Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1999-04-23
Phys. Rev. E 60 5352-5366 (1999)
Physics
Condensed Matter
Disordered Systems and Neural Networks
32 pages, 12 figures, to appear in PRE
Scientific paper
10.1103/PhysRevE.60.5352
We investigate the performance of parity check codes using the mapping onto Ising spin systems proposed by Sourlas. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C checks per message bit. We show, using the replica method, that these codes saturate Shannon's coding bound for $K\to\infty$ when the code rate K/C is finite. We then examine the finite temperature case to asses the use of simulated annealing methods for decoding, study the performance of the finite K case and extend the analysis to accommodate different types of noisy channels. The connection between statistical physics and belief propagation decoders is discussed and the dynamics of the decoding itself is analyzed. Further insight into new approaches for improving the code performance is given.
Kabashima Yoshiyuki
Saad David
Vicente Renato
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