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

International Symposium on Information Science and Engineering

Simulation Research of Nonbinary LDPC Code Based on Finite Fields

Yuxiang Li, Guolong Liang, Guangpu Zhang

Published Dec 1, 2009• 2 citations
Publisher

Abstract

The encoding and decoding of binary LDPC codes are expanded using characteristics of the Finite Fields concept, a nonbinary LDPC code encoding and decoding method based on the Finite Fields are investigated and the computational complexity of this algorithm is estimated, providing a foundation for the practical applications of this method. Then this algorithm is compared with the binary algorithm. The results show that its performance is superior to the binary BP iterative algorithm. Finally, the effects of the relevant factors such as the number of iterations selected, the structure of the check matrix etc on the algorithm performance were analyzed.

DOI
10.1109/isise.2009.106

Related papers

Study on Decoding Algorithm for Non-Binary LDPC Codes

Lei Wen

Non-binary LDPC codes are obtained by generalizing binary LDPC coeds from finite field GF(2) to finite field GF(q).Its elements of parity check matrix are not(0,1),but ensemble(0,1,…,q-1),and its decoding method still employs belief propagation and iterative algorithm.This paper mainly derives the iterative formulas of decoding algorithm for Non-Binary LDPC codes and analyzes an improved algorithm based on FFT.Finally,the predominant performance of FFT decoding algorithm is verified by simulation.

Communications technology•Jan 1, 2011•0 citations

Iterative Linear Programming Decoding of Nonbinary LDPC Codes With Linear Complexity

Dina Goldin, David Burshtein

The problem of low-complexity linear programming (LP) decoding of nonbinary low-density parity-check (LDPC) codes is considered, and an iterative LP decoding algorithm is presented. Results that were previously derived for binary LDPC codes are extended to the nonbinary case. Both simple and generalized nonbinary LDPC codes are considered. It is shown how the algorithm can be implemented efficiently using a finite-field fast Fourier transform. Then, the convergence rate of the algorithm is analyzed. The complexity of the algorithm scales linearly in the block length, and it can approximate, up to an arbitrarily small relative error, the objective function of the exact LP solution. When applied to a typical code from an appropriate nonbinary LDPC code ensemble, the algorithm can correct a constant fraction of errors in linear (in the block length) computational complexity. Computer experiments with the new iterative LP decoding algorithm show that, in the error floor region, it can have better performance compared to belief propagation decoding, with similar computational requirements.

IEEE Transactions on Information Theory•Aug 6, 2012•17 citations

Research on encoding and decoding algorithms of non-binary LDPC code and FPGA implementation

Zhongxun Wang, Baojun Liu, Min Zhang +1 more

Low density parity check (LDPC) code is a kind of linear block code with excellent performance which is proposed by Dr. Gallager. It overcomes the shortcomings of other error correcting codes and it is the nearest channel code from Shannon limit at the present discover. The decoding algorithms of L DPC code can reduce the decoding delay by the parallel decoding structure, so this has caused great concern in many fields. In recent years more and more scholars begin to study LDPC code, this makes the coding and decoding algorithms of LDPC code improved continuously. LDPC code has been widely used in many fields such as optical fiber communication, digital watermarking, underwater communication and deep space communication because of its excellent performance. Non-binary LDPC code has better performance compared with binary LDPC code. In this paper, FFT-BP decoding algorithm of non-binary LDPC code is studied, and on this basis, we proposed an improved FFT-BP algorithm. The improved decoding algorithm can effectively reduce the average iteration number. Finally, we achieved encode and decode algorithm of non-binary LDPC code with FPGA.

Journal of Computational Methods in Sciences and Engineering•Aug 20, 2019•1 citation

Research into Non-binary LDPC Decoding Performance Factors

Ming Diao

The non-binary LDPC is the promotion to the finite GF(q) of binary LDPC codes.The parity check matrix elements is no longer 0 and 1,but collections(0,1,2,…,q-1),while the decoding still uses the efficient iterative decoding based on belief propagation algorithm.This paper focuses on the check matrix of structure of the quasi-cyclic LDPC codes(QC-LDPC) as well as the min-sum decoding algorithm.Then the LDPC codes decoding performance is simulated under different conditions in white Gaussian noise channel(AWGN) with Matlab.Finally,the impact of non-binary LDPC Decoding performance factors is analyzed.

Electronic Science and Technology•Jan 1, 2013•0 citations

Decoding Algorithms for Nonbinary LDPC Codes Over GF$(q)$

David Declercq, M.P.C. Fossorier

In this letter, we address the problem of decoding nonbinary low-density parity-check (LDPC) codes over finite fields GF(q), with reasonable complexity and good performance. In the first part of the letter, we recall the original belief propagation (BP) decoding algorithm and its Fourier domain implementation. We show that the use of tensor notations for the messages is very convenient for the algorithm description and understanding. In the second part of the letter, we introduce a simplified decoder which is inspired by the min-sum decoder for binary LDPC codes. We called this decoder extended min-sum (EMS). We show that it is possible to greatly reduce the computational complexity of the check-node processing by computing approximate reliability measures with a limited number of values in a message. By choosing appropriate correction factors or offsets, we show that the EMS decoder performance is quite good, and in some cases better than the regular BP decoder. The optimal values of the factor and offset correction are obtained asymptotically with simulated density evolution. Our simulations on ultra-sparse codes over very-high-order fields show that nonbinary LDPC codes are promising for applications which require low frame-error rates for small or moderate codeword lengths. The EMS decoder is a good candidate for practical hardware implementations of such codes

IEEE Transactions on Communications•Apr 1, 2007•724 citations

Reduced complexity and improved performance decoding algorithm for nonbinary LDPC codes over GF(q)

Xin Chen, Aidong Men

Low-density parity-check (LDPC) codes over finite fields GF(q) have a better performance than those of the binary low-density parity-check codes, at short and medium block lengths, but the decoder of GF(q)-LDPC has more complexity. In this paper, we present a new reduced-complexity belief propagation (BP) decoding algorithm for GF(q)-LDPC codes by analyzing the reliability of code symbols. Instead of update all the variable nodes during iteration, we just update variable nodes which are mostly to be in an error. The algorithm also shows a property to reduce the effects of oscillating on decoding. The simulations prove that we could improve performance and reduce complexity at the same time for short and medium GF(q)-LDPC codes.

IEEE International Conference on Communication Technology (ICCT)•Nov 1, 2008•6 citations
The encoding and decoding of binary LDPC codes are expanded using characteristics of the Finite Fields concept, a nonbinary LDPC code encoding and decoding method based on the Finite Fields are investigated and the computational complexity of this algorithm is estimated, providing a foundation for the practical applications of this method. Then this algorithm is compared with the binary algorithm. The results show that its performance is superior to the binary BP iterative algorithm. Finally, the effects of the relevant factors such as the number of iterations selected, the structure of the check matrix etc on the algorithm performance were analyzed.
Non-binary LDPC codes are obtained by generalizing binary LDPC coeds from finite field GF(2) to finite field GF(q).Its elements of parity check matrix are not(0,1),but ensemble(0,1,…,q-1),and its decoding method still employs belief propagation and iterative algorithm.This paper mainly derives the iterative formulas of decoding algorithm for Non-Binary LDPC codes and analyzes an improved algorithm based on FFT.Finally,the predominant performance of FFT decoding algorithm is verified by simulation.
The problem of low-complexity linear programming (LP) decoding of nonbinary low-density parity-check (LDPC) codes is considered, and an iterative LP decoding algorithm is presented. Results that were previously derived for binary LDPC codes are extended to the nonbinary case. Both simple and generalized nonbinary LDPC codes are considered. It is shown how the algorithm can be implemented efficiently using a finite-field fast Fourier transform. Then, the convergence rate of the algorithm is analyzed. The complexity of the algorithm scales linearly in the block length, and it can approximate, up to an arbitrarily small relative error, the objective function of the exact LP solution. When applied to a typical code from an appropriate nonbinary LDPC code ensemble, the algorithm can correct a constant fraction of errors in linear (in the block length) computational complexity. Computer experiments with the new iterative LP decoding algorithm show that, in the error floor region, it can have better performance compared to belief propagation decoding, with similar computational requirements.
Low density parity check (LDPC) code is a kind of linear block code with excellent performance which is proposed by Dr. Gallager. It overcomes the shortcomings of other error correcting codes and it is the nearest channel code from Shannon limit at the present discover. The decoding algorithms of L DPC code can reduce the decoding delay by the parallel decoding structure, so this has caused great concern in many fields. In recent years more and more scholars begin to study LDPC code, this makes the coding and decoding algorithms of LDPC code improved continuously. LDPC code has been widely used in many fields such as optical fiber communication, digital watermarking, underwater communication and deep space communication because of its excellent performance. Non-binary LDPC code has better performance compared with binary LDPC code. In this paper, FFT-BP decoding algorithm of non-binary LDPC code is studied, and on this basis, we proposed an improved FFT-BP algorithm. The improved decoding algorithm can effectively reduce the average iteration number. Finally, we achieved encode and decode algorithm of non-binary LDPC code with FPGA.
The non-binary LDPC is the promotion to the finite GF(q) of binary LDPC codes.The parity check matrix elements is no longer 0 and 1,but collections(0,1,2,…,q-1),while the decoding still uses the efficient iterative decoding based on belief propagation algorithm.This paper focuses on the check matrix of structure of the quasi-cyclic LDPC codes(QC-LDPC) as well as the min-sum decoding algorithm.Then the LDPC codes decoding performance is simulated under different conditions in white Gaussian noise channel(AWGN) with Matlab.Finally,the impact of non-binary LDPC Decoding performance factors is analyzed.
Decoding Algorithms for Nonbinary LDPC Codes Over GF(q)(q)(q)
In this letter, we address the problem of decoding nonbinary low-density parity-check (LDPC) codes over finite fields GF(q), with reasonable complexity and good performance. In the first part of the letter, we recall the original belief propagation (BP) decoding algorithm and its Fourier domain implementation. We show that the use of tensor notations for the messages is very convenient for the algorithm description and understanding. In the second part of the letter, we introduce a simplified decoder which is inspired by the min-sum decoder for binary LDPC codes. We called this decoder extended min-sum (EMS). We show that it is possible to greatly reduce the computational complexity of the check-node processing by computing approximate reliability measures with a limited number of values in a message. By choosing appropriate correction factors or offsets, we show that the EMS decoder performance is quite good, and in some cases better than the regular BP decoder. The optimal values of the factor and offset correction are obtained asymptotically with simulated density evolution. Our simulations on ultra-sparse codes over very-high-order fields show that nonbinary LDPC codes are promising for applications which require low frame-error rates for small or moderate codeword lengths. The EMS decoder is a good candidate for practical hardware implementations of such codes
Low-density parity-check (LDPC) codes over finite fields GF(q) have a better performance than those of the binary low-density parity-check codes, at short and medium block lengths, but the decoder of GF(q)-LDPC has more complexity. In this paper, we present a new reduced-complexity belief propagation (BP) decoding algorithm for GF(q)-LDPC codes by analyzing the reliability of code symbols. Instead of update all the variable nodes during iteration, we just update variable nodes which are mostly to be in an error. The algorithm also shows a property to reduce the effects of oscillating on decoding. The simulations prove that we could improve performance and reduce complexity at the same time for short and medium GF(q)-LDPC codes.