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

Jisuanji gongcheng

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

Xiaoming Liu

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

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.

Related papers

An improved algorithm for constructing QC-LDPC codes based on the PEG algorithm

Zhiyong Fan, Weibo Zhang, Xingcheng Liu +1 more

The Progressive edge-growth (PEG) algorithm was proven to be a simple and effective approach in designing Low-density parity-check (LDPC) codes. However, the Tanner graph constructed with the PEG algorithm is non-structured, which leads to random distributions of the positions of 1's in the corresponding parity-check matrix. In this paper, an improved algorithm based on the PEG algorithm for constructing quasi-cyclic (QC) LDPC codes is proposed. The proposed algorithm can eliminate short cycles efficiently and gain low error-floors. What is more important, the proposed QC-LDPC codes construction method is hardware-friendly because of its quasi-cyclic structure. Our simulation results demonstrate that the codes constructed with the proposed algorithm has better performance than the PEG algorithm over the additive white Gaussian noise (AWGN) channel and Rayleigh flat fading channel.

International Conference on Communications and Networking in China (ChinaCom)•Aug 1, 2009•5 citations

Designing Linear Encoder for Structured LDPC Codes with Large Girth

Qiongxia Shen

A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.In this paper,a novel method based on Column-Difference Search Algorithm and Progressive Edge Growth Algorithm is proposed to design Quasi-Cyclic LDPC codes with arbitrary girth and code rate.Due to its almost lower triangular form,CP-LDPC code has linear encoding complexity.The experimental results show that CP-LDPC codes perform better than Tanner codes and Array codes,which are another two classical QC-LDPC codes,and random codes.The code in this paper outperforms random code,Tanner code and Array code by 1.35dB-3.95dB.

Journal of Chinese Computer Systems•Jan 1, 2010•0 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

Study on the Construction Method of Quasi-Cyclic LDPC Codes Based on Progressive Edge-Growth (PEG) Algorithm

Cheng Hao-hui

Progressive Edge-Growth(PEG) algorithm is a method for constructing Low Density Parity-Check(LDPC) codes based on Tanner graph.Studies show that LDPC codes constructed with the algorithm can achieve excellent error-correcting performance.Based on the algorithm,the Quasi-Cyclic(QC) LDPC codes are proposed in this paper and simulations show that the QC-LDPC codes have almost the same excellent performance as the random codes constructed with the PEG algorithm.In addition,these codes have the property of quasi-cyclic structure,and the encoding and decoding can be implemented with simple shift registers.Besides,the code rates of the LDPC codes constructed with the proposed algorithm are more flexible to be adjusted.

Journal of Circuits and Systems•Jan 1, 2009•5 citations

Quasi Cyclic-LDPC codes based on PEG algorithm with maximized girth property

Patanasak Prompakdee, Watid Phakphisut, Pornchai Supnithi

In this paper, we propose a method to construct parity-check matrices of Quasi Cyclic (QC) LDPC codes based on the progressive edge-growth (PEG) algorithm with maximized girth property. The proposed algorithm can eliminate short cycles and improve the decoding performance. Simulation results illustrate that the codes constructed with the proposed algorithm have superior performance to the previous PEG-QC codes over the additive white Gaussian noise (AWGN) channel. At the BER of 10-7, the coding gain of 0.005 dB.

International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS)•Dec 1, 2011•9 citations

Novel construction and cycle analysis of Quasi-Cyclic Low-Density Parity-Check codes

Wenwen Li, Mao Ai, Jie Qiu +1 more

Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes have practical significance in the field of engineering, thus their construction algorithm is a hot issue in the field of LDPC codes. Based on existing construction methods, particularly the method based on Progressive Edge-Growth (PEG) algorithm, a new construction method of shift matrix is proposed. It can effectively avoid the copy of cycle structures, especially short cycles in base matrix after extension. Besides, it also relieves the time cost caused by random search, and greatly improves the length of cycles when compared with algorithms based on methods such as quadratic congruence and arithmetic sequence. Those algorithms can only eliminate short cycles with length 4, while our method can provide QC-LDPC codes without length 6 at least. Cycle analysis and simulation results show that the newly constructed QC-LDPC codes have good cycle structure and error correction performance.

IEEE International Conference on Progress in Informatics and Computing•Dec 1, 2015•2 citations
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.
The Progressive edge-growth (PEG) algorithm was proven to be a simple and effective approach in designing Low-density parity-check (LDPC) codes. However, the Tanner graph constructed with the PEG algorithm is non-structured, which leads to random distributions of the positions of 1's in the corresponding parity-check matrix. In this paper, an improved algorithm based on the PEG algorithm for constructing quasi-cyclic (QC) LDPC codes is proposed. The proposed algorithm can eliminate short cycles efficiently and gain low error-floors. What is more important, the proposed QC-LDPC codes construction method is hardware-friendly because of its quasi-cyclic structure. Our simulation results demonstrate that the codes constructed with the proposed algorithm has better performance than the PEG algorithm over the additive white Gaussian noise (AWGN) channel and Rayleigh flat fading channel.
A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.In this paper,a novel method based on Column-Difference Search Algorithm and Progressive Edge Growth Algorithm is proposed to design Quasi-Cyclic LDPC codes with arbitrary girth and code rate.Due to its almost lower triangular form,CP-LDPC code has linear encoding complexity.The experimental results show that CP-LDPC codes perform better than Tanner codes and Array codes,which are another two classical QC-LDPC codes,and random codes.The code in this paper outperforms random code,Tanner code and Array code by 1.35dB-3.95dB.
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.
Progressive Edge-Growth(PEG) algorithm is a method for constructing Low Density Parity-Check(LDPC) codes based on Tanner graph.Studies show that LDPC codes constructed with the algorithm can achieve excellent error-correcting performance.Based on the algorithm,the Quasi-Cyclic(QC) LDPC codes are proposed in this paper and simulations show that the QC-LDPC codes have almost the same excellent performance as the random codes constructed with the PEG algorithm.In addition,these codes have the property of quasi-cyclic structure,and the encoding and decoding can be implemented with simple shift registers.Besides,the code rates of the LDPC codes constructed with the proposed algorithm are more flexible to be adjusted.
In this paper, we propose a method to construct parity-check matrices of Quasi Cyclic (QC) LDPC codes based on the progressive edge-growth (PEG) algorithm with maximized girth property. The proposed algorithm can eliminate short cycles and improve the decoding performance. Simulation results illustrate that the codes constructed with the proposed algorithm have superior performance to the previous PEG-QC codes over the additive white Gaussian noise (AWGN) channel. At the BER of 10-7, the coding gain of 0.005 dB.
Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes have practical significance in the field of engineering, thus their construction algorithm is a hot issue in the field of LDPC codes. Based on existing construction methods, particularly the method based on Progressive Edge-Growth (PEG) algorithm, a new construction method of shift matrix is proposed. It can effectively avoid the copy of cycle structures, especially short cycles in base matrix after extension. Besides, it also relieves the time cost caused by random search, and greatly improves the length of cycles when compared with algorithms based on methods such as quadratic congruence and arithmetic sequence. Those algorithms can only eliminate short cycles with length 4, while our method can provide QC-LDPC codes without length 6 at least. Cycle analysis and simulation results show that the newly constructed QC-LDPC codes have good cycle structure and error correction performance.