### 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.

Original language | English |
---|---|

Pages (from-to) | 347-363 |

Number of pages | 17 |

Journal | New Generation Computing |

Volume | 27 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 Aug |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*New Generation Computing*,

*27*(4), 347-363. https://doi.org/10.1007/s00354-008-0069-1

**Decoding algorithm of low-density parity-check codes based on bowman-levin approximation.** / Tamura, Ken Ichi; Komiya, Miho; Inoue, Masato; Kabashima, Yoshiyuki.

Research output: Contribution to journal › Article

*New Generation Computing*, vol. 27, no. 4, pp. 347-363. https://doi.org/10.1007/s00354-008-0069-1

}

TY - JOUR

T1 - Decoding algorithm of low-density parity-check codes based on bowman-levin approximation

AU - Tamura, Ken Ichi

AU - Komiya, Miho

AU - Inoue, Masato

AU - Kabashima, Yoshiyuki

PY - 2009/8

Y1 - 2009/8

N2 - 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.

AB - 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.

KW - Belief Propagation (BP)

KW - Bethe Free Energy

KW - Bowman-Levin Approximation

KW - Error Correcting Code

KW - Low-density Parity-check (LDPC) Codes

UR - http://www.scopus.com/inward/record.url?scp=70450172956&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70450172956&partnerID=8YFLogxK

U2 - 10.1007/s00354-008-0069-1

DO - 10.1007/s00354-008-0069-1

M3 - Article

AN - SCOPUS:70450172956

VL - 27

SP - 347

EP - 363

JO - New Generation Computing

JF - New Generation Computing

SN - 0288-3635

IS - 4

ER -