### Abstract

The decoding of Low-Density Parity-Check codes by the Belief Propagation (BP) algorithm is revisited. To check the iterative algorithm for its convergence to a codeword (termination), we run Monte Carlo simulations and find the probability distribution function of the termination time, n<inf>it</inf>. Tested on the [155, 64, 20] code, this termination curve shows a maximum and an extended algebraic tail at the highest values of n<inf>it</inf>. Aiming to reduce the tail of the termination curve we consider a family of iterative algorithms modifying the standard BP by means of a simple relaxation. The relaxation parameter controls the convergence of the modified BP algorithm to a minimum of the Bethe free energy. The improvement is experimentally demonstrated for Additive-White-Gaussian-Noise channel in some range of the signal-to-noise ratios. We also discuss the trade-off between the relaxation parameter of the improved iterative scheme and the number of iterations.

Original language | English (US) |
---|---|

Title of host publication | 44th Annual Allerton Conference on Communication, Control, and Computing 2006 |

Publisher | University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering |

Pages | 947-951 |

Number of pages | 5 |

Volume | 2 |

ISBN (Print) | 9781604237924 |

State | Published - 2006 |

Event | 44th Annual Allerton Conference on Communication, Control, and Computing 2006 - Monticello, United States Duration: Sep 27 2006 → Sep 29 2006 |

### Other

Other | 44th Annual Allerton Conference on Communication, Control, and Computing 2006 |
---|---|

Country | United States |

City | Monticello |

Period | 9/27/06 → 9/29/06 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science Applications
- Computer Networks and Communications

### Cite this

*44th Annual Allerton Conference on Communication, Control, and Computing 2006*(Vol. 2, pp. 947-951). University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering.

**Improving convergence of belief propagation decoding.** / Stepanov, Mikhail; Chertkov, M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*44th Annual Allerton Conference on Communication, Control, and Computing 2006.*vol. 2, University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering, pp. 947-951, 44th Annual Allerton Conference on Communication, Control, and Computing 2006, Monticello, United States, 9/27/06.

}

TY - GEN

T1 - Improving convergence of belief propagation decoding

AU - Stepanov, Mikhail

AU - Chertkov, M.

PY - 2006

Y1 - 2006

N2 - The decoding of Low-Density Parity-Check codes by the Belief Propagation (BP) algorithm is revisited. To check the iterative algorithm for its convergence to a codeword (termination), we run Monte Carlo simulations and find the probability distribution function of the termination time, nit. Tested on the [155, 64, 20] code, this termination curve shows a maximum and an extended algebraic tail at the highest values of nit. Aiming to reduce the tail of the termination curve we consider a family of iterative algorithms modifying the standard BP by means of a simple relaxation. The relaxation parameter controls the convergence of the modified BP algorithm to a minimum of the Bethe free energy. The improvement is experimentally demonstrated for Additive-White-Gaussian-Noise channel in some range of the signal-to-noise ratios. We also discuss the trade-off between the relaxation parameter of the improved iterative scheme and the number of iterations.

AB - The decoding of Low-Density Parity-Check codes by the Belief Propagation (BP) algorithm is revisited. To check the iterative algorithm for its convergence to a codeword (termination), we run Monte Carlo simulations and find the probability distribution function of the termination time, nit. Tested on the [155, 64, 20] code, this termination curve shows a maximum and an extended algebraic tail at the highest values of nit. Aiming to reduce the tail of the termination curve we consider a family of iterative algorithms modifying the standard BP by means of a simple relaxation. The relaxation parameter controls the convergence of the modified BP algorithm to a minimum of the Bethe free energy. The improvement is experimentally demonstrated for Additive-White-Gaussian-Noise channel in some range of the signal-to-noise ratios. We also discuss the trade-off between the relaxation parameter of the improved iterative scheme and the number of iterations.

UR - http://www.scopus.com/inward/record.url?scp=84940638942&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940638942&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781604237924

VL - 2

SP - 947

EP - 951

BT - 44th Annual Allerton Conference on Communication, Control, and Computing 2006

PB - University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering

ER -