Statistical Mechanics and error-correction Codes

Details Statistical Mechanics and error-correction Codes Statistical Mechanics and error-correction Codes

1998-11-29

arxiv.org/abs/cond-mat/9811406v1

Physics

Condensed Matter

Statistical Mechanics

Proceedings of the Marseille Satellite Colloquium "Mathematical Results in Stat. Mechanics"

Scientific paper

I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin system. The most probable value of a symbol is related to the magnetization at a different temperature. Convolutional codes correspond to one-dimensional spin systems and Viterbi's decoding algorithm to the transfer matrix algorithm of Statistical Mechanics. A particular spin-glass model, which is exactly soluble, corresponds to an ideal code, i.e. a code which allows error-free communication if the rate is below channel capacity.

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