Statistical Mechanical Approach to Error Exponents of Lossy Data Compression

Details Statistical Mechanical Approach to Error Exponents of Lossy Data Compression Statistical Mechanical Approach to Error Exponents of Lossy Data Compression

2003-11-06

arxiv.org/abs/cond-mat/0311123v2

Physics

Condensed Matter

Statistical Mechanics

20 pages, 4 figures

Scientific paper

We present herein a scheme by which to accurately evaluate the error exponents of a lossy data compression problem, which characterize average probabilities over a code ensemble of compression failure and success above or below a critical compression rate, respectively, utilizing the replica method (RM). Although the existing method used in information theory (IT) is, in practice, limited to ensembles of randomly constructed codes, the proposed RM-based approach can be applied to a wider class of ensembles. This approach reproduces the optimal expressions of the error exponents achieved by the random code ensembles, which are known in IT. In addition, the proposed framework is used to show that codes composed of non-monotonic perceptrons of a specific type can provide the optimal exponents in most cases, which is supported by numerical experiments.

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