Statistical physics of low density parity check error correcting codes

David Saad, Yoshiyuki Kabashima, Tatsuto Murayama, Renato Vicente

Research output: Chapter in Book/Published conference outputChapter


We study the performance of Low Density Parity Check (LDPC) error-correcting codes using the methods of statistical physics. LDPC codes are based on the generation of codewords using Boolean sums of the original message bits by employing two randomly-constructed sparse matrices. These codes can be mapped onto Ising spin models and studied using common methods of statistical physics. We examine various regular constructions and obtain insight into their theoretical and practical limitations. We also briefly report on results obtained for irregular code constructions, for codes with non-binary alphabet, and on how a finite system size effects the error probability.
Original languageEnglish
Title of host publicationCryptography and Coding
EditorsB. Honary
Place of PublicationBerlin / Heidelberg
Number of pages10
ISBN (Print)9783540430261
Publication statusPublished - 1 Jan 2001
EventCryptography and Coding, 8-th IMA International Conference -
Duration: 1 Jan 20011 Jan 2001

Publication series

NameLecture Notes in Computer Science


ConferenceCryptography and Coding, 8-th IMA International Conference

Bibliographical note

The original publication is available at


  • Low Density Parity Check (LDPC)
  • error correcting codes
  • statistical physics
  • boolean
  • sparse matrices
  • Ising spin models
  • irregular code
  • error probability


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