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70 <a href="http://www.xiph.org/"><img src="fish_xiph_org.png" alt="Fish Logo and Xiph.org"/></a>
\r
73 <h1>Ogg Vorbis stereo-specific channel coupling discussion</h1>
\r
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>
\r
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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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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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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119 <h3>Square Polar Mapping</h3>
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121 <h4>maximal correlation</h4>
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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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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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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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150 <h4>point and diffuse imaging</h4>
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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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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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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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180 <h4>controlling bit leakage and symbol crosstalk</h4>
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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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193 <h4>eliminating trigonometry and rounding</h4>
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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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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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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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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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239 <p><img src="squarepolar.png" alt="square polar"/></p>
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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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249 -1,-2 -1,-1 -1, 0 -1, 1
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251 1,-2 1,-1 1, 0 1, 1
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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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255 2,-4 2,-3 ... following the pattern ...
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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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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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267 <h3>Channel interleaving</h3>
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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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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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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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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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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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309 <h2>Stereo Models</h2>
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311 <h3>Dual Stereo</h3>
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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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317 <h3>Lossless Stereo</h3>
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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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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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329 <h3>Phase Stereo</h3>
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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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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>
\r
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>
\r
350 <h4>example: eight phase stereo</h4>
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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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359 <p><img src="eightphase.png" alt="eight phase"/></p>
\r
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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364 <h4>example: four phase stereo</h4>
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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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369 <p><img src="fourphase.png" alt="four phase"/></p>
\r
371 <h3>example: point stereo</h3>
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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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388 <h3>Mixed Stereo</h3>
\r
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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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>
\r
397 <h3>Vorbis Stereo Modes</h3>
\r
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>
\r
404 <div id="copyright">
\r
405 The Xiph Fish Logo is a
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406 trademark (™) of Xiph.Org.<br/>
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408 These pages © 1994 - 2005 Xiph.Org. All rights reserved.
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