Tighter Decoding Reliability Bound for Gallager's Error-Correcting Code

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  • 12 October 2000
Abstract
Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length by examining the reliability function for Gallager's error correcting code. We follow Gallager's derivation of an upper bound to the decoding reliability, but invoke the replica method to obtain the tightest bound to date, and to improve the most accurate zero-error noise level threshold reported to date; the relation between the methods presented in the information theory literature and those of statistical physics are explored.

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