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Phys. Rev. E 64, 046113 (2001) [4 pages]

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

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Yoshiyuki Kabashima1, Naoya Sazuka1, Kazutaka Nakamura1, and David Saad2
1Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 2268502, Japan
2The Neural Computing Research Group, Aston University, Birmingham B4 7ET, United Kingdom

Received 7 October 2000; published 21 September 2001

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.


©2001 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevE.64.046113
DOI: 10.1103/PhysRevE.64.046113
PACS: 89.70.+c, 05.50.+q, 75.10.Hk, 89.20.Ff

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