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Statistical physics is employed to evaluate the performance oferror-correcting codes in the case of finite message length for an ensemble ofGallager's error correcting codes. We follow Gallager's approach ofupper-bounding the average decoding error rate, but invoke the replica methodto reproduce the tightest general bound to date, and to improve on the mostaccurate zero-error noise level threshold reported in the literature. Therelation between the methods used and those presented in the information theoryliterature are explored.Comment: 11 pages, 1 figur

Tighter decoding reliability bound for Gallager’s error-correcting code