Row-weight Universal Algebraic Constructions of Girth-8 Quasi-Cyclic Low-Density Parity-Check Codes with Large Column Weights

ZHANG Guohua; QIN Yu; LOU Mengjuan; FANG Yi

doi:10.11999/JEIT231111

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ZHANG Guohua, QIN Yu, LOU Mengjuan, FANG Yi. Row-weight Universal Algebraic Constructions of Girth-8 Quasi-Cyclic Low-Density Parity-Check Codes with Large Column Weights[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT231111

Citation:

ZHANG Guohua, QIN Yu, LOU Mengjuan, FANG Yi. Row-weight Universal Algebraic Constructions of Girth-8 Quasi-Cyclic Low-Density Parity-Check Codes with Large Column Weights[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT231111

Citation:

ZHANG Guohua, QIN Yu, LOU Mengjuan, FANG Yi. Row-weight Universal Algebraic Constructions of Girth-8 Quasi-Cyclic Low-Density Parity-Check Codes with Large Column Weights[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT231111

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Row-weight Universal Algebraic Constructions of Girth-8 Quasi-Cyclic Low-Density Parity-Check Codes with Large Column Weights

doi: 10.11999/JEIT231111

1.
Xi’an University of Posts and Telecommunications, Xi’an 710121, China
2.
Guangdong University of Technology, Guangzhou 510006, China

Funds: The National Natural Science Foundation of China (62322106, 62071131), International Collaborative Research Program of Guangdong Science and Technology Department (2022A0505050070)

Received Date: 2023-10-12
Rev Recd Date: 2024-01-25

Available Online: 2024-02-07

Abstract

Abstract

Short Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes without small cycles suitable for an arbitrary row weight (i.e., Row-Weight Universal (RWU)), are of great significance for both theoretical research and engineering application. Existing methods having RWU property and guaranteeing the nonexistence of 4-cycles and 6-cycles, can only offer short QC-LDPC codes for the column weights of 3 and 4. Based on the Greatest Common Divisor (GCD) framework, three new methods are proposed in this paper for the column weights of 5 and 6, which can possess RWU property and at the same time remove all 4-cycles and 6-cycles. Compared with existing methods with RWU property, the code lengths of the novel methods are sharply reduced from the fourth power of row weight to the third power of row weight. Therefore, the new methods can provide short RWU QC-LDPC codes without 4-cycles and 6-cycles for occasions where base codes with large column weights are required, such as composite constructions and advanced optimization pertaining to QC-LDPC codes. Moreover, compared with the search-based symmetric QC-LDPC codes, the new codes need no search, have lower description complexity, and exhibit better decoding performance.
- Low-Density Parity-Check (LDPC) codes,
- Quasi-Cyclic(QC),
- Girth,
- Greatest Common Divisor (GCD)

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References(21)

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