Error-correcting code on a cactus: a solvable model
Disordered Systems and Neural Networks
2009-10-31 v2
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.
Cite
@article{arxiv.cond-mat/0005109,
title = {Error-correcting code on a cactus: a solvable model},
author = {Renato Vicente and David Saad and Yoshiyuki Kabashima},
journal= {arXiv preprint arXiv:cond-mat/0005109},
year = {2009}
}
Comments
7 pages, 3 figures, with minor corrections