Critical noise levels for low-density parity check decoding

Jort van Mourik, David Saad, Yoshiyuki Kabashima

Research output: Contribution to journalArticlepeer-review


We determine the critical noise level for decoding low-density parity check error-correcting codes based on the magnetization enumerator (M), rather than on the weight enumerator (W) 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 using the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Original languageEnglish
Article number026705
Number of pages8
JournalPhysical Review E
Issue number2
Publication statusPublished - 28 Aug 2002

Bibliographical note

©2002 American Physical Society. Critical noise levels for low-density parity check decoding
J. van Mourik, D. Saad, and Y. Kabashima
Phys. Rev. E 66, 026705 – Published 28 August 2002


  • critical
  • noise levels
  • low-density
  • parity check decoding


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