Error-correcting code on a cactus: A solvable model

Renato Vicente, David Saad, Yoshiyuki Kabashima

Research output: Contribution to journalArticlepeer-review


An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica-symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.

Original languageEnglish
Pages (from-to)698-704
Number of pages7
JournalEurophysics Letters
Issue number6
Publication statusPublished - 15 Sept 2000

Bibliographical note

Copyright of EDP Sciences


  • error-correcting codes
  • replica symmetric theory
  • finite systems
  • propagation decoding algorithm


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