# Advances in Source Coding by Toby Berger, Lee D. Davisson (auth.)

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

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Eng. Dept. T. Cam bridge, Mass. , (1956) "On the Shannon Theory of Information Theory and Peredecü Reliable 38 References Transmission in the Case of Continuous Signals", Trans. IEEE, IT-2, 102-108. 47-160. Y. A. VAN DER HORST (1973) "BCH Source Codes", Submitted to IEEE Trans. on Information Theory. Y. Chapter 2. , (1969) "Tree Encoding of Memoryless Time-Discrete Sources with a Fidelity Criterion", Trans. IEEE, IT-15, 584-590. B. ANDERSON (1971) "Instrumentable Tree Encoding and Information Sources", Trans.

The second part consists of the codeward for ~ in the j(x N )th codebook. As an example of the application of the codebook theorem, consider of eqn. 5 ). •. ,N. lj = {~N: Hammingweightj }. p. N(lj ) = (N +lf 1 • Obviously log(N + 1) N Fixed Rate Noiseless Coding 55 The codebook theorem can be used to solve many other coding problems. Suppose for any ftxed 8 , the source is stationary and ergodie. The source is then called conditionally stationary ergodie. 4: For any conditionally stationary ergodie source, weighted universal codes exist.

Alternative definitions and properdes of the p distance are given in [ 7 ] and [ 8] . In particular, it is there proved that p is a metric and that p has the following simple (but less useful here) alternative definition: p(O,l/>) = inf {Wn }:= E(P(X0 ,Y0 )) -oo where {Wn } n=- oo are stationary random processes of pairs Wn = (X , Y• ) n n such that the coordinate process { ~ } is the 8 process and {YJ is the l/> process. Thus p measures how weil the processes can fit tagether in the p sense at a single time if the processes are stochastically linked in a jointly stationary manner.