Statistical mechanics of typical set decoding

Yoshiyuki Kabashima*, Kazutaka Nakamura, Jort van Mourik

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The performance of "typical set (pairs) decoding" for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding method, errors occur, either when the information transmission is corrupted by atypical noise, or when multiple typical sequences satisfy the parity check equation as provided by the received corrupted codeword. We show that the average error rate for the second type of error over a given code ensemble can be accurately evaluated using the replica method, including the sensitivity to message length. Our approach generally improves the existing analysis known in the information theory community, which was recently reintroduced in IEEE Trans. Inf. Theory 45, 399 (1999), and is believed to be the most accurate to date. © 2002 The American Physical Society.

Original languageEnglish
Article number036125
Pages (from-to)1-6
Number of pages6
JournalPhysical Review E
Issue number3
Publication statusPublished - 24 Sep 2002

Bibliographical note

Copyright of the American Physical Society


  • Gallager's linear code
  • statistical physics
  • information transmission
  • noise
  • average error rate


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