© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

QC-LDPC Code Construction by Proto-Matrix Extension Based on Depth Tree

蔡佳育

Published Jan 1, 2014• 0 citations

Abstract

The error-correcting code (ECC) is one of the channel coding technique widely used in many applications. Low density parity check (LDPC) codes have a remarkable performance Among the error-correcting codes, and have drawn significant attention for their error-correcting capability using the message-passing decoding algorithm. The PEG algorithm is a good sub-optimal method to construct the Tanner graph for a LDPC code. By progressively establishing edges between the furthest nodes, the PEG algorithm is able to build a Tanner graph while maximizing length of the cycle caused in the edge adding progress. In this thesis, we introduces a greedy algorithm for quasi-cyclic (QC) LDPC code construction, which works in the same manner as the PEG algorithm. QC-LDPC codes are a subclass of LDPC codes which gains benefits on encoding/decodng complexity reduction from their circular shifting structures. In the proposed algorithm, a QC-LDPC code is built by extending a small size matrix to the target size with large cycles. Our algorithm focuses on cycle length stretching during the matrix extension. The matrix extension is implemented by fitting proper circulant matrix while eliminating short cycles. We present a new kind of depth tree for circulant search in matrix extension procedure. Our algorithm brings out the QC-LDPC code with reconfigurable code parameter settings and has good performance close to PEG LDPC codes. Furthermore, the use of matrix extension reduces the computation scale, and provides a efficient and easy-to-implement method to construct a QC-LDPC code.

Related papers

Optimized Construction of Short and High Rate Protograph QC-LDPC Codes

Jianrong Bao, Xiaorong Xu, Chao Liu +2 more

To obtain efficient and pragmatic channel codes high signal-to-noise ratios (SNRs), an optimized construction of short and high rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is presented. Based on an optimized protograph template, the code framework is firstly produced by the extensions of the variable nodes. By enlarging the dimension of the sub-matrices related to the protograph framework, the base quasi-cyclic (QC) matrix is generated with required code rate and length. Then, the elements in the base matrix are split with even smaller square sub-matrices of the same row and column weights. In this procedure, a progressive edge growth (PEG) algorithm is employed to find the optimized positions of the QC submatrices, which brings larger girth for better code performance. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC improved approximated cycle extrinsic message degree (QCI-ACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph and thus it improves the error floor. Simulation results show that the codes produced by the proposed method demonstrate quite good bit error rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency by the high code rate, as well as the low complexity by the short code length. Therefore, the proposed code construction can be efficiently applied in the design of short and high rate protograph QC-LDPC codes with high rate and rational complexity.

International Conference on Wireless Communications and Signal Processing (WCSP)•Oct 20, 2021•1 citation

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

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

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

Modified PEG algorithm for large girth Quasi-cyclic protograph LDPC codes

Xueqin Jiang, Moon Ho Lee, Hui-Ming Wang +2 more

For a given base graph, the protograph can be obtained by a copy-and-permute procedure. If the permutation is cyclic, the protograph corresponds to a quasi-cyclic (QC) protograph LDPC code. The girth of the QC protograph LDPC code is determined by the girth of the base graph and the permutation shifts. Progressive edge-growth (PEG) construction builds up a Tanner graph, or equivalently a parity-check matrix, for an LDPC code by maximizing the local girth at symbol nodes in a greedy algorithm. In this paper, we introduce a modified version of the PEG algorithm which can construct large girth base graph and determine the optimal permutation shifts, simultaneously, for QC protograph LDPC codes. Simulation results show that the QC protograph LDPC codes constructed by the proposed modified PEG algorithm have good frame error rate (FER) performance over the AWGN channel.

2012 International Conference on Computing, Networking and Communications (ICNC)•Feb 1, 2016•5 citations

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

The error-correcting code (ECC) is one of the channel coding technique widely used in many applications. Low density parity check (LDPC) codes have a remarkable performance Among the error-correcting codes, and have drawn significant attention for their error-correcting capability using the message-passing decoding algorithm. The PEG algorithm is a good sub-optimal method to construct the Tanner graph for a LDPC code. By progressively establishing edges between the furthest nodes, the PEG algorithm is able to build a Tanner graph while maximizing length of the cycle caused in the edge adding progress. In this thesis, we introduces a greedy algorithm for quasi-cyclic (QC) LDPC code construction, which works in the same manner as the PEG algorithm. QC-LDPC codes are a subclass of LDPC codes which gains benefits on encoding/decodng complexity reduction from their circular shifting structures. In the proposed algorithm, a QC-LDPC code is built by extending a small size matrix to the target size with large cycles. Our algorithm focuses on cycle length stretching during the matrix extension. The matrix extension is implemented by fitting proper circulant matrix while eliminating short cycles. We present a new kind of depth tree for circulant search in matrix extension procedure. Our algorithm brings out the QC-LDPC code with reconfigurable code parameter settings and has good performance close to PEG LDPC codes. Furthermore, the use of matrix extension reduces the computation scale, and provides a efficient and easy-to-implement method to construct a QC-LDPC code.

To obtain efficient and pragmatic channel codes high signal-to-noise ratios (SNRs), an optimized construction of short and high rate protograph quasi-cyclic (QC) low-density parity-check (LDPC) codes is presented. Based on an optimized protograph template, the code framework is firstly produced by the extensions of the variable nodes. By enlarging the dimension of the sub-matrices related to the protograph framework, the base quasi-cyclic (QC) matrix is generated with required code rate and length. Then, the elements in the base matrix are split with even smaller square sub-matrices of the same row and column weights. In this procedure, a progressive edge growth (PEG) algorithm is employed to find the optimized positions of the QC submatrices, which brings larger girth for better code performance. Also the circulant offsets in all QC sub-matrices are optimally searched by a QC improved approximated cycle extrinsic message degree (QCI-ACE) algorithm, which improves the relationship of the unavoidable loops in the code's Tanner graph and thus it improves the error floor. Simulation results show that the codes produced by the proposed method demonstrate quite good bit error rate (BER) performance. In addition, they exhibit good properties of high spectrum efficiency by the high code rate, as well as the low complexity by the short code length. Therefore, the proposed code construction can be efficiently applied in the design of short and high rate protograph QC-LDPC codes with high rate and rational complexity.

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.

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.

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.

For a given base graph, the protograph can be obtained by a copy-and-permute procedure. If the permutation is cyclic, the protograph corresponds to a quasi-cyclic (QC) protograph LDPC code. The girth of the QC protograph LDPC code is determined by the girth of the base graph and the permutation shifts. Progressive edge-growth (PEG) construction builds up a Tanner graph, or equivalently a parity-check matrix, for an LDPC code by maximizing the local girth at symbol nodes in a greedy algorithm. In this paper, we introduce a modified version of the PEG algorithm which can construct large girth base graph and determine the optimal permutation shifts, simultaneously, for QC protograph LDPC codes. Simulation results show that the QC protograph LDPC codes constructed by the proposed modified PEG algorithm have good frame error rate (FER) performance over the AWGN channel.

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.