title: Tighter decoding reliability bound for Gallager's error-correcting code.
abstract: 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.
authors.affiliation: Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 2268502, Japan.
authors.forename: Y
authors.initials: Y
authors.lastname: Kabashima
authors.forename: N
authors.initials: N
authors.lastname: Sazuka
authors.forename: K
authors.initials: K
authors.lastname: Nakamura
authors.forename: D
authors.initials: D
authors.lastname: Saad