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Decoding Algorithm of Low-density Parity-check Codes based on Bowman-Levin Approximation

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Abstract

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.

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Authors and Affiliations

  1. Department of Electrical Engineering and Bioscience, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Ken-ichi Tamura & Masato Inoue

  2. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259 Nagatsuda, Midori-ku, Yokohama, 226-8502, Japan

    Miho Komiya & Yoshiyuki Kabashima

Authors
  1. Ken-ichi Tamura
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  2. Miho Komiya
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  3. Masato Inoue
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  4. Yoshiyuki Kabashima
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Correspondence to Ken-ichi Tamura.

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Tamura, Ki., Komiya, M., Inoue, M. et al. Decoding Algorithm of Low-density Parity-check Codes based on Bowman-Levin Approximation. New Gener. Comput. 27, 347–363 (2009). https://doi.org/10.1007/s00354-008-0069-1

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  • DOI: https://doi.org/10.1007/s00354-008-0069-1

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