Error-correcting codes on a Bethe-like lattice

Renato Vicente; David Saad; Yoshiyuki Kabashima

Error-correcting codes on a Bethe-like lattice

Renato Vicente, David Saad, Yoshiyuki Kabashima

Mathematics

Research output: Chapter in Book/Published conference output › Chapter

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 language	English
Title of host publication	Advances in neural information processing systems
Editors	Todd K. Leen, Volker Tresp, Thomas G. Dietterich
Publisher	MIT
Pages	322-328
Number of pages	7
Volume	13
ISBN (Print)	0-2621-2241-3, 978-0-2621-2241-2
Publication status	Published - Apr 2001
Event	14th Annual Neural Information Processing Systems Conference - Denver, CO, United States Duration: 27 Nov 2000 → 2 Dec 2000

Conference

Conference	14th Annual Neural Information Processing Systems Conference
Abbreviated title	NIPS 2000
Country/Territory	United States
City	Denver, CO
Period	27/11/00 → 2/12/00

Cite this

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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.",

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AU - Vicente, Renato

AU - Saad, David

AU - Kabashima, Yoshiyuki

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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.

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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

T2 - 14th Annual Neural Information Processing Systems Conference

Y2 - 27 November 2000 through 2 December 2000

ER -

Error-correcting codes on a Bethe-like lattice

Abstract

Conference

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