Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2002-03-07
Physics
Condensed Matter
Disordered Systems and Neural Networks
9 pages, 5 figures
Scientific paper
We determine the critical noise level for decoding low density parity check error correcting codes based on the magnetization enumerator ($\cM$), rather than on the weight enumerator ($\cW$) employed in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. In addition, our analysis provides an explanation for the difference in performance between MN and Gallager codes. Our results are more optimistic than those derived via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.
Kabashima Yoshiyuki
Mourik Jort van
Saad David
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