Weight vs Magnetization Enumerator for Gallager Codes
Disordered Systems and Neural Networks
2007-05-23 v1
Abstract
We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator (), rather than on the weight enumerator () presented recently 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. 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.
Keywords
Cite
@article{arxiv.cond-mat/0110023,
title = {Weight vs Magnetization Enumerator for Gallager Codes},
author = {J. van Mourik and D. Saad and Y. Kabashima},
journal= {arXiv preprint arXiv:cond-mat/0110023},
year = {2007}
}
Comments
10 pages, 4 figures, 8th IMA int. conf. on cryptography and Coding