© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

IEEE Communications Letters

Construction of Quasi-Cyclic LDPC Codes via Masking With Successive Cycle Elimination

Hengzhou Xu, Dan Feng, Rui Luo, Baoming Bai

Published Sep 21, 2016• 50 citations

Abstract

In this letter, we study the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes by array dispersion and masking. We first propose a class of arrays of circulant permutation matrices (CPMs) of arbitrary size obtained by dispersion. Based on this class of arrays of CPMs, a class of QC-LDPC codes is constructed. For these resulting codes, we analyze their cycle structure and derive the numbers, which indicate how many cycles pass through each CPM in their parity-check matrices. Following the indication numbers with the order from largest to smallest, we replace the corresponding CPMs with zero matrices (ZMs) of the same size one by one until a targeted masking termination condition is satisfied. Then, the resultant arrays of CPMs and ZMs give a large class of QC-LDPC codes. Numerical results show that the codes constructed perform well over the additive white Gaussian noise (AWGN) channel when decoded with the sum-product algorithm.

DOI: 10.1109/lcomm.2016.2608938

Related papers

Construction of QC-LDPC Codes Based on Pre-Masking and Local Optimal Searching

Dongdong Wang, Liqian Wang, Xue Chen +3 more

In this letter, we consider the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes by jointly optimizing the girth g and the number of g-cycles. We first propose a sub-array detection method to accelerate the detection of cycles, and by detecting the non-repeated automatic enumerative cycles in the frame of sub-arrays, cycle detection time can be greatly reduced. Furthermore, a local optimal searching algorithm combined with pre-masking is presented, by orderly searching the local optimal p j,l for each circulant permutation matrix (CPM), a class of QC-LDPC codes with possibly enlarged g, less number of g-cycles, and arbitrary attainable degree distribution could be constructed. Simulation results show that the codes constructed by the proposed method perform well in error floor region.

IEEE Communications Letters•Sep 25, 2017•9 citations

NEW CONSTRUCTIONS OF LDPC CODES BASED ON CIRCULANT PERMUTATION MATRICES FOR AWGN CHANNEL

Song, Zixi, Zhang +1 more

Two new design approaches for constructing Low-Density Parity-Check(LDPC) codes are proposed.One is used to design regular Quasi-Cyclic LDPC(QC-LDPC) codes with girth at least 8.The other is used to design irregular LDPC codes.Both of their parity-check matrices are composed of Circulant Permutation Matrices(CPMs).When iteratively decoded with the Sum-Product Algorithm(SPA),these proposed codes exhibit good performances over the AWGN channel.

Journal of Electronics (China)•Jan 1, 2014•2 citations

Construction of Quasi-Cyclic LDPC codes with large girth based on circulant permutation matirx

Peng Yang, Xiaoxiao Bao, Hui Zhao

In this paper, we propose an algorithm for removing short-cycles in Quasi-Cyclic (QC) Low-density parity-check (LDPC) codes. First using an algorithm with lower computational complexity, all the cycles in the parity check matrix H are found. Then following a ruler, we adjust the shift value of circulant permutation matrix (CPM) to remove the short-cycles. This algorithm could ensure that the code after cycle removal process preserves the quasi-cyclic structure. Simulation results show that: comparing with the codes (504,252) and (1008, 504), we achieve 0.1dB improvement both.

Wireless and Optical Communications Conference•May 1, 2013•4 citations

Quasi-cyclic LDPC codes: Construction and rank analysis of their parity-check matrices

Keke Liu, Qin Huang, Shu Lin +1 more

A construction of binary and non-binary quasi-cyclic (QC)-LDPC codes based on partitions of finite fields of characteristic 2 is proposed. The construction is carried out in the Fourier transform domain. The parity-check matrices of these QC-LDPC codes are arrays of circulant permutation matrices. The ranks of these arrays are analyzed and combinatorial expressions are derived. Example codes are given and simulations show that they perform well over the AWGN channel decoded with message-passing decoding algorithms.

Information Theory and Applications Workshop (ITA)•Feb 1, 2012•15 citations

A Method for Constructing Parity-Check Matrices of Quasi-Cyclic LDPC Codes Over GF(q)

Stanislav Kruglik, Valeriya Potapova, Alexey Frolov

Abstract An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). The algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of the algorithm is demonstrated by means of simulations. In order to explain the simulation results we also derive upper bounds on the minimum distance of NB QC-LDPC codes.

Journal of Communications Technology and Electronics•Dec 1, 2018•2 citations

A method for constructing parity-check matrices of non-binary quasi-cyclic LDPC codes

Stanislav Kruglik, Valeriya Potapova, Alexey Frolov

An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). Firstly the algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of the algorithm is demonstrated by means of simulations. In particular, it was shown that NB QC-LDPC codes constructed with use of our algorithm loose less that 0.1 dB in comparison to the best NB LDPC codes.

arXiv:1705.10717•May 30, 2017•0 citations

In this letter, we study the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes by array dispersion and masking. We first propose a class of arrays of circulant permutation matrices (CPMs) of arbitrary size obtained by dispersion. Based on this class of arrays of CPMs, a class of QC-LDPC codes is constructed. For these resulting codes, we analyze their cycle structure and derive the numbers, which indicate how many cycles pass through each CPM in their parity-check matrices. Following the indication numbers with the order from largest to smallest, we replace the corresponding CPMs with zero matrices (ZMs) of the same size one by one until a targeted masking termination condition is satisfied. Then, the resultant arrays of CPMs and ZMs give a large class of QC-LDPC codes. Numerical results show that the codes constructed perform well over the additive white Gaussian noise (AWGN) channel when decoded with the sum-product algorithm.

In this letter, we consider the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes by jointly optimizing the girth g and the number of g-cycles. We first propose a sub-array detection method to accelerate the detection of cycles, and by detecting the non-repeated automatic enumerative cycles in the frame of sub-arrays, cycle detection time can be greatly reduced. Furthermore, a local optimal searching algorithm combined with pre-masking is presented, by orderly searching the local optimal p j,l for each circulant permutation matrix (CPM), a class of QC-LDPC codes with possibly enlarged g, less number of g-cycles, and arbitrary attainable degree distribution could be constructed. Simulation results show that the codes constructed by the proposed method perform well in error floor region.

In this paper, we propose an algorithm for removing short-cycles in Quasi-Cyclic (QC) Low-density parity-check (LDPC) codes. First using an algorithm with lower computational complexity, all the cycles in the parity check matrix H are found. Then following a ruler, we adjust the shift value of circulant permutation matrix (CPM) to remove the short-cycles. This algorithm could ensure that the code after cycle removal process preserves the quasi-cyclic structure. Simulation results show that: comparing with the codes (504,252) and (1008, 504), we achieve 0.1dB improvement both.

A construction of binary and non-binary quasi-cyclic (QC)-LDPC codes based on partitions of finite fields of characteristic 2 is proposed. The construction is carried out in the Fourier transform domain. The parity-check matrices of these QC-LDPC codes are arrays of circulant permutation matrices. The ranks of these arrays are analyzed and combinatorial expressions are derived. Example codes are given and simulations show that they perform well over the AWGN channel decoded with message-passing decoding algorithms.

Abstract An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). The algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of the algorithm is demonstrated by means of simulations. In order to explain the simulation results we also derive upper bounds on the minimum distance of NB QC-LDPC codes.

An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). Firstly the algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of the algorithm is demonstrated by means of simulations. In particular, it was shown that NB QC-LDPC codes constructed with use of our algorithm loose less that 0.1 dB in comparison to the best NB LDPC codes.