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 China Institute of Communications

Construction of low-density parity-check codes using cyclic difference sets

Ming Jiang

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

A new method to construct LDPC codes based on cyclic difference sets of combinatorics was proposed. A large number of regular LDPC codes could be generated, with the same column weight and the same row weight. And this method could eliminate the cycles with length equal to four and decrease the ones with length equal to six. Sum-product decoding algorithm was used to decode the new constructed LDPC codes and simulation results showed that they exhibit good performance.

Related papers

Construction of Low-density Parity-check Codes Based on Cyclic Difference Sets

Guo Zhi-rong

This paper proposes a method to construct Quasi-Cyclic Low-Density Parity-Check(QC-LDPC) codes based on Cyclic Difference Sets(CDS) of combinatory. The constructed regular QC-LDPC codes are free of 4-cycles and with low complexity shift register encoding. Simulations results show that the constructed LDPC codes perform well under sum-product decoding algorithm.

Jisuanji gongcheng•Jan 1, 2010•0 citations

Can cyclic codes be useful low-density parity-check codes?

Sarah J. Johnson, Steven R. Weller

Traditionally, low-density parity-check (LDPC) codes are constructed randomly and it is not clear whether algebraically constructed codes, such as cyclic codes, can compete with the error correction performances of the random codes. We consider in this paper new cyclic low-density parity-check codes decoded with the sum-product algorithm. The cyclic codes we present have sparse parity-check matrices, good minimum distance and girth 6. Using frnite-length analysis and simulation results we show that the most significant benefit of the new codes, in terms of error correction performance, is the linearly dependent rows in their parity-check matrices. Our results suggest that increasing column weight to improve the minimum distance and the minimum stopping set size of the code proves beneficial at low erasure probabilities but adversely affects performance in channels with high erasure probabilities.

•Jan 1, 2003•1 citation

Generalized Construction of Quasi-Cyclic Regular LDPC Codes Based on Permutation Matrices

E.M. Gabidulin, Abdolhosein Moinian, Bahram Honary

A new approach is proposed for constructing regular low-density parity-check (LDPC) codes based on tensor product of matrices. In this paper, first a general construction method of regular LDPC codes exploiting permutation matrices is described. Constructed codes have a quasi-cyclic structure with no short cycles of length 4 in their Tanner graph, hence simple encoding while maintaining good performance is achieved. The paper also demonstrates a generalized design, which covers a large family of LDPC codes and number of other construction methods. The new generalized LDPC codes are defined by a small number of parameters and cover a large set of code lengths and rates. Using these codes, LDPC matrices of any column weight and row weight can be constructed. Performance of these codes under iterative decoding compares well with other well-structured as well as random LDPC codes

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2006•16 citations

4-Cycle Free LDPC Codes Based on Difference Sets

Morteza Esmaeili, M. Javedankherad

Difference sets are used to give a novel method for constructing structured regular quasi-cyclic low-density parity-check codes. Let Fqbe a field with q elements and assume that D={d1,..., dk} is a (v,k,1)-difference set for Zvwith d12k. Depending on v=q-1, v≥ 2dkor v≥ 2dk-1, three code construction methods are given that produce regular 4-cycle free codes, that is codes with girth at least 6. Simulation results show that the constructed codes perform well over the AWGN channel with an iterative sum-product message-passing decoding algorithm.

IEEE Transactions on Communications•Sep 21, 2012•12 citations

Construction of High-Rate Regular Quasi-Cyclic LDPC Codes Based on Cyclic Difference Families

Hosung Park, Seokbeom Hong, Jong‐Seon No +1 more

For a high-rate case, it is difficult to randomly construct good low-density parity-check (LDPC) codes of short and moderate lengths because their Tanner graphs are prone to have short cycles. Also, the existing high-rate quasi-cyclic (QC) LDPC codes can be constructed only for very restricted code parameters. In this paper, based on special classes of cyclic difference families, we propose a new construction method of high-rate regular QC LDPC codes having parity-check matrices consisting of a single row of circulants with column-weight 3 or 4. The proposed QC LDPC codes can be constructed for various code rates and lengths including the minimum achievable length for given column-weight and design rate under girth 6. It is observed that the parity-check matrices of the proposed QC LDPC codes have full rank for column-weight 3 and just one redundant row for column-weight 4. It is shown that the error correcting performance of the proposed QC LDPC codes of short and moderate lengths is almost the same as that of the existing ones through numerical analysis.

arXiv:1211.3828•IEEE Transactions on Communications•Jul 16, 2013•33 citations

A new random construction for low-density parity-check codes

Zhonghu Huang, Shen Lianfeng, Zhihui Ye

This paper gives a new random construction for LDPC codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has low complexity and great flexible choice in LDPC code parameters including code length, code rate, least girth of the graph, and the weight of column and row in the parity-check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Simulations show that the method performs well with iterative decoding.

International Conference on Communications, Circuits and Systems•Aug 16, 2005•0 citations
A new method to construct LDPC codes based on cyclic difference sets of combinatorics was proposed. A large number of regular LDPC codes could be generated, with the same column weight and the same row weight. And this method could eliminate the cycles with length equal to four and decrease the ones with length equal to six. Sum-product decoding algorithm was used to decode the new constructed LDPC codes and simulation results showed that they exhibit good performance.
Traditionally, low-density parity-check (LDPC) codes are constructed randomly and it is not clear whether algebraically constructed codes, such as cyclic codes, can compete with the error correction performances of the random codes. We consider in this paper new cyclic low-density parity-check codes decoded with the sum-product algorithm. The cyclic codes we present have sparse parity-check matrices, good minimum distance and girth 6. Using frnite-length analysis and simulation results we show that the most significant benefit of the new codes, in terms of error correction performance, is the linearly dependent rows in their parity-check matrices. Our results suggest that increasing column weight to improve the minimum distance and the minimum stopping set size of the code proves beneficial at low erasure probabilities but adversely affects performance in channels with high erasure probabilities.
A new approach is proposed for constructing regular low-density parity-check (LDPC) codes based on tensor product of matrices. In this paper, first a general construction method of regular LDPC codes exploiting permutation matrices is described. Constructed codes have a quasi-cyclic structure with no short cycles of length 4 in their Tanner graph, hence simple encoding while maintaining good performance is achieved. The paper also demonstrates a generalized design, which covers a large family of LDPC codes and number of other construction methods. The new generalized LDPC codes are defined by a small number of parameters and cover a large set of code lengths and rates. Using these codes, LDPC matrices of any column weight and row weight can be constructed. Performance of these codes under iterative decoding compares well with other well-structured as well as random LDPC codes
Difference sets are used to give a novel method for constructing structured regular quasi-cyclic low-density parity-check codes. Let Fqbe a field with q elements and assume that D={d1,..., dk} is a (v,k,1)-difference set for Zvwith d12k. Depending on v=q-1, v≥ 2dkor v≥ 2dk-1, three code construction methods are given that produce regular 4-cycle free codes, that is codes with girth at least 6. Simulation results show that the constructed codes perform well over the AWGN channel with an iterative sum-product message-passing decoding algorithm.
For a high-rate case, it is difficult to randomly construct good low-density parity-check (LDPC) codes of short and moderate lengths because their Tanner graphs are prone to have short cycles. Also, the existing high-rate quasi-cyclic (QC) LDPC codes can be constructed only for very restricted code parameters. In this paper, based on special classes of cyclic difference families, we propose a new construction method of high-rate regular QC LDPC codes having parity-check matrices consisting of a single row of circulants with column-weight 3 or 4. The proposed QC LDPC codes can be constructed for various code rates and lengths including the minimum achievable length for given column-weight and design rate under girth 6. It is observed that the parity-check matrices of the proposed QC LDPC codes have full rank for column-weight 3 and just one redundant row for column-weight 4. It is shown that the error correcting performance of the proposed QC LDPC codes of short and moderate lengths is almost the same as that of the existing ones through numerical analysis.
This paper gives a new random construction for LDPC codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has low complexity and great flexible choice in LDPC code parameters including code length, code rate, least girth of the graph, and the weight of column and row in the parity-check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Simulations show that the method performs well with iterative decoding.