Bounds on the thresholds of non-binary LDPC codes

Oron Levi; David Burshtein

doi:10.1109/EEEI.2008.4736544

Bounds on the thresholds of non-binary LDPC codes

Oron Levi^*, David Burshtein

^*Corresponding author for this work

School of Electrical Engineering

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

LDPC codes over non-binary Galois fields were proposed for reliable transmission over arbitrary discrete memoryless channels and in particular for transmission in the bandwidth efficient regime. It was shown that some properties, originally derived for binary LDPC codes, extend to the appropriately defined non-binary ensemble. However, the extension of density evolution to this ensemble results in a prohibitive computational complexity. In this paper we analyze the performance by tracking the evolution of the Bhattacharya noise parameter associated with the decoding messages, and derive upper and lower bounds on its evolution. These bounds are then used to obtain upper and lower bounds on the asymptotic threshold required for reliable communication.

Original language	English
Title of host publication	2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008
Pages	348-352
Number of pages	5
DOIs	https://doi.org/10.1109/EEEI.2008.4736544
State	Published - 2008
Event	2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008 - Eilat, Israel Duration: 3 Dec 2008 → 5 Dec 2008

Publication series

Name	IEEE Convention of Electrical and Electronics Engineers in Israel, Proceedings

Conference

Conference	2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008
Country/Territory	Israel
City	Eilat
Period	3/12/08 → 5/12/08

Keywords

Iterative decoding
Low-density parity-check (LDPC) codes
Nonbinary codes

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10.1109/EEEI.2008.4736544

Cite this

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title = "Bounds on the thresholds of non-binary LDPC codes",

abstract = "LDPC codes over non-binary Galois fields were proposed for reliable transmission over arbitrary discrete memoryless channels and in particular for transmission in the bandwidth efficient regime. It was shown that some properties, originally derived for binary LDPC codes, extend to the appropriately defined non-binary ensemble. However, the extension of density evolution to this ensemble results in a prohibitive computational complexity. In this paper we analyze the performance by tracking the evolution of the Bhattacharya noise parameter associated with the decoding messages, and derive upper and lower bounds on its evolution. These bounds are then used to obtain upper and lower bounds on the asymptotic threshold required for reliable communication.",

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Levi, O & Burshtein, D 2008, Bounds on the thresholds of non-binary LDPC codes. in 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008., 4736544, IEEE Convention of Electrical and Electronics Engineers in Israel, Proceedings, pp. 348-352, 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008, Eilat, Israel, 3/12/08. https://doi.org/10.1109/EEEI.2008.4736544

Bounds on the thresholds of non-binary LDPC codes. / Levi, Oron; Burshtein, David.
2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008. 2008. p. 348-352 4736544 (IEEE Convention of Electrical and Electronics Engineers in Israel, Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Bounds on the thresholds of non-binary LDPC codes

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Keywords

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