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Abstract:
The performance of regular and irregular Gallager-type
error-correcting codes is investigated via methods of statistical
physics. 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 regular 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. We show that irregular codes
also saturate Shannon's capacity but have improved dynamical
(decoding) properties.
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