Statistical physics of irregular low-density parity-check codes

Renato Vicente*, David Saad, Yoshiyuki Kabashima

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

Original languageEnglish
Pages (from-to)6527-6542
Number of pages16
JournalJournal of Physics A: Mathematical and General
Volume33
Issue number37
DOIs
Publication statusPublished - 22 Sep 2000

Fingerprint

Low-density Parity-check (LDPC) Codes
Statistical Physics
Irregular
parity
physics
Replica Method
Belief Propagation
Error-correcting Codes
error correcting codes
Decoding
decoding
Phase Transition
Coding
replicas
coding
propagation
Simulation
simulation

Bibliographical note

Copyright of the Institute of Physics

Keywords

  • low-density parity check codes
  • error-correcting codes
  • statistical physics

Cite this

Vicente, Renato ; Saad, David ; Kabashima, Yoshiyuki. / Statistical physics of irregular low-density parity-check codes. In: Journal of Physics A: Mathematical and General. 2000 ; Vol. 33, No. 37. pp. 6527-6542.
@article{8a2ffb0b27ea4883a2f924c5a550f20a,
title = "Statistical physics of irregular low-density parity-check codes",
abstract = "Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.",
keywords = "low-density parity check codes, error-correcting codes, statistical physics",
author = "Renato Vicente and David Saad and Yoshiyuki Kabashima",
note = "Copyright of the Institute of Physics",
year = "2000",
month = "9",
day = "22",
doi = "10.1088/0305-4470/33/37/305",
language = "English",
volume = "33",
pages = "6527--6542",
journal = "Journal of Physics A: Mathematical and General",
issn = "0305-4470",
publisher = "IOP Publishing Ltd.",
number = "37",

}

Statistical physics of irregular low-density parity-check codes. / Vicente, Renato; Saad, David; Kabashima, Yoshiyuki.

In: Journal of Physics A: Mathematical and General, Vol. 33, No. 37, 22.09.2000, p. 6527-6542.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Statistical physics of irregular low-density parity-check codes

AU - Vicente, Renato

AU - Saad, David

AU - Kabashima, Yoshiyuki

N1 - Copyright of the Institute of Physics

PY - 2000/9/22

Y1 - 2000/9/22

N2 - Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

AB - Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

KW - low-density parity check codes

KW - error-correcting codes

KW - statistical physics

UR - http://www.scopus.com/inward/record.url?scp=0034702988&partnerID=8YFLogxK

UR - http://iopscience.iop.org/0305-4470/33/37/305

U2 - 10.1088/0305-4470/33/37/305

DO - 10.1088/0305-4470/33/37/305

M3 - Article

VL - 33

SP - 6527

EP - 6542

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 37

ER -