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Critical Behavior in Lossy Source Coding

Amir Dembo·Ioannis Kontoyiannis
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Abstract

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 the optimal $R(D)$ bits/symbol is either $O(\sqrt{n})$ or $O(\log n)$. We show it is always $O(\sqrt{n})$, except for discrete, uniformly distributed sources.

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Amir Dembo, Ioannis Kontoyiannis. 2000-09-01. Critical Behavior in Lossy Source Coding. https://arxiv.org/abs/math/0009018

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