Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2000-03-08
Phys. Rev. E 62(2) 1577-1591 (2000)
Physics
Condensed Matter
Disordered Systems and Neural Networks
35 pages, 4 figures
Scientific paper
10.1103/PhysRevE.62.1577
A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword which comprises Boolean sums of message bits selected by two randomly constructed sparse matrices. The similarity of these codes to Ising spin systems with random interaction makes it possible to assess their typical performance by analytical methods developed in the study of disordered systems. The typical case solutions obtained via the replica method are consistent with those obtained in simulations using belief propagation (BP) decoding. We discuss the practical implications of the results obtained and suggest a computationally efficient construction for one of the more practical configurations.
Kabashima Yoshiyuki
Murayama Tatsuto
Saad David
Vicente Renato
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