consists of
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| 286 | matching magnitude and angle values.</p>
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| 287 |
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| 288 | <p>The astute reader, at this point, will notice that in the theoretical
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| 289 | case in which we can use monolithic codebooks of arbitrarily large
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| 290 | size, we can directly interleave and encode left and right without
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| 291 | polar mapping; in fact, the polar mapping does not appear to lend any
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| 292 | benefit whatsoever to the efficiency of the entropy coding. In fact,
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| 293 | it is perfectly possible and reasonable to build a Vorbis encoder that
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| 294 | dispenses with polar mapping entirely and merely interleaves the
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| 295 | channel. Libvorbis based encoders may configure such an encoding and
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| 296 | it will work as intended.</p>
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| 297 |
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| 298 | <p>However, when we leave the ideal/theoretical domain, we notice that
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| 299 | polar mapping does give additional practical benefits, as discussed in
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| 300 | the above section on polar mapping and summarized again here:</p>
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| 301 |
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| 302 | <ul>
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| 303 | <li>Polar mapping aids in controlling entropy 'leakage' between stages
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| 304 | of a cascaded codebook.</li>
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| 305 | <li>Polar mapping separates the stereo image
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| 306 | into point and diffuse components which may be analyzed and handled
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| 307 | differently.</li>
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| 308 | </ul>
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| 309 |
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| 310 | <h2>Stereo Models</h2>
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| 311 |
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| 312 | <h3>Dual Stereo</h3>
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| 313 |
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| 314 | <p>Dual stereo refers to stereo encoding where the channels are entirely
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| 315 | separate; they are analyzed and encoded as entirely distinct entities.
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| 316 | This terminology is familiar from mp3.</p>
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| 317 |
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| 318 | <h3>Lossless Stereo</h3>
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| 319 |
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| 320 | <p>Using polar mapping and/or channel interleaving, it's possible to
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| 321 | couple Vorbis channels losslessly, that is, construct a stereo
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| 322 | coupling encoding that both saves space but also decodes
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| 323 | bit-identically to dual stereo. OggEnc 1.0 and later uses this
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| 324 | mode in all high-bitrate encoding.</p>
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| 325 |
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| 326 | <p>Overall, this stereo mode is overkill; however, it offers a safe
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| 327 | alternative to users concerned about the slightest possible
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| 328 | degradation to the stereo image or archival quality audio.</p>
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| 329 |
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| 330 | <h3>Phase Stereo</h3>
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| 331 |
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| 332 | <p>Phase stereo is the least aggressive means of gracefully dropping
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| 333 | resolution from the stereo image; it affects only diffuse imaging.</p>
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| 334 |
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| 335 | <p>It's often quoted that the human ear is deaf to signal phase above
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| 336 | about 4kHz; this is nearly true and a passable rule of thumb, but it
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| 337 | can be demonstrated that even an average user can tell the difference
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| 338 | between high frequency in-phase and out-of-phase noise. Obviously
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| 339 | then, the statement is not entirely true. However, it's also the case
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| 340 | that one must resort to nearly such an extreme demonstration before
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| 341 | finding the counterexample.</p>
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| 342 |
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| 343 | <p>'Phase stereo' is simply a more aggressive quantization of the polar
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| 344 | angle vector; above 4kHz it's generally quite safe to quantize noise
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| 345 | and noisy elements to only a handful of allowed phases, or to thin the
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| 346 | phase with respect to the magnitude. The phases of high amplitude
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| 347 | pure tones may or may not be preserved more carefully (they are
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| 348 | relatively rare and L/R tend to be in phase, so there is generally
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| 349 | little reason not to spend a few more bits on them)</p>
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| 350 |
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| 351 | <h4>example: eight phase stereo</h4>
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| 352 |
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| 353 | <p>Vorbis may implement phase stereo coupling by preserving the entirety
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| 354 | of the magnitude vector (essential to fine amplitude and energy
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| 355 | resolution overall) and quantizing the angle vector to one of only
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| 356 | four possible values. Given that the magnitude vector may be positive
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| 357 | or negative, this results in left and right phase having eight
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| 358 | possible permutation, thus 'eight phase stereo':</p>
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| 359 |
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| 360 | <p><img src="eightphase.png" alt="eight phase"/></p>
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| 361 |
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| 362 | <p>Left and right may be in phase (positive or negative), the most common
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| 363 | case by far, or out of phase by 90 or 180 degrees.</p>
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| 364 |
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| 365 | <h4>example: four phase stereo</h4>
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| 366 |
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| 367 | <p>Similarly, four phase stereo takes the quantization one step further;
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| 368 | it allows only in-phase and 180 degree out-out-phase signals:</p>
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| 369 |
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| 370 | <p><img src="fourphase.png" alt="four phase"/></p>
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| 371 |
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| 372 | <h3>example: point stereo</h3>
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| 373 |
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| 374 | <p>Point stereo eliminates the possibility of out-of-phase signal
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| 375 | entirely. Any diffuse quality to a sound source tends to collapse
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| 376 | inward to a point somewhere within the stereo image. A practical
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| 377 | example would be balanced reverberations within a large, live space;
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| 378 | normally the sound is diffuse and soft, giving a sonic impression of
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| 379 | volume. In point-stereo, the reverberations would still exist, but
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| 380 | sound fairly firmly centered within the image (assuming the
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| 381 | reverberation was centered overall; if the reverberation is stronger
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| 382 | to the left, then the point of localization in point stereo would be
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| 383 | to the left). This effect is most noticeable at low and mid
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| 384 | frequencies and using headphones (which grant perfect stereo
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| 385 | separation). Point stereo is is a graceful but generally easy to
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| 386 | detect degradation to the sound quality and is thus used in frequency
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| 387 | ranges where it is least noticeable.</p>
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| 388 |
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| 389 | <h3>Mixed Stereo</h3>
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| 390 |
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| 391 | <p>Mixed stereo is the simultaneous use of more than one of the above
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| 392 | stereo encoding models, generally using more aggressive modes in
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| 393 | higher frequencies, lower amplitudes or 'nearly' in-phase sound.</p>
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| 394 |
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| 395 | <p>It is also the case that near-DC frequencies should be encoded using
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| 396 | lossless coupling to avoid frame blocking artifacts.</p>
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| 397 |
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| 398 | <h3>Vorbis Stereo Modes</h3>
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| 399 |
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| 400 | <p>Vorbis, as of 1.0, uses lossless stereo and a number of mixed modes
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| 401 | constructed out of lossless and point stereo. Phase stereo was used
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| 402 | in the rc2 encoder, but is not currently used for simplicity's sake. It
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| 403 | will likely be re-added to the stereo model in the future.</p>
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| 404 |
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| 405 | <div id="copyright">
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| 406 | The Xiph Fish Logo is a
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| 407 | trademark (™) of Xiph.Org.<br/>
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| 408 |
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| 409 | These pages © 1994 - 2005 Xiph.Org. All rights reserved.
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| 410 | </div>
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| 411 |
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| 412 | </body>
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| 413 | </html>
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| 414 |
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