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