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Vicente, Renato; Saad, David; Kabashima, Yoshiyuki (2000)
Languages: English
Types: Article
Subjects: Condensed Matter - Disordered Systems and Neural Networks
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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