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Source code error bound in the excess rate region

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2 Author(s)

The problem of encoding a discrete memoryless source with respect to a single-letter fidelity criterion, using a block code of length n and rate R , is considered. The probability of error, p_{n}(R,D) , is defined to be the minimum probability, over all such codes, that the source will generate a sequence which cannot be encoded with distortion D or less. For sufficiently large R , that p_{n}(R,D) decreases doubly exponentially with blocklength, n is shown. It is known that p_{n}(R,D) = 0 for some finite n , denoted by n_{0}(R,D) . An upper bound to n_{0}(R,D) is also presented and numerically evaluated. The results derived hold independently of the source statistics. It is shown that a theorem of Omura and Shohara for symmetric sources is a special case of the results herein. Additionally, a useful characterization of R \ast (D) for row-balanced distortion matrices is obtained.

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Information Theory, IEEE Transactions on  (Volume:23 ,  Issue: 1 )