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 (M), rather than on the weight enumerator (W) presented recently in the information theory literature. The interpretation ofour 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.
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van Mourik, J., Saad, D., Kabashima, Y. (2001). Weight vs. Magnetization Enumerator for Gallager Codes. In: Honary, B. (eds) Cryptography and Coding. Cryptography and Coding 2001. Lecture Notes in Computer Science, vol 2260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45325-3_14
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DOI: https://doi.org/10.1007/3-540-45325-3_14
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