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The following critical phenomenon was recently discovered. When a memoryless source is compressed using a variable-length fixed-distortion code, the fastest convergence rate of the (pointwise) compression ratio to R(D) is either O(/spl radic/n) or O(log n). We show it is always O(/spl radic/n), except for discrete, uniformly distributed sources.
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Dembo et al. (2001) studied this question.
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