Two algebraic methods for constructing efficiently encodable quasi-cyclic LDPC codes

Keke Liu; Zesong Fei; Jingming Kuang

doi:10.1109/WiCom.2008.360

Two algebraic methods for constructing efficiently encodable quasi-cyclic LDPC codes

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

Abstract

In this paper, we present two algebraic methods for constructing Quasi-Cyclic LDPC codes. The first method is based on the quadratic residues modulo p (where p is a prime), the second method is based on the multiplicative inverses in finite fields. The codes constructed based on these methods are efficiently encodable and have a girth at least 6. Simulation results show that with SPA decoding, the constructed codes based on our methods perform very well over the AWGN channel compared to some other types of famous codes, such as random Mackay code or extended EG-LDPC code recommended by NASA.

Original language	English
Title of host publication	2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008
DOIs	https://doi.org/10.1109/WiCom.2008.360
Publication status	Published - 2008
Event	2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008 - Dalian, China Duration: 12 Oct 2008 → 14 Oct 2008

Publication series

Name	2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008

Conference

Conference	2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008
Country/Territory	China
City	Dalian
Period	12/10/08 → 14/10/08

Keywords

Multiplicative inverses infinite fields
Quadratic residues
Quasi-cyclic LDPC codes

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10.1109/WiCom.2008.360

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Liu, K., Fei, Z., & Kuang, J. (2008). Two algebraic methods for constructing efficiently encodable quasi-cyclic LDPC codes. In 2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008 Article 4678269 (2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008). https://doi.org/10.1109/WiCom.2008.360

@inproceedings{e1b41111fcaf46e5a2c88cc39b852d97,

title = "Two algebraic methods for constructing efficiently encodable quasi-cyclic LDPC codes",

abstract = "In this paper, we present two algebraic methods for constructing Quasi-Cyclic LDPC codes. The first method is based on the quadratic residues modulo p (where p is a prime), the second method is based on the multiplicative inverses in finite fields. The codes constructed based on these methods are efficiently encodable and have a girth at least 6. Simulation results show that with SPA decoding, the constructed codes based on our methods perform very well over the AWGN channel compared to some other types of famous codes, such as random Mackay code or extended EG-LDPC code recommended by NASA.",

keywords = "Multiplicative inverses infinite fields, Quadratic residues, Quasi-cyclic LDPC codes",

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

year = "2008",

doi = "10.1109/WiCom.2008.360",

language = "English",

isbn = "9781424421084",

series = "2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008",

booktitle = "2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008",

note = "2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008 ; Conference date: 12-10-2008 Through 14-10-2008",

}

Liu, K, Fei, Z & Kuang, J 2008, Two algebraic methods for constructing efficiently encodable quasi-cyclic LDPC codes. in 2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008., 4678269, 2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008, 2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008, Dalian, China, 12/10/08. https://doi.org/10.1109/WiCom.2008.360

Two algebraic methods for constructing efficiently encodable quasi-cyclic LDPC codes. / Liu, Keke; Fei, Zesong; Kuang, Jingming.
2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008. 2008. 4678269 (2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008).

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

TY - GEN

T1 - Two algebraic methods for constructing efficiently encodable quasi-cyclic LDPC codes

AU - Liu, Keke

AU - Fei, Zesong

AU - Kuang, Jingming

PY - 2008

Y1 - 2008

N2 - In this paper, we present two algebraic methods for constructing Quasi-Cyclic LDPC codes. The first method is based on the quadratic residues modulo p (where p is a prime), the second method is based on the multiplicative inverses in finite fields. The codes constructed based on these methods are efficiently encodable and have a girth at least 6. Simulation results show that with SPA decoding, the constructed codes based on our methods perform very well over the AWGN channel compared to some other types of famous codes, such as random Mackay code or extended EG-LDPC code recommended by NASA.

AB - In this paper, we present two algebraic methods for constructing Quasi-Cyclic LDPC codes. The first method is based on the quadratic residues modulo p (where p is a prime), the second method is based on the multiplicative inverses in finite fields. The codes constructed based on these methods are efficiently encodable and have a girth at least 6. Simulation results show that with SPA decoding, the constructed codes based on our methods perform very well over the AWGN channel compared to some other types of famous codes, such as random Mackay code or extended EG-LDPC code recommended by NASA.

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KW - Quadratic residues

KW - Quasi-cyclic LDPC codes

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DO - 10.1109/WiCom.2008.360

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SN - 9781424421084

T3 - 2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008

BT - 2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008

T2 - 2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008

Y2 - 12 October 2008 through 14 October 2008

ER -

Two algebraic methods for constructing efficiently encodable quasi-cyclic LDPC codes

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