Decoding algorithm of low-density parity-check codes based on bowman-levin approximation

Ken Ichi Tamura*, Miho Komiya, Masato Inoue, Yoshiyuki Kabashima

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Belief propagation (BP) and the concave-convex procedure (CCCP) are algorithms that use the Bethe free energy as a cost function and are used to solve information processing tasks. We have developed a new algorithm that also uses the Bethe free energy but changes the roles of the master and slave variables. This is called the Bowman-Levin (BL) approximation in the domain of statistical physics. When we applied the BL approximation to decode the regular low-density parity-check (LDPC) codes over an additive white Gaussian noise (AWGN) channel, its average performance was roughly similar to that of either BP or CCCP, but slightly outperforms them if the vast calculation cost is not prohibitive. This implies that our algorithm based on the BL approximation can be successfully applied to other problems to which BP or CCCP have already been applied. We also found that the decoding dynamics of the BL algorithm particularly depend on the number of inner loops. These differences from BP may be important in understanding the complicated landscape of the Bethe free energy.

Original languageEnglish
Pages (from-to)347-363
Number of pages17
JournalNew Generation Computing
Issue number4
Publication statusPublished - 2009 Aug


  • Belief Propagation (BP)
  • Bethe Free Energy
  • Bowman-Levin Approximation
  • Error Correcting Code
  • Low-density Parity-check (LDPC) Codes

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computer Networks and Communications


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