Typical performance of gallager-type error-correcting codes

Kabashima, Yoshiyuki; Murayama, Tatsuto and Saad, David (2000). Typical performance of gallager-type error-correcting codes. Physical Review Letters, 84 (6), pp. 1355-1358.


The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this method, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity is saturated for many of the codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding.

Divisions: Engineering & Applied Sciences > Mathematics
Additional Information: Copyright of the American Physical Society
Uncontrolled Keywords: Gallager's error-correcting code,statistical physics,transmitted codeword,matrices,Shannon's channel capacity,decoding aspects,TAP approach
Published Date: 2000-02-07



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