Statistical mechanics of low-density parity-check codes

Yoshiyuki Kabashima*, David Saad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multispin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems.

Original languageEnglish
Pages (from-to)R1-R43
JournalJournal of Physics A: Mathematical and General
Issue number6
Publication statusPublished - 13 Feb 2004

Bibliographical note

This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and General. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at 10.1088/0305-4470/37/6/R01.


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