By Toby Berger, Lee D. Davisson (auth.)
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Extra info for Advances in Source Coding
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).
K (6. 2) Obviously by choosing N large enough and € sroall enough, the rate can be roade arbitrarily close to R 8 (D) for 8 = 1,2, ... ,K. The achieveroent of D and ~ (D) for the Rorobined supercode depends upon the actual choice of a codeward out of the L= ~ L codewords total. The j =1 J coding rule is as follows. Upon observing an output block of length N, among the Variable Rate Coding with Distordon 67 codewords of distortion less than D- e /2, fmd the one of minimum rate, ifany. If there is no codeward with distortion less than D- e /2, make a random choice.
They do, 68 Conclusions however, provide Hgures of merit and optimal performance bounds that can serve as an absolute yardstick for comparison justification for overall design philosophies that have proved useful in practice. , "The Mathematical Theory of Communication", University of Illinois Press, 1949, Urbana, Illinois. , pt. 4, pp. 142-163, 1959. , "Station~ Random Processes", Holden-Day, San Francisco, 196 7. , "Source Coding Theorems without the Ergodie Assumption", IEEE Trans. IT, July 1974.