Three algebraic methods for constructing nonbinary LDPC codes based on finite fields

Keke Liu; Zesong Fei; Jingming Kuang

doi:10.1109/PIMRC.2008.4699586

Three algebraic methods for constructing nonbinary LDPC codes based on finite fields

Keke Liu^*, Zesong Fei, Jingming Kuang

^*Corresponding author for this work

School of Information and Electronics

Beijing Institute of Technology

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

4 Citations (Scopus)

Abstract

In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is used to construct quasi-cyclic codes with girth at least 6 based on the automorphisms of finite fields, the second method gives a class of (4, ρ) quasi-cyclic codes with girth at least 8, the third method gives a class of codes with cycles limited. Simulation results show that the constructed codes perform very well over AWGN channel, and they have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Lin.

Original language	English
Title of host publication	2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2008
DOIs	https://doi.org/10.1109/PIMRC.2008.4699586
Publication status	Published - 2008
Event	2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2008 - Poznan, Poland Duration: 15 Sept 2008 → 18 Sept 2008

Publication series

Name	IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC

Conference

Conference	2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2008
Country/Territory	Poland
City	Poznan
Period	15/09/08 → 18/09/08

Keywords

Automorphism
Cycles-limited LDPC codes
Finite fields
Nonbinary LDPC codes

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10.1109/PIMRC.2008.4699586

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Liu, K., Fei, Z., & Kuang, J. (2008). Three algebraic methods for constructing nonbinary LDPC codes based on finite fields. In 2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2008 Article 4699586 (IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC). https://doi.org/10.1109/PIMRC.2008.4699586

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title = "Three algebraic methods for constructing nonbinary LDPC codes based on finite fields",

abstract = "In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is used to construct quasi-cyclic codes with girth at least 6 based on the automorphisms of finite fields, the second method gives a class of (4, ρ) quasi-cyclic codes with girth at least 8, the third method gives a class of codes with cycles limited. Simulation results show that the constructed codes perform very well over AWGN channel, and they have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Lin.",

keywords = "Automorphism, Cycles-limited LDPC codes, Finite fields, Nonbinary LDPC codes",

author = "Keke Liu and Zesong Fei and Jingming Kuang",

year = "2008",

doi = "10.1109/PIMRC.2008.4699586",

language = "English",

isbn = "9781424426447",

series = "IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC",

booktitle = "2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2008",

note = "2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2008 ; Conference date: 15-09-2008 Through 18-09-2008",

}

Liu, K, Fei, Z & Kuang, J 2008, Three algebraic methods for constructing nonbinary LDPC codes based on finite fields. in 2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2008., 4699586, IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC, 2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2008, Poznan, Poland, 15/09/08. https://doi.org/10.1109/PIMRC.2008.4699586

Three algebraic methods for constructing nonbinary LDPC codes based on finite fields. / Liu, Keke; Fei, Zesong; Kuang, Jingming.
2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2008. 2008. 4699586 (IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC).

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

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AU - Liu, Keke

AU - Fei, Zesong

AU - Kuang, Jingming

PY - 2008

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N2 - In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is used to construct quasi-cyclic codes with girth at least 6 based on the automorphisms of finite fields, the second method gives a class of (4, ρ) quasi-cyclic codes with girth at least 8, the third method gives a class of codes with cycles limited. Simulation results show that the constructed codes perform very well over AWGN channel, and they have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Lin.

AB - In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is used to construct quasi-cyclic codes with girth at least 6 based on the automorphisms of finite fields, the second method gives a class of (4, ρ) quasi-cyclic codes with girth at least 8, the third method gives a class of codes with cycles limited. Simulation results show that the constructed codes perform very well over AWGN channel, and they have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Lin.

KW - Automorphism

KW - Cycles-limited LDPC codes

KW - Finite fields

KW - Nonbinary LDPC codes

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DO - 10.1109/PIMRC.2008.4699586

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T3 - IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC

BT - 2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2008

T2 - 2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2008

Y2 - 15 September 2008 through 18 September 2008

ER -

Three algebraic methods for constructing nonbinary LDPC codes based on finite fields

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