%0 Journal Article
%T Tighter Decoding Reliability Bound for Gallager's Error-Correcting Code
%A Yoshiyuki Kabashima
%A Naoya Sazuka
%A Kazutaka Nakamura
%A David Saad
%J Physics
%D 2000
%I arXiv
%R 10.1103/PhysRevE.64.046113
%X Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average decoding error rate, but invoke the replica method to reproduce the tightest general bound to date, and to improve on the most accurate zero-error noise level threshold reported in the literature. The relation between the methods used and those presented in the information theory literature are explored.
%U http://arxiv.org/abs/cond-mat/0010173v2