Improving convergence of belief propagation decoding

Mikhail Stepanov, M. Chertkov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publication44th Annual Allerton Conference on Communication, Control, and Computing 2006
PublisherUniversity of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering
Pages947-951
Number of pages5
Volume2
ISBN (Print)9781604237924
StatePublished - 2006
Event44th Annual Allerton Conference on Communication, Control, and Computing 2006 - Monticello, United States
Duration: Sep 27 2006Sep 29 2006

Other

Other44th Annual Allerton Conference on Communication, Control, and Computing 2006
CountryUnited States
CityMonticello
Period9/27/069/29/06

Fingerprint

Decoding
Probability distributions
Free energy
Distribution functions
Signal to noise ratio

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Networks and Communications

Cite this

Stepanov, M., & Chertkov, M. (2006). Improving convergence of belief propagation decoding. In 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.

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, 2006. p. 947-951.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Stepanov, M & Chertkov, M 2006, Improving convergence of belief propagation decoding. in 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.
Stepanov M, Chertkov M. Improving convergence of belief propagation decoding. In 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. 2006. p. 947-951
Stepanov, Mikhail ; Chertkov, M. / Improving convergence of belief propagation decoding. 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, 2006. pp. 947-951
@inproceedings{1f7f7f7a036a4a8497d0e0990dd92cb1,
title = "Improving convergence of belief propagation decoding",
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, 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.",
author = "Mikhail Stepanov and M. Chertkov",
year = "2006",
language = "English (US)",
isbn = "9781604237924",
volume = "2",
pages = "947--951",
booktitle = "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",

}

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 -