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7 Stereo Channel Coupling in the Vorbis CODEC
10 <em>Last update to this document: June 27, 2001</em><br>
12 <h2>Abstract</h2> The Vorbis audio CODEC provides a channel coupling
13 mechanisms designed to reduce effective bitrate by both eliminating
14 interchannel redundancy and eliminating stereo image information
15 labelled inaudible or undesireable according to spatial psychoacoustic
16 models. This document describes both the mechanical coupling
17 mechanisms available within the Vorbis specification, as well as the
18 specific stereo coupling models used by the reference
19 <tt>libvorbis</tt> CODEC provided by xiph.org.
21 <h2>Terminology</h2> Terminology as used in this document is based on
22 common terminology associated with contemporary CODECs such as MPEG I
23 audio layer 3 (mp3). However, some differences in terminology are
24 useful in the context of Vorbis as Vorbis functions somewhat
25 differently than most current formats. For clarity, a few terms are
26 defined beforehand here, and others will be defined where they first
29 <h3>Subjective and Objective</h3>
31 <em>Objective</em> fidelity is a measure, based on a computable,
32 mechanical metric, of how carefully an output matches an input. For
33 example, a stereo amplifier may claim to intorduce less that .01%
34 total harmonic distortion when amplifying an input signal; this claim
35 is easy to verify given proper equiment, and any number of testers are
36 likely to arrive at the same, exact results. One need not listen to
37 the equipment to make this measurement.<p>
39 However, given two amplifiers with identical, verifiable objective
40 specifications, listeners may strongly prefer the sound quality of one
41 over the other. This is actually the case in the decades old debate
42 [some would say jihad] among audiophiles involving vacuum tube versus
43 solid state amplifiers. There are people who can tell the difference,
44 and strongly prefer one over the other despite seemingly identical,
45 measurable quality. This preference is <em>subjective</em> and
46 difficult to measure but nonetheless real.
48 Individual elements of subjective differences often can be qualified,
49 but overall subjective quality generally is not measurable. Different
50 observers are likely to disagree on the exact results of a subjective
51 test as each observer's perspective differs. When measuring
52 subjective qualities, the best one can hope for is average, empirical
53 results that show statistical significance across a group.<p>
55 Perceptual codecs are most concerned with subjective, not objective,
56 quality. This is why evaluating a perceptual codec via distortion
57 measures and sonograms alone is useless; these objective measures may
58 provide insight into the quality or functioning of a codec, but cannot
59 answer the much squishier subjective question, "Does it sound
60 good?". The tube amplifier example is perhaps not the best as very few
61 people can hear, or care to hear, the minute differences between tubes
62 and transistors, whereas the subjective differences in perceptual
63 codecs tend to be quite large even when objective differences are
66 <h3>Fidelity, Artifacts and Differences</h3> Audio <em>artifacts</em>
67 and loss of fidelity or more simply put, audio <em>differences</em>
68 are not the same thing.<p>
70 A loss of fidelity implies differences between the perceived input and
71 output signal; it does not necessarily imply that the differences in
72 output are displeasing or that the output sounds poor (although this
73 is often the case). Tube amplifiers are <em>not</em> higher fidelity
74 than modern solid state and digital systems. They simply produce a
75 form of distortion and coloring that is either unnoticable or actually
76 pleasing to many ears.<p>
78 As compared to an original signal using hard metrics, all perceptual
79 codecs [ASPEC, ATRAC, MP3, WMA, AAC, TwinVQ, AC3 and Vorbis included]
80 lose objective fidelity in order to reduce bitrate. This is fact. The
81 idea is to lose fidelity in ways that cannot be perceived. However,
82 most current streaming applications demand bitrates lower than what
83 can be acheived by sacrificing only objective fidelity; this is also
84 fact, despite whatever various company press releases might claim.
85 Subjective fidelity eventually must suffer in one way or another.<p>
87 The goal is to choose the best possible tradeoff such that the
88 fidelity loss is graceful and not obviously noticable. Most listeners
89 of FM radio do not realize how much lower fidelity that medium is as
90 compared to compact discs or DAT. However, when compared directly to
91 source material, the difference is obvious. A cassette tape is lower
92 fidelity still, and yet the degredation, relatively speaking, is
93 graceful and generally easy not to notice. Compare this graceful loss
94 of quality to an average 44.1kHz stereo mp3 encoded at 80 or 96kbps.
95 The mp3 might actually be higher objective fidelity but subjectively
98 Thus, when a CODEC <em>must</em> sacrifice subjective quality in order
99 to satisfy a user's requirements, the result should be a
100 <em>difference</em> that is generally either difficult to notice
101 without comparison, or easy to ignore. An <em>artifact</em>, on the
102 other hand, is an element introduced into the output that is
103 immediately noticable, obviously foreign, and undesired. The famous
104 'underwater' or 'twinkling' effect synonymous with low bitrate (or
105 poorly encoded) mp3 is an example of an <em>artifact</em>. This
106 working definition differs slightly from common usage, but the coined
107 distinction between differences and artifacts is useful for our
110 The goal, when it is absolutely necessary to sacrifice subjective
111 fidelity, is obviously to strive for differences and not artifacts.
112 The vast majority of CODECs today fail at this task miserably,
113 predictably, and regularly in one way or another. Avoiding such
114 failures when it is necessary to sacrifice subjective quality is a
115 fundamental design objective of Vorbis and that objective is reflected
116 in Vorbis's channel coupling design.<p>
120 In encoder release beta 4 and earlier, Vorbis supported multiple
121 channel encoding, but the channels were encoded entirely seperately
122 with no cross-analysis or redundancy elimination between channels.
123 This multichannel strategy is very similar to the mp3's <em>dual
124 stereo</em> mode and Vorbis uses the same name for it's analagous
125 uncoupled multichannel modes.
127 However, the Vorbis spec provides for, and Vorbis release 1.0 rc1 and
128 later implement a coupled channel strategy. Vorbis has two specific
129 mechanisms that may be used alone or in conjunction to implement
130 channel coupling. The first is <em>channel interleaving</em> via
131 residue backend #2, and the second is <em>square polar mapping</em>.
132 These two general mechanisms are particularly well suited to coupling
133 due to the structure of Vorbis encoding, as we'll explore below, and
134 using both we can implement both totally <em>lossless stereo image
135 coupling</em>, as well as various lossy models that seek to eliminate
136 inaudible or unimportant aspects of the stereo image in order to
137 enhance bitrate. The exact coupling implementation is generalized to
138 allow the encoder a great deal of flexibility in implementation of a
139 stereo model without requiring any significant complexity increase
140 over the combinatorically simpler mid/side joint stereo of mp3 and
141 other current audio codecs.<p>
143 Channel interleaving may be applied directly to more than a single
144 channel and polar mapping is hierarchical such that polar coupling may be
145 extrapolated to an arbitrary number of channels and is not restricted
146 to only stereo, quadriphonics, ambisonics or 5.1 surround. However,
147 the scope of this document restricts itself to the stereo coupling
150 <h3>Square Polar Mapping</h3>
152 <h4>maximal correlation</h4>
154 Recall that the basic structure of a a Vorbis I stream first generates
155 from input audio a spectral 'floor' function that serves as an
156 MDCT-domain whitening filter. This floor is meant to represent the
157 rough envelope of the frequency spectrum, using whatever metric the
158 encoder cares to define. This floor is subtracted from the log
159 frequency spectrum, effectively normalizing the spectrum by frequency.
160 Each input channel is associated with a unique floor function.<p>
162 The basic idea behind any stereo coupling is that the left and right
163 channels usually correlate. This correlation is even stronger if one
164 first accounts for energy differences in any given frequency band
165 across left and right; think for example of individual instruments
166 mixed into different portions of the stereo image, or a stereo
167 recording with a dominant feature not perfectly in the center. The
168 floor functions, each specific to a channel, provide the perfect means
169 of normaizing left and right energies across the spectrum to maximize
170 correlation before coupling. This feature of the Vorbis format is not
171 a convenient accident.<p>
173 Because we strive to maximally correlate the left and right channels
174 and generally succeed in doing so, left and right residue is typically
175 nearly identical. We could use channel interleaving (discussed below)
176 alone to efficiently remove the redundancy between the left and right
177 channels as a side effect of entropy encoding, but a polar
178 representation gives benefits when left/right correlation is
181 <h4>point and diffuse imaging</h4>
183 The first advantage of a polar representation is that it effectively
184 seperates the spatial audio information into a 'point image'
185 (magnitude) at a given frequency and located somewhere in the sound
186 field, and a 'diffuse image' (angle) that fills a large amount of
187 space silmultaneously. Even if we preserve only the magnitude (point)
188 data, a detailed and carefully chosen floor function in each channel
189 provides us with a free, fine-grained, frequency relative intensity
190 stereo*. Angle information represents diffuse sound fields, such as
191 reverberation that fills the entre space silmultaneously.<p>
193 *<em>Because the Vorbis model supports a number of different possible
194 stereo models and these models may be mixed, we do not use the term
195 'intensity stereo' talking about Vorbis; instead we use the terms
196 'point stereo', 'phase stereo' and subcategories of each.</em><p>
198 The majority of a stereo image is representable by polar magnitude
199 alone, as strong sounds tend to be produced at near-point sources;
200 even non-diffuse, fast, sharp echoes track very accurately using
201 magnitude representation almost alone (for those experimenting with
202 Vorbis tuning, this strategy works much better with the precise,
203 piecewise control of floor 1; the continuous approximation of floor 0
204 results in unstable imaging). Reverberation and diffuse sounds tend
205 to contain less energy and be psychoacoustically dominated by the
206 point sources embedded in them. Thus, we again tend to concentrate
207 more represented energy into a predictably smaller number of numbers.
208 Seperating representation of point and diffuse imaging also allows us
209 to model and manipulate point and diffuse qualities seperately.<p>
211 <h4>controlling bit leakage and symbol crosstalk</h4> Because polar
212 representation concentrates represented energy into fewer large
213 values, we reduce bit 'leakage' during cascading (multistage VQ
214 encoding) as a secondary benefit. A single large, monolithic VQ
215 codebook is more efficient than a cascaded book due to entropy
216 'crosstalk' among symbols between different stages of a multistage cascade.
217 Polar representation is a way of further concentrating entropy into
218 predictable locations so that codebook design can take steps to
219 improve multistage codebook efficiency. It also allows us to cascade
220 various elements of the stereo image independently.<p>
222 <h4>eliminating trigonometry and rounding</h4>
224 Rounding and computational complexity are potential problems with a
225 polar representation. As our encoding process involves quantization,
226 mixing a polar representation and quantization makes it potentially
227 impossible, depending on implementation, to construct a coupled stereo
228 mechanism that results in bit-identical decompressed output compared
229 to an uncoupled encoding should the encoder desire it.<p>
231 Vorbis uses a mapping that preserves the most useful qualities of
232 polar representation, relies only on addition/subtraction, and makes
233 it trivial before or after quantization to represent an
234 angle/magnitude through a one-to-one mapping from possible left/right
235 value permutations. We do this by basing our polar representation on
236 the unit square rather than the unit-circle.<p>
238 Given a magnitude and angle, we recover left and right using the
239 following function (note that A/B may be left/right or right/left
240 depending on the coupling definition used by the encoder):<p>
262 The function is antisymmetric for positive and negative magnitudes in
263 order to eliminate a redundant value when quantizing. For example, if
264 we're quantizing to integer values, we can visualize a magnitude of 5
265 and an angle of -2 as follows:<p>
267 <img src="squarepolar.png">
270 This representation loses or replicates no values; if the range of A
271 and B are integral -5 through 5, the number of possible Cartesian
272 permutations is 121. Represented in square polar notation, the
278 -1,-2 -1,-1 -1, 0 -1, 1
282 -2,-4 -2,-3 -2,-2 -2,-1 -2, 0 -2, 1 -2, 2 -2, 3
284 2,-4 2,-3 ... following the pattern ...
286 ... 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 5, 7 5, 8 5, 9
290 ...for a grand total of 121 possible values, the same number as in
291 Cartesian representation (note that, for example, <tt>5,-10</tt> is
292 the same as <tt>-5,10</tt>, so there's no reason to represent
293 both. 2,10 cannot happen, and there's no reason to account for it.)
294 It's also obvious that this mapping is exactly reversable.<p>
296 <h3>Channel interleaving</h3>
298 We can remap and A/B vector using polar mapping into a magnitude/angle
299 vector, and it's clear that, in general, this concentrates energy in
300 the magnitude vector and reduces the amount of information to encode
301 in the angle vector. Encoding these vectors independently with
302 residue backend #0 or residue backend #1 will result in substantial
303 bitrate savings. However, there are still implicit correlations
304 between the magnitude and angle vectors. The most obvious is that the
305 amplitude of the angle is bounded by its corresponding magnitude
308 Entropy coding the results, then, further benefits from the entropy
309 model being able to compress magnitude and angle silmultaneously. For
310 this reason, Vorbis implements residuebackend #2 which preinterleaves
311 a number of input vectors (in the stereo case, two, A and B) into a
312 single output vector (with the elements in the order of
313 A_0, B_0, A_1, B_1, A_2 ... A_n-1, B_n-1) before entropy encoding. Thus
314 each vector to be coded by the vector quantization backend consists of
315 matching magnitude and angle values.<p>
317 The astute reader, at this point, will notice that in the theoretical
318 case in which we can use monolithic codebooks of arbitrarily large
319 size, we can directly interleave and encode left and right without
320 polar mapping; in fact, the polar mapping does not appear to lend any
321 benefit whatsoever to the efficiency of the entropy coding. In fact,
322 it is perfectly possible and reasonable to build a Vorbis encoder that
323 dispenses with polar mapping entirely and merely interleaves the
324 channel. Libvorbis based encoders may configure such an encoding and
325 it will work as intended.<p>
327 However, when we leave the ideal/theoretical domain, we notice that
328 polar mapping does give additional practical benefits, as discussed in
329 the above section on polar mapping and summarised again here:<p>
331 <li>Polar mapping aids in controlling entropy 'leakage' between stages
332 of a cascaded codebook. <li>Polar mapping seperates the stereo image
333 into point and diffuse components which may be analyzed and handled
337 <h2>Stereo Models</h2>
341 Dual stereo referrs to stereo encoding where the channels are entirely
342 seperate; they are analyzed and encoded as entirely distinct entities.
343 This terminology is familiar from mp3.<p>
345 <h3>Lossless Stereo</h3>
347 Using polar mapping and/or channel interleaving, it's possible to
348 couple Vorbis channels losslessly, that is, construct a stereo
349 coupling encoding that both saves space but also decodes
350 bit-identically to dual stereo. OggEnc 1.0 and later offers this
353 Overall, this stereo mode is overkill; however, it offers a safe
354 alternative to users concerned about the slightest possible
355 degredation to the stereo image or archival quality audio.<p>
357 <h3>Phase Stereo</h3>
359 Phase stereo is the least aggressive means of gracefully dropping
360 resolution from the stereo image; it affects only diffuse imaging.<p>
362 It's often quoted that the human ear is nearly entirely deaf to signal
363 phase above about 4kHz; this is nearly true and a passable rule of
364 thumb, but it can be demonstrated that even an average user can tell
365 the difference between high frequency in-phase and out-of-phase noise.
366 Obviously then, the statement is not entirely true. However, it's
367 also the case that one must resort to nearly such an extreme
368 demostration before finding the counterexample.<p>
370 'Phase stereo' is simply a more aggressive quantization of the polar
371 angle vector; above 4kHz it's generally quite safe to quantize noise
372 and noisy elements to only a handful of allowed phases. The phases of
373 high ampliude pure tones may or may not be preserved more carefully
374 (they are relatively rare and L/R tend to be in phase, so there is
375 generally little reason not to spend a few more bits on them) <p>
377 <h4>eight phase stereo</h4>
379 Vorbis implements phase stereo coupling by preserving the entirety of the magnitude vector (essential to fine amlitdude and energy resolution overall) and quantizing the angle vector to one of only four possible values. Given that the magnitude vector may be positive or negative, this results in left and right phase having eight possible permutation, thus 'eight phase stereo':<p>
381 <img src="eightphase.png"><p>
383 Left and right may be in phase (positive or negative), the most common
384 case by far, or out of phase by 90 or 180 degrees.<p>
386 <h4>four phase stereo</h4>
388 Four phase stereo takes the quantization one step further; it allows
389 only in-phase and 180 degree out-out-phase signals:<p>
391 <img src="fourphase.png"><p>
393 <h3>Point Stereo</h3>
395 Point stero eliminates the possibility of out-of-phase signal
396 entirely. Any diffuse quality to a sound source tends to collapse
397 inward to a point somewhere within the stereo image. A practical
398 example would be balanced reverberations within a large, live space;
399 normally the sound is diffuse and soft, giving a sonic impression of
400 volume. In point-stereo, the reverberations would still exist, but
401 sound fairly firmly centered within the image (assuming the
402 reverberation was centered overall; if the reverberation is stronger
403 to the left, then the point of localization in point stereo would be
404 to the left). This effect is most noticable at low and mid
405 frequencies and using headphones (which grant perfect stereo
406 seperation). Point stereo is is a graceful but generally easy to
407 detect degrdation to the sound quality and is thus used in frequency
408 ranges where it is least noticable.<p>
410 <h3>Mixed Stereo</h3>
412 Mixed stereo is the silmultaneous use of more than one of the above
413 stereo encoding models, generally using more aggressive modes in
414 higher frequencies, lower amplitudes or 'nearly' in-phase sound.<p>
416 It is also the case that near-DC frequencies should be encoded using
417 lossless coupling to avoid frame blocking artifacts.<p>
419 <h3>Vorbis Stereo Modes</h3>
421 Vorbis, for the most part, uses lossless stereo and a number of mixed
422 modes constructed out of the above models. As of the current pre-1.0
423 testing version of the encoder, oggenc supports the following modes.
424 Oggenc's default choice varies by bitrate and each mode is selectable
429 <dd>uncoupled stereo encoding<p>
432 <dd>lossless stereo coupling; produces exactly equivalent output to dual stereo<p>
434 <dt>eight phase stereo
435 <dd>a mixed mode combining lossless stereo for frequencies to approximately 4 kHz (and all strong pure tones) and eight phase stereo above<p>
437 <dt>aggressive eight phase stereo
438 <dd>a mixed mode combining lossless stereo for frequencies to approximately 2 kHz (and for all strong pure tones) and eight phase stereo above<p>
440 <dt>eight phase/point stero <dd>A mixed mode combining lossless stereo
441 for bass, eight phase stereo for noisy content and lossless stereo for
442 tones to approximately 4kHz and point stereo above 4kHz.<p>
444 <dt>aggressive eight phase/point stero
445 <dd>A mixed mode combining lossless stereo
446 for bass, eight phase stereo to approximately 2kHz and point stereo above 2kHz.<p>
449 <dd>A mixed mode combining lossless stereo to approximately 4kHz and point stereo above 4kHz.<p>
451 <dt>aggressive point stereo
452 <dd>A mixed mode combining lossless stereo to approximately 1-2kHz and point stereo above.<p>
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