Statistical physics of irregular low-density parity-check codes

Renato Vicente*, David Saad, Yoshiyuki Kabashima

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Low-density parity-check codes with irregular constructions have recently been 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 simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

Original languageEnglish
Pages (from-to)6527-6542
Number of pages16
JournalJournal of Physics A: Mathematical and General
Issue number37
Publication statusPublished - 22 Sep 2000

Bibliographical note

Copyright of the Institute of Physics


  • low-density parity check codes
  • error-correcting codes
  • statistical physics


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