Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IET Communications

Construction of girth‐eight quasi‐cyclic low‐density parity‐check codes with low encoding complexity

Ruyan Wang, Yong Li, Hui Zhao, Liang Qin, Hong Zhang

Published Jan 1, 2016• 6 citations
Publisher

Abstract

A construction method for girth‐eight quasi‐cyclic low‐density parity‐check codes (QC‐LDPCs) with low encoding complexity is proposed in this study. To avoid short cycles and further improve the performance of the authors proposed codes, the greatest common divisor (GCD)‐based method is utilised to construct the information part with girth‐eight of the parity‐check matrix with systematic form. Furthermore, the quasi‐dual‐diagonal structure is adopted as the parity part of the parity‐check matrix for fast encoding, which not only maintains the parity‐check matrix with girth‐eight, but also efficiently decreases the encoding complexity of their proposed codes. Simulation results show that their proposed codes perform better than Mackay's codes and the QC‐LDPCs constructed by the GCD‐based method, and have comparable performance compared with progressive edge growth based QC‐LDPCs. Besides, their proposed codes have lower encoding complexity due to the property of fast encoding.

DOI
10.1049/iet-com.2015.0056

Related papers

Construction of Girth-Eight QC-LDPC Codes from Greatest Common Divisor

Guohua Zhang, Rong Xia Sun, Xinmei Wang

For any column weight J and any row weight L, a novel framework is proposed such that a girth-eight (J,L) quasi-cyclic low-density parity-check (QC-LDPC) code with any block length above a lower bound can be constructed via a simple inequality in terms of greatest common divisor (GCD). The main advantage is that the construction of a class of (J,L) girth-eight QC-LDPC codes is transformed into a rather simple task, searching for J integers satisfying the so-called GCD constraint for L. Combining the new method with masking matrices, a class of type-1 QC-LDPC codes is presented with girth at least eight. Simulation results show that the type-1 codes perform better than the random QC-LDPC codes and quadratic-congruence-based QC-LDPC codes for moderate block lengths and low code rates.

IEEE Communications Letters•Jan 2, 2013•47 citations

Constructions of Girth-Eight QC-LDPC Codes with Dual-Diagonal Structure Based on GCD Framework

Guohua Zhang, Haiyang Liu, Mengjuan Lou +1 more

A novel class of quasi-cyclic (QC) low-density parity-check (LDPC) codes is explicitly proposed without 4-cycles and 6-cycles via the greatest-common-divisor (GCD) framework. From the new codes, a novel type of girth-eight QC-LDPC codes with a dual-diagonal (DD) structure is presented, in which the single undetermined entry in the associated exponent matrix can be determined by simple formulae. The proposed DD codes have similar or better performance compared with DD codes obtained from computer search. Moreover, a lower bound on circulant sizes which guarantees the existence of qualified undetermined entries is also provided.

International Conference on Wireless Communications and Signal Processing (WCSP)•Nov 2, 2023•5 citations

Construction of LDPC Code with Big Girth and Linear-encoding Complexity

Xiaoming Liu

Based on cycle search algorithm and Progressive Edge Growth(PEG) algorithm,this paper proposes a method to construct quasi-cyclic Low-density Parity Check(LDPC) codes with big girth and linear-encoding complexity.A parity-check matrix with a form of approximate lower triangle structure is designed to achieve iterative encoding with linear-encoding complexity.PEG algorithm is used to construct the base matrix and the cycle search algorithm is used to optimize the cycle distribution.And a fast encoding method is proposed.Experimental results show that the LDPC codes constructed with the proposed method can avoid error floor and achieve better BER performance than Tanner-QC-LDPC codes and equivalent BER performance to the ones of random codes.

Jisuanji gongcheng•Jan 1, 2011•0 citations

Improved combining method for design of quasi‐cyclic LDPC codes

Yuanhua Liu, Meiling Zhang, Xinliang Niu

An improved combining method is proposed for constructing quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes with large girth and few short cycles. Large girth QC‐LDPC codes can be obtained by carefully designing one component code with large girth. By properly designing the other component codes, a lot of QC‐LDPC codes with very few short cycles can be designed. Simulations show that compared with Chinese remainder theorem based QC‐LDPC codes and progressive edge‐growth based QC‐LDPC codes, the proposed QC‐LDPC codes have much less short cycles and better performance.

Electronics Letters•Mar 1, 2014•2 citations

Quasi-Cyclic Low-Density Parity-Check Codes Based on Progressive Cycle Growth Algorithm

Yuanhua Liu, Meiling Zhang, Niu Xin-Liang

Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.

International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC)•Jul 1, 2016•1 citation

A Method for Geometric Construction of Low-density Parity-check Codes

Xiaoguang Wang

A new method for geometric construction of QC-LDPC is proposed. The parity-check matrix constructed through this method has a girth more than eight,which promises good performance. Since the parity-check matrix is composed of cyclic sub-matrices,the hardware encoder is simple. Simulations show that this type of LDPC codes has remarkable performance with low encoding complexity.

•Jan 1, 2008•0 citations
A construction method for girth‐eight quasi‐cyclic low‐density parity‐check codes (QC‐LDPCs) with low encoding complexity is proposed in this study. To avoid short cycles and further improve the performance of the authors proposed codes, the greatest common divisor (GCD)‐based method is utilised to construct the information part with girth‐eight of the parity‐check matrix with systematic form. Furthermore, the quasi‐dual‐diagonal structure is adopted as the parity part of the parity‐check matrix for fast encoding, which not only maintains the parity‐check matrix with girth‐eight, but also efficiently decreases the encoding complexity of their proposed codes. Simulation results show that their proposed codes perform better than Mackay's codes and the QC‐LDPCs constructed by the GCD‐based method, and have comparable performance compared with progressive edge growth based QC‐LDPCs. Besides, their proposed codes have lower encoding complexity due to the property of fast encoding.
For any column weight J and any row weight L, a novel framework is proposed such that a girth-eight (J,L) quasi-cyclic low-density parity-check (QC-LDPC) code with any block length above a lower bound can be constructed via a simple inequality in terms of greatest common divisor (GCD). The main advantage is that the construction of a class of (J,L) girth-eight QC-LDPC codes is transformed into a rather simple task, searching for J integers satisfying the so-called GCD constraint for L. Combining the new method with masking matrices, a class of type-1 QC-LDPC codes is presented with girth at least eight. Simulation results show that the type-1 codes perform better than the random QC-LDPC codes and quadratic-congruence-based QC-LDPC codes for moderate block lengths and low code rates.
A novel class of quasi-cyclic (QC) low-density parity-check (LDPC) codes is explicitly proposed without 4-cycles and 6-cycles via the greatest-common-divisor (GCD) framework. From the new codes, a novel type of girth-eight QC-LDPC codes with a dual-diagonal (DD) structure is presented, in which the single undetermined entry in the associated exponent matrix can be determined by simple formulae. The proposed DD codes have similar or better performance compared with DD codes obtained from computer search. Moreover, a lower bound on circulant sizes which guarantees the existence of qualified undetermined entries is also provided.
Based on cycle search algorithm and Progressive Edge Growth(PEG) algorithm,this paper proposes a method to construct quasi-cyclic Low-density Parity Check(LDPC) codes with big girth and linear-encoding complexity.A parity-check matrix with a form of approximate lower triangle structure is designed to achieve iterative encoding with linear-encoding complexity.PEG algorithm is used to construct the base matrix and the cycle search algorithm is used to optimize the cycle distribution.And a fast encoding method is proposed.Experimental results show that the LDPC codes constructed with the proposed method can avoid error floor and achieve better BER performance than Tanner-QC-LDPC codes and equivalent BER performance to the ones of random codes.
An improved combining method is proposed for constructing quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes with large girth and few short cycles. Large girth QC‐LDPC codes can be obtained by carefully designing one component code with large girth. By properly designing the other component codes, a lot of QC‐LDPC codes with very few short cycles can be designed. Simulations show that compared with Chinese remainder theorem based QC‐LDPC codes and progressive edge‐growth based QC‐LDPC codes, the proposed QC‐LDPC codes have much less short cycles and better performance.
Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.