Weight vs. Magnetization enumerator for Gallager codes

Jort van Mourik; David Saad; Yoshiyuki Kabashima

Weight vs. Magnetization enumerator for Gallager codes

Jort van Mourik, David Saad, Yoshiyuki Kabashima

Aston University

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

Abstract

We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator (M), rather than on the weight enumerator (W) presented recently in the information theory literature. The interpretation ofour method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. Our results are more optimistic than those derived via the methods ofinf ormation theory and are in excellent agreement with recent results from another statistical physics approach.

Original language	English
Title of host publication	Cryptography and coding: Prooceeding of the8th IMA International Conference
Editors	Bahram Honary
Publisher	Springer
Pages	148-157
Number of pages	10
Volume	2260
ISBN (Print)	3540430261, 9783540430261
Publication status	Published - 17 Dec 2001
Event	8th IMA International Conference on Cryptography and Coding, 2001 - Cirencester, United Kingdom Duration: 17 Dec 2001 → 19 Dec 2001

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	2260

Conference

Conference	8th IMA International Conference on Cryptography and Coding, 2001
Country/Territory	United Kingdom
City	Cirencester
Period	17/12/01 → 19/12/01

Keywords

critical noise level
decoding
Gallager type low density parity check error correcting codes
magnetization enumerator

Cite this

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title = "Weight vs. Magnetization enumerator for Gallager codes",

abstract = "We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator (M), rather than on the weight enumerator (W) presented recently in the information theory literature. The interpretation ofour method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. Our results are more optimistic than those derived via the methods ofinf ormation theory and are in excellent agreement with recent results from another statistical physics approach.",

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van Mourik, J, Saad, D & Kabashima, Y 2001, Weight vs. Magnetization enumerator for Gallager codes. in B Honary (ed.), Cryptography and coding: Prooceeding of the8th IMA International Conference. vol. 2260, Lecture Notes in Computer Science, vol. 2260, Springer, pp. 148-157, 8th IMA International Conference on Cryptography and Coding, 2001, Cirencester, United Kingdom, 17/12/01.

Weight vs. Magnetization enumerator for Gallager codes. / van Mourik, Jort; Saad, David; Kabashima, Yoshiyuki.
Cryptography and coding: Prooceeding of the8th IMA International Conference. ed. / Bahram Honary. Vol. 2260 Springer, 2001. p. 148-157 (Lecture Notes in Computer Science; Vol. 2260).

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

TY - GEN

T1 - Weight vs. Magnetization enumerator for Gallager codes

AU - van Mourik, Jort

AU - Saad, David

AU - Kabashima, Yoshiyuki

PY - 2001/12/17

Y1 - 2001/12/17

N2 - We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator (M), rather than on the weight enumerator (W) presented recently in the information theory literature. The interpretation ofour method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. Our results are more optimistic than those derived via the methods ofinf ormation theory and are in excellent agreement with recent results from another statistical physics approach.

AB - We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator (M), rather than on the weight enumerator (W) presented recently in the information theory literature. The interpretation ofour method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. Our results are more optimistic than those derived via the methods ofinf ormation theory and are in excellent agreement with recent results from another statistical physics approach.

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KW - decoding

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KW - magnetization enumerator

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ER -

Weight vs. Magnetization enumerator for Gallager codes

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