Statistical Physics of Irregular Low-Density Parity-Check Codes

Abstract

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.

20 pages, 9 figures, revised version submitted to JPA

References in corpus (6)

• 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 Codes That Nearly Saturate Shannon's Bound
• Finite-connectivity systems as error-correcting codes
• Finite size effects and error-free communication in Gaussian channels

Cited by in corpus (9)

• Statistical Mechanics of Low-Density Parity Check Error-Correcting Codes over Galois Fields
• Gallager error correcting codes for binary asymmetric channels
• Propagating beliefs in spin glass models
• Average and reliability error exponents in low-density parity-check codes
• Statistical Mechanics Analysis of LDPC Coding in MIMO Gaussian Channels
• Parallel vs. Sequential Belief Propagation Decoding of LDPC Codes over GF(q) and Markov Sources
• Typical kernel size and number of sparse random matrices over GF(q) - a statistical physics approach
• Typical Performance of Irregular Low-Density Generator-Matrix Codes for Lossy Compression
• Code optimization, frozen glassy phase and improved decoding algorithms for low-density parity-check codes