### Abstract

The best-known algorithm for the decoding of low-density parity-check (LDPC) codes is the sum-product algorithm (SPA). The SPA is a message-passing algorithm on a graphical model called a factor graph (FG). The performance of the SPA depends on a structure of loops in a FG. Pearl showed that loops in a graphical model could be erased by the clustering method. This method clusters plural nodes into a single node. In this paper, we show several examples about a decoding on a FG to which the clustering method is applied. And we propose an efficient decoding algorithm for it.

Original language | English |
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Title of host publication | Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005 |

Pages | 108-112 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2005 Dec 1 |

Event | IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005 - Rotorua, New Zealand Duration: 2005 Aug 29 → 2005 Sep 1 |

### Publication series

Name | Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005 |
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### Conference

Conference | IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005 |
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Country | New Zealand |

City | Rotorua |

Period | 05/8/29 → 05/9/1 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

Kobayashi, N., Matsushima, T., & Hirasawa, S. (2005). A note on a decoding algorithm of codes on graphs with small loops. In

*Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005*(pp. 108-112). [1531867] (Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005). https://doi.org/10.1109/ITW.2005.1531867