Statistical mechanics of error exponents for error-correcting codes

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dc.creatorMora, Thierry
dc.creatorRivoire, Olivier
dc.date2006-06-27
dc.date.accessioned2026-07-07T08:17:39Z
dc.date.available2026-07-07T08:17:39Z
dc.descriptionError exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general, thermodynamic, formalism that we illustrate with maximum-likelihood decoding of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and the binary symmetric channel (BSC). In this formalism, we apply the cavity method for large deviations to derive expressions for both the average and typical error exponents, which differ by the procedure used to select the codes from specified ensembles. When decreasing the noise intensity, we find that two phase transitions take place, at two different levels: a glass to ferromagnetic transition in the space of codewords, and a paramagnetic to glass transition in the space of codes.
dc.description32 pages, 13 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0606696
dc.identifierhttp://arxiv.org/abs/cond-mat/0606696
dc.identifierPhys. Rev. E 74, 056110 (2006)
dc.identifierdoi:10.1103/PhysRevE.74.056110
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134165
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.subjectInformation Theory
dc.titleStatistical mechanics of error exponents for error-correcting codes
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