Tighter decoding reliability bound for Gallager's error-correcting code

Yoshiyuki Kabashima, Naoya Sazuka, Kazutaka Nakamura, David Saad

Research output: Contribution to journalArticlepeer-review


Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average decoding error rate, but invoke the replica method to reproduce the tightest general bound to date, and to improve on the most accurate zero-error noise level threshold reported in the literature. The relation between the methods used and those presented in the information theory literature are explored.
Original languageEnglish
Pages (from-to)1-4
Number of pages4
JournalPhysical Review E
Issue number4
Publication statusPublished - 2001

Bibliographical note

Copyright of the American Physical Society


  • Statistical physics
  • error-correcting code
  • finite message length
  • decoding error rate


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