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

Yoshiyuki Kabashima·Naoya Sazuka·Kazutaka Nakamura·David Saad
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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.

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Yoshiyuki Kabashima, Naoya Sazuka, Kazutaka Nakamura, David Saad. 2001-04-12. Tighter Decoding Reliability Bound for Gallager's Error-Correcting Code. https://doi.org/10.1103/physreve.64.046113

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