By Toby Berger, Lee D. Davisson (auth.)
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Extra info for Advances in Source Coding
Despite the fact that the data rate has been ~ompressed by a factor of two, most of the original source digits can be recovcred correctly. 1875. 110. It should be clear that tree codes can be designed with any desired rate. If there are b branches per node and t letters per branch, then the rate is R = Q- 1 1og d Also, the letters an the branches can be chosen from any reproducing alphabet whatsoever including a continuous alphabet, so tree coding is not restricted to GF(q). Tree encoding of sourceswas first proposed by Gabliek (1962).
Instead, for some rate R one must encode each source block of length N into a fi;;ed length coded representation of RN bits. Assuming that there are more than 2 RN possible message blocks, there will be some nonzero probability of error associated with this operation. For "noiseless" coding we would like to know how big R must be so that vanishing probability of error can be assured by choosing N large enough. In direct analogy to Section II, weighted, maximin, minimax and weakly minimax universal codes can be defmed over a source parametrized by a random variable ® on a space A, with performance measured by error probability rather than redundancy.
Theory, Vol. IT-19, pp. 783-795, November 1973. , "A Generalization of Ornstein's d Metrie with Applications to Information Theory", Annals ofProbabiliry (tobe published). M. , "Fixed Rate Universal Source Coding with a Fidelity Criterion", submitted to IEEE Trans. IT. , "Coding Theorems for Non-Ergodie Sources and Sources with Unknown Parameters", USC Technieal Report, February 1974. , vol IT-18, No. 4, July 1972, pp. 460-473.