Error-correcting code on a cactus: a solvable model

Details Error-correcting code on a cactus: a solvable model Error-correcting code on a cactus: a solvable model

2000-05-05

arxiv.org/abs/cond-mat/0005109v2

Europhys. Lett. 51 (2000), 698-704

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 3 figures, with minor corrections

Scientific paper

10.1209/epl/i2000-00395-x

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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