Statistical Mechanics of Source Coding with a Fidelity Criterion

概要

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We provide a method to evaluate the typical performance of lossy data compression schemes for general (discrete or continuous) memoryless sources using the replica method (RM). The proposed method reproduces a known formula to compute the rate-distortion function representing the optimal tradeoff in the limit of infinite data lengths between the compression rate and permissible distortion level, which is consistent with existing methods in information theory literature. The advantage of the RM-based method is the ability to accurately assess the performance of sub-optimal code ensembles, demonstrated here for Gaussian memoryless sources. The obtained result is used to construct a family of error correcting codes that are composed of practical-size codebooks and asymptotically achieve the capacity of the Gaussian channel.
理論物理学刊行会の論文
2005-04-30