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

Beijing Youdian Xueyuan xuebao

Construction of Quasi-Cyclic GF(q)-LDPC Codes Achieving the Upper Bound on the Minimum Hamming Distance

Xinmei Wang

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

In order to construct nonbinary low-density parity-check(LDPC) codes with good waterfall and error floor properties,a method to improve the minimum Hamming distance of a class of nonbinary quasi-cyclic(QC) LDPC codes is presented.Two upper bounds on the minimum Hamming distance are derived for the nonbinary QC LDPC codes whose parity-check matrices consist of weight-2 columns.A special base matrix design allowing linear encoding in a parallel manner is also proposed.In addition,the design principals are given,according to which,the parallel and efficiently encodable codes reaching the upper bound on the minimum Hamming distance can be developed.Simulation shows that the proposed codes have both good waterfall and error floor properties.

Related papers

Design of Quasi-Cyclic Cycle LDPC Codes over GF(q)

HU Shu-kai, Chao Chen, Rong Xia Sun +1 more

Quasi-cyclic (QC) low-density parity-check (LDPC) codes have several appealing properties regarding decoding, storage requirements and encoding aspects. In this paper, we focus on the QC LDPC codes over GF(q) whose parity-check matrices have fixed column weight j=2. By investigating two subgraphs in the Tanner graphs of the corresponding base matrices, we derive two upper bounds on the minimum Hamming distance for this class of codes. In addition, a method is proposed to construct QC LDPC codes over GF(q), which have good Hamming distance distributions. Simulations show that our designed codes have good performance.

IEICE Transactions on Communications•Jan 1, 2012•0 citations

Computing the Minimum Distance of Nonbinary LDPC Codes

Lei Liu, Jie Huang, Wuyang Zhou +1 more

Finding the minimum distance of low-density-parity-check (LDPC) codes is an NP-hard problem. Different from all existing works that focus on binary LDPC codes, we in this paper aim to compute the minimum distance of nonbinary LDPC codes, motivated by the fact that operating in a large Galois field provides one important degree of freedom to achieve both good waterfall and error-floor performance. Our method is based on the existing nearest nonzero codeword search (NNCS) method, but several modifications are incorporated for nonbinary LDPC codes, including the modified error impulse pattern, the dithering method, and the nonbinary decoder. Numerical results on the estimated minimum distances show that a code's minimum distance can be increased by careful selection of nonzero elements of the parity check matrix, or by increasing the mean column weight, or by increasing the size of the Galois field. These results support observations that have been made based on simulated performance in the literature. Finally, we provide an upper bound on the minimum distance for nonbinary quasi-cyclic LDPC codes.

IEEE Transactions on Communications•Jul 1, 2012•8 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

Construction of nonbinary quasi-cyclic LDPC cycle codes based on singer perfect difference set

Chao Chen, Baoming Bai, Xinmei Wang

A low-density parity-check (LDPC) code whose parity-check matrix consists of weight-2 columns is known as a cycle code. In this letter, we propose a construction of nonbinary quasi-cyclic (QC) LDPC cycle codes based on Singer perfect difference set. The Tanner graph has girth 12 and the code length achieves the Gallager lower bound. We further show that constructed codes have exactly a minimum symbol Hamming distance 6. Simulation results show that the proposed codes perform better than random nonbinary LDPC cycle codes.

IEEE Communications Letters•Feb 1, 2010•27 citations

Nonbinary Quasi-Cyclic LDPC Codes with Efficient Richardson-Urbanke Encoding Algorithm

Xinmei Wang

In order to implement efficient encoding,a class of nonbinary quasi-cyclic low-density parity-check(QC-LDPC) codes is proposed,which can be encoded with Richardson-Urbanke algorithm.The right part of the parity-check matrix has weight-2 columns,which allows the construction of both regular and irregular codes.Constraints on the parity-check matrix ensure a linear encoding complexity. Simulation results show that the proposed codes,when combined with higher order modulation,perform favorably with the codes constructed by the progressive-edge-growth(PEG) constructed code and close to the Shannon limits.

Beijing Youdian Xueyuan xuebao•Jan 1, 2009•0 citations

Optimization of NB-QC-LDPC Codes with Column Weight Not Exceeding Three

Jingke Zou, Liqian Wang

The non-binary quasi cyclic low-density parity-check (NB-QC-LDPC) code is a strong candidate code in optical communication. However, the presence of elementary absorbing sets in NB-QC-LDPC codes can degrade the frame error rate (FER) performance of the codes in the error floor region. Additionally, better minimum Hamming distance distribution can improve the FER performance of codes in the waterfall region. In this paper, a joint optimization of absorbing sets and minimum Hamming distance distribution is proposed for NB-QC-LDPC codes with a maximum column weight not exceeding 3. Simulation results show that the constructed codes could achieve comparable or better FER compared to the recently proposed NB-QC-LDPC codes with the same codes parameters.

Asia Communications and Photonics Conference•Nov 4, 2023•0 citations
In order to construct nonbinary low-density parity-check(LDPC) codes with good waterfall and error floor properties,a method to improve the minimum Hamming distance of a class of nonbinary quasi-cyclic(QC) LDPC codes is presented.Two upper bounds on the minimum Hamming distance are derived for the nonbinary QC LDPC codes whose parity-check matrices consist of weight-2 columns.A special base matrix design allowing linear encoding in a parallel manner is also proposed.In addition,the design principals are given,according to which,the parallel and efficiently encodable codes reaching the upper bound on the minimum Hamming distance can be developed.Simulation shows that the proposed codes have both good waterfall and error floor properties.
Quasi-cyclic (QC) low-density parity-check (LDPC) codes have several appealing properties regarding decoding, storage requirements and encoding aspects. In this paper, we focus on the QC LDPC codes over GF(q) whose parity-check matrices have fixed column weight j=2. By investigating two subgraphs in the Tanner graphs of the corresponding base matrices, we derive two upper bounds on the minimum Hamming distance for this class of codes. In addition, a method is proposed to construct QC LDPC codes over GF(q), which have good Hamming distance distributions. Simulations show that our designed codes have good performance.
Finding the minimum distance of low-density-parity-check (LDPC) codes is an NP-hard problem. Different from all existing works that focus on binary LDPC codes, we in this paper aim to compute the minimum distance of nonbinary LDPC codes, motivated by the fact that operating in a large Galois field provides one important degree of freedom to achieve both good waterfall and error-floor performance. Our method is based on the existing nearest nonzero codeword search (NNCS) method, but several modifications are incorporated for nonbinary LDPC codes, including the modified error impulse pattern, the dithering method, and the nonbinary decoder. Numerical results on the estimated minimum distances show that a code's minimum distance can be increased by careful selection of nonzero elements of the parity check matrix, or by increasing the mean column weight, or by increasing the size of the Galois field. These results support observations that have been made based on simulated performance in the literature. Finally, we provide an upper bound on the minimum distance for nonbinary quasi-cyclic LDPC codes.
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.
A low-density parity-check (LDPC) code whose parity-check matrix consists of weight-2 columns is known as a cycle code. In this letter, we propose a construction of nonbinary quasi-cyclic (QC) LDPC cycle codes based on Singer perfect difference set. The Tanner graph has girth 12 and the code length achieves the Gallager lower bound. We further show that constructed codes have exactly a minimum symbol Hamming distance 6. Simulation results show that the proposed codes perform better than random nonbinary LDPC cycle codes.
In order to implement efficient encoding,a class of nonbinary quasi-cyclic low-density parity-check(QC-LDPC) codes is proposed,which can be encoded with Richardson-Urbanke algorithm.The right part of the parity-check matrix has weight-2 columns,which allows the construction of both regular and irregular codes.Constraints on the parity-check matrix ensure a linear encoding complexity. Simulation results show that the proposed codes,when combined with higher order modulation,perform favorably with the codes constructed by the progressive-edge-growth(PEG) constructed code and close to the Shannon limits.
The non-binary quasi cyclic low-density parity-check (NB-QC-LDPC) code is a strong candidate code in optical communication. However, the presence of elementary absorbing sets in NB-QC-LDPC codes can degrade the frame error rate (FER) performance of the codes in the error floor region. Additionally, better minimum Hamming distance distribution can improve the FER performance of codes in the waterfall region. In this paper, a joint optimization of absorbing sets and minimum Hamming distance distribution is proposed for NB-QC-LDPC codes with a maximum column weight not exceeding 3. Simulation results show that the constructed codes could achieve comparable or better FER compared to the recently proposed NB-QC-LDPC codes with the same codes parameters.