Error-correcting codes on a Bethe-like lattice

Renato Vicente, David Saad, Yoshiyuki Kabashima

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We analyse Gallager codes by employing a simple mean-field approximation that distorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decoding algorithm as a minimization of a proper free-energy. We find a thermodynamical phase transition that coincides with information theoretical upper-bounds and explain the practical code performance in terms of the free-energy landscape.
Original languageEnglish
Title of host publicationAdvances in neural information processing systems
EditorsTodd K. Leen, Volker Tresp, Thomas G. Dietterich
PublisherMIT
Pages322-328
Number of pages7
Volume13
ISBN (Print)0-2621-2241-3, 978-0-2621-2241-2
Publication statusPublished - Apr 2001
Event14th Annual Neural Information Processing Systems Conference - Denver, CO, United States
Duration: 27 Nov 20002 Dec 2000

Conference

Conference14th Annual Neural Information Processing Systems Conference
Abbreviated titleNIPS 2000
CountryUnited States
CityDenver, CO
Period27/11/002/12/00

Fingerprint

Free energy
Decoding
Phase transitions
Geometry

Cite this

Vicente, R., Saad, D., & Kabashima, Y. (2001). Error-correcting codes on a Bethe-like lattice. In T. K. Leen, V. Tresp, & T. G. Dietterich (Eds.), Advances in neural information processing systems (Vol. 13, pp. 322-328). MIT.
Vicente, Renato ; Saad, David ; Kabashima, Yoshiyuki. / Error-correcting codes on a Bethe-like lattice. Advances in neural information processing systems. editor / Todd K. Leen ; Volker Tresp ; Thomas G. Dietterich. Vol. 13 MIT, 2001. pp. 322-328
@inbook{acfc860180be40d0a01aee1849a2f348,
title = "Error-correcting codes on a Bethe-like lattice",
abstract = "We analyse Gallager codes by employing a simple mean-field approximation that distorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decoding algorithm as a minimization of a proper free-energy. We find a thermodynamical phase transition that coincides with information theoretical upper-bounds and explain the practical code performance in terms of the free-energy landscape.",
author = "Renato Vicente and David Saad and Yoshiyuki Kabashima",
year = "2001",
month = "4",
language = "English",
isbn = "0-2621-2241-3",
volume = "13",
pages = "322--328",
editor = "Leen, {Todd K.} and Volker Tresp and Dietterich, {Thomas G.}",
booktitle = "Advances in neural information processing systems",
publisher = "MIT",

}

Vicente, R, Saad, D & Kabashima, Y 2001, Error-correcting codes on a Bethe-like lattice. in TK Leen, V Tresp & TG Dietterich (eds), Advances in neural information processing systems. vol. 13, MIT, pp. 322-328, 14th Annual Neural Information Processing Systems Conference, Denver, CO, United States, 27/11/00.

Error-correcting codes on a Bethe-like lattice. / Vicente, Renato; Saad, David; Kabashima, Yoshiyuki.

Advances in neural information processing systems. ed. / Todd K. Leen; Volker Tresp; Thomas G. Dietterich. Vol. 13 MIT, 2001. p. 322-328.

Research output: Chapter in Book/Report/Conference proceedingChapter

TY - CHAP

T1 - Error-correcting codes on a Bethe-like lattice

AU - Vicente, Renato

AU - Saad, David

AU - Kabashima, Yoshiyuki

PY - 2001/4

Y1 - 2001/4

N2 - We analyse Gallager codes by employing a simple mean-field approximation that distorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decoding algorithm as a minimization of a proper free-energy. We find a thermodynamical phase transition that coincides with information theoretical upper-bounds and explain the practical code performance in terms of the free-energy landscape.

AB - We analyse Gallager codes by employing a simple mean-field approximation that distorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decoding algorithm as a minimization of a proper free-energy. We find a thermodynamical phase transition that coincides with information theoretical upper-bounds and explain the practical code performance in terms of the free-energy landscape.

UR - http://www.scopus.com/inward/record.url?scp=84899010218&partnerID=8YFLogxK

UR - http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=8662

M3 - Chapter

SN - 0-2621-2241-3

SN - 978-0-2621-2241-2

VL - 13

SP - 322

EP - 328

BT - Advances in neural information processing systems

A2 - Leen, Todd K.

A2 - Tresp, Volker

A2 - Dietterich, Thomas G.

PB - MIT

ER -

Vicente R, Saad D, Kabashima Y. Error-correcting codes on a Bethe-like lattice. In Leen TK, Tresp V, Dietterich TG, editors, Advances in neural information processing systems. Vol. 13. MIT. 2001. p. 322-328