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

China Communications

Algebraic-based nonbinary ldpc codes with flexible field orders and code rates

Hengzhou Xu, Dan Feng, Cheng Sun, Baoming Bai

Published Apr 1, 2017• 3 citations
Publisher

Abstract

In this paper, we study the rank of matrices over and propose two construction methods for algebraic-based nonbinary LDPC codes from an existing LDPC code, referred to as the original code. By multiplying all elements of each column of the binary parity-check matrix H corresponding to the original code with the same nonzero element of any field, the first class of nonbinary LDPC codes with flexible field order is proposed. The second method is to replace the nonzero elements of some columns in H with different nonzero field elements in a given field, and then another class of nonbinary LDPC codes with various rates is obtained. Simulation results show that the proposed nonbinary LDPC codes perform well over the AWGN channel with the iterative decoding algorithms.

DOI
10.1109/cc.2017.7927569

Related papers

Construction of short-block nonbinary LDPC codes based on cyclic codes

Hengzhou Xu, Baoming Bai, Min Zhu +2 more

In this paper, we focus on short-block nonbinary LDPC (NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDPC codes. Notice that the parity-check matrix H of the resulting code is square and not of full rank, and its row weight and column weight are the same. By replacing the ones in the same column of H with a nonzero element of finite fields GF(q), a class of NB-LDPC codes over GF(q) is obtained. Numerical results show that the constructed codes perform well over the AWGN channel and have fast decoding convergence. Therefore, the proposed NB-LDPC codes provide a promising coding scheme for low-latency and high-reliability communications.

China Communications•Aug 1, 2017•5 citations

Novel Algebraic Constructions of Nonbinary Structured LDPC Codes over Finite Fields

Keke Liu, Zesong Fei, Jingming Kuang

In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is based on the multiplicative inverses of nonzero elements in finite fields and gives a class of quasi-cyclic codes with girth 6, the second method gives a class of (3, rho) quasi-cyclic codes with girth 8, the third method gives a class of structured codes with cycles limited. The codes given in examples perform well over AWGN channel and have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Shu Lin.

IEEE Vehicular Technology Conference•Sep 1, 2008•6 citations

A Construction of Algebraic Geometric LDPC Codes*

Dongliang Xiao, Huizhen Li, Ke Wen +1 more

This paper presents an original method for constructing high performance non-binary LDPC codes based on algebraic geometric codes’ parity check matrix. Codes constructed based on this method perform very well over the AWGN channel. With iterative decoding using a Fast Fourier Transform (FFT) based q-ary sum-product algorithm (QSPA), AG-LDPC codes achieve significantly large coding gains over the PEG non-binary LDPC and binary LDPC. Simulation results also show that the AG-LDPC significantly lower the decoding error floor, and the undetected error rate.

IEEE/CIC International Conference on Communications in China (ICCC)•Aug 7, 2024•0 citations

A unified approach to the construction of binary and nonbinary quasi-cyclic LDPC codes based on finite fields

Shumei Song, Bo Zhou, Shu Hwa Lin +1 more

A unified approach for constructing binary and nonbinary quasi-cyclic LDPC codes under a single framework is presented. Six classes of binary and nonbinary quasi-cyclic LDPC codes are constructed based on primitive elements, additive subgroups, and cyclic subgroups of finite fields. Numerical results show that the codes constructed perform well over the AWGN channel with iterative decoding.

IEEE Transactions on Communications•Jan 1, 2009•104 citations

Three algebraic methods for constructing nonbinary LDPC codes based on finite fields

Keke Liu, Zesong Fei, Jingming Kuang

In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is used to construct quasi-cyclic codes with girth at least 6 based on the automorphisms of finite fields, the second method gives a class of (4,ρ) quasi-cyclic codes with girth at least 8, the third method gives a class of codes with cycles limited. Simulation results show that the constructed codes perform very well over AWGN channel, and they have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Lin.

IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)•Sep 1, 2008•2 citations

Column weights optimization for semi-regular nonbinary LDPC codes

Wojciech Sułek, Marcin Kucharczyk

The paper concerns Low Density Parity Check (LDPC) codes over nonbinary Galois Fields GF(q), that are a generalization of the industrial standard binary LDPC codes for forward error correction in communication and information systems. The semi-regular nonbinary LDPC codes can outperform their binary counterparts in the case of short to moderate code word lengths. The methods for the good code construction based on a computer search techniques are already well investigated. However, there is a lack of systematic results for optimal weight distribution of columns of parity check matrices for codes over different field order and different rate. In this article we present a Monte Carlo like algorithm for column weight optimization devoted to nonbinary semi-regular codes along with optimization results that facilitate the codes construction computer-based methods.

International Conference on Telecommunications and Signal Processing (TSP)•Jul 1, 2015•1 citation
In this paper, we study the rank of matrices over and propose two construction methods for algebraic-based nonbinary LDPC codes from an existing LDPC code, referred to as the original code. By multiplying all elements of each column of the binary parity-check matrix H corresponding to the original code with the same nonzero element of any field, the first class of nonbinary LDPC codes with flexible field order is proposed. The second method is to replace the nonzero elements of some columns in H with different nonzero field elements in a given field, and then another class of nonbinary LDPC codes with various rates is obtained. Simulation results show that the proposed nonbinary LDPC codes perform well over the AWGN channel with the iterative decoding algorithms.
In this paper, we focus on short-block nonbinary LDPC (NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDPC codes. Notice that the parity-check matrix H of the resulting code is square and not of full rank, and its row weight and column weight are the same. By replacing the ones in the same column of H with a nonzero element of finite fields GF(q), a class of NB-LDPC codes over GF(q) is obtained. Numerical results show that the constructed codes perform well over the AWGN channel and have fast decoding convergence. Therefore, the proposed NB-LDPC codes provide a promising coding scheme for low-latency and high-reliability communications.
In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is based on the multiplicative inverses of nonzero elements in finite fields and gives a class of quasi-cyclic codes with girth 6, the second method gives a class of (3, rho) quasi-cyclic codes with girth 8, the third method gives a class of structured codes with cycles limited. The codes given in examples perform well over AWGN channel and have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Shu Lin.
This paper presents an original method for constructing high performance non-binary LDPC codes based on algebraic geometric codes’ parity check matrix. Codes constructed based on this method perform very well over the AWGN channel. With iterative decoding using a Fast Fourier Transform (FFT) based q-ary sum-product algorithm (QSPA), AG-LDPC codes achieve significantly large coding gains over the PEG non-binary LDPC and binary LDPC. Simulation results also show that the AG-LDPC significantly lower the decoding error floor, and the undetected error rate.
In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is used to construct quasi-cyclic codes with girth at least 6 based on the automorphisms of finite fields, the second method gives a class of (4,ρ) quasi-cyclic codes with girth at least 8, the third method gives a class of codes with cycles limited. Simulation results show that the constructed codes perform very well over AWGN channel, and they have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Lin.
The paper concerns Low Density Parity Check (LDPC) codes over nonbinary Galois Fields GF(q), that are a generalization of the industrial standard binary LDPC codes for forward error correction in communication and information systems. The semi-regular nonbinary LDPC codes can outperform their binary counterparts in the case of short to moderate code word lengths. The methods for the good code construction based on a computer search techniques are already well investigated. However, there is a lack of systematic results for optimal weight distribution of columns of parity check matrices for codes over different field order and different rate. In this article we present a Monte Carlo like algorithm for column weight optimization devoted to nonbinary semi-regular codes along with optimization results that facilitate the codes construction computer-based methods.