Statistical Physics of Irregular Low-Density Parity-Check Codes

Details Statistical Physics of Irregular Low-Density Parity-Check Codes Statistical Physics of Irregular Low-Density Parity-Check Codes

1999-08-25

arxiv.org/abs/cond-mat/9908358v2

J. Phys. A 33 (2000) 6527-6542

Physics

Condensed Matter

Disordered Systems and Neural Networks

20 pages, 9 figures, revised version submitted to JPA

Scientific paper

10.1088/0305-4470/33/37/305

Low-density parity-check codes with irregular constructions have been recently shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulations. We compare the performance of irregular with that of regular codes and discuss the factors that contribute to the improvement in performance.

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