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By Toby Berger, Lee D. Davisson (auth.)

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In practice one might reverse the order of construction by frrst choosing a reasonable number, K, of representative subcodes and ~f rate R and blocklength N with resulting rate R + tr 1 log K and average distortion within e (K) of the optimal. An appropriate choice of blocklength will allow use of this construction on nonstationary sources that are locally stationary [ 15). VI. Variable-Rate Coding with Distordon The average distortion of the encoding at a Hxed rate as in the last section depends upon the actual value of 8 in effect, that is, the actual stationary ergodie source seen by the encoder.

Since thcrc arc 26 = 64 different words of length 6 that might be produced by ·the source, thcre usually will not be a code word that matches the source word exactly. _,y). For example, if.!. = 010110, then~ = 000110 is closest in the sense of the Hamming metric. When traversing the path- from the root to the leaf y = 000110, we branch first up, then down, and then up at the successive nodes cncountcrcd. Hence, this path is specified by the binary path map sequence 010, whcrc 0 represents "up" and 1 represents "down".

An example of a totally bounded dass of sources under p is the dass of all stationary finite-state wide-sense Markov chains of order less than some fmite integer. Extensions to more general dasses along with partial converses may be found in [ 8). In practice one might reverse the order of construction by frrst choosing a reasonable number, K, of representative subcodes and ~f rate R and blocklength N with resulting rate R + tr 1 log K and average distortion within e (K) of the optimal. An appropriate choice of blocklength will allow use of this construction on nonstationary sources that are locally stationary [ 15).

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