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

Journal of Electronics (China)

New constructions of LDPC codes based on circulant permutation matrices for AWGN channel

Zixi Song, Lijun Zhang

Published Apr 1, 2014• 1 citation
Publisher
DOI
10.1007/s11767-014-3130-x

Related papers

LDPC codes based on circulant permutation matrices for fast encoding

Ma -, Lee, Xiao Xiao

•Jan 1, 2006•0 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

Quasi-Cyclic LDPC Codes on Cyclic Subgroups of Finite Fields

Li Guo Zhang, Shu Lin, Khaled Abdel-Ghaffar +2 more

A new class of quasi-cyclic LDPC codes whose parity-check matrices are arrays of circulant permutation matrices constructed based on cyclic subgroups of finite fields is presented. This class of codes contains several known classes of algebraic quasi-cyclic LDPC codes as subclasses. Experimental results show that the codes constructed perform very well over the AWGN channel when decoded with iterative decoding based on belief propagation. This class of new QC-LDPC codes contains a subclass of codes which have large minimum distances. Combinatorial expressions for the ranks of the parity-check matrices of a subclass of codes constructed based on fields of characteristic two are given.

IEEE Transactions on Communications•Jun 28, 2011•34 citations

Construction of LDPC Codes from Affine Permutation Matrices

Michael E. O’Sullivan, Marcus Greferath, Roxana Smarandache

•Oct 2, 2002•0 citations

Large-Girth Nonbinary QC-LDPC Codes of Various Lengths

Jie Huang, Lei Liu, Wuyang Zhou +1 more

In this paper, we construct nonbinary quasi-cyclic low-density parity-check (QC-LDPC) codes whose parity check matrices consist of an array of square sub-matrices which are either zero matrices or circulant permutation matrices. We propose a novel method to design the shift offset values of the circulant permutation sub-matrices, so that the code length can vary while maintaining a large girth. Extensive Monte Carlo simulations demonstrate that the obtained codes of a wide range of rates (from 1/2 to 8/9) with length from 1000 to 10000 bits have very good performance over both AWGN and Rayleigh fading channels. Furthermore, the proposed method is extended to design multiple nonbinary QC-LDPC codes simultaneously where each individual code can achieve large girth with variable lengths. The proposed codes are appealing to practical adaptive systems where the block length and code rate need to be adaptively adjusted depending on traffic characteristics and channel conditions.

IEEE Transactions on Communications•Oct 27, 2010•36 citations

Research on Construction Algorithm of Large Circulant LDPC Codes

Xiao Yuan Wu, Yupeng Li, Yanyue Zhang

Lecture notes in electrical engineering•Jan 1, 2024•0 citations
A new class of quasi-cyclic LDPC codes whose parity-check matrices are arrays of circulant permutation matrices constructed based on cyclic subgroups of finite fields is presented. This class of codes contains several known classes of algebraic quasi-cyclic LDPC codes as subclasses. Experimental results show that the codes constructed perform very well over the AWGN channel when decoded with iterative decoding based on belief propagation. This class of new QC-LDPC codes contains a subclass of codes which have large minimum distances. Combinatorial expressions for the ranks of the parity-check matrices of a subclass of codes constructed based on fields of characteristic two are given.
In this paper, we construct nonbinary quasi-cyclic low-density parity-check (QC-LDPC) codes whose parity check matrices consist of an array of square sub-matrices which are either zero matrices or circulant permutation matrices. We propose a novel method to design the shift offset values of the circulant permutation sub-matrices, so that the code length can vary while maintaining a large girth. Extensive Monte Carlo simulations demonstrate that the obtained codes of a wide range of rates (from 1/2 to 8/9) with length from 1000 to 10000 bits have very good performance over both AWGN and Rayleigh fading channels. Furthermore, the proposed method is extended to design multiple nonbinary QC-LDPC codes simultaneously where each individual code can achieve large girth with variable lengths. The proposed codes are appealing to practical adaptive systems where the block length and code rate need to be adaptively adjusted depending on traffic characteristics and channel conditions.