Statistical Mechanics of Low-Density Parity Check Error-Correcting Codes over Galois Fields

Abstract

A variation of low density parity check (LDPC) error correcting codes defined over Galois fields ($GF(q)$) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of $C$ nonzero elements per column. We examine the dependence of the code performance on the value of $q$, for finite and infinite $C$ values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different $q$-dependencies in the cases of C=2 and $C\ge 3$; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

7 pages, 1 figure

References in corpus (5)

• The Nishimori line and Bayesian Statistics
• Typical Performance of Gallager-type Error-Correcting Codes
• The Statistical Physics of Regular Low-Density Parity-Check Error-Correcting Codes
• Error-correcting code on a cactus: a solvable model
• Statistical Physics of Irregular Low-Density Parity-Check Codes

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