Typical performance of gallager-type error-correcting codes

Yoshiyuki Kabashima, Tatsuto Murayama, David Saad

Research output: Contribution to journalArticlepeer-review


The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this method, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity is saturated for many of the codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding.
Original languageEnglish
Pages (from-to)1355-1358
Number of pages4
JournalPhysical Review Letters
Issue number6
Publication statusPublished - 7 Feb 2000

Bibliographical note

Copyright of the American Physical Society


  • Gallager's error-correcting code
  • statistical physics
  • transmitted codeword
  • matrices
  • Shannon's channel capacity
  • decoding aspects
  • TAP approach


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