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Error-correcting code on a cactus: a solvable model

Renato Vicente·David Saad·Yoshiyuki Kabashima
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Abstract

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.

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Renato Vicente, David Saad, Yoshiyuki Kabashima. 2000-05-30. Error-correcting code on a cactus: a solvable model. https://doi.org/10.1209/epl%2Fi2000-00395-x

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