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

IEEE/CIC International Conference on Communications in China (ICCC)

A Construction of Algebraic Geometric LDPC Codes*

Dongliang Xiao, Huizhen Li, Ke Wen, Chaoyang Dai

Published Aug 7, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1109/iccc62479.2024.10681681

Related papers

Construction of Structured Regular LDPC Codes: A Design-Theoretic Approach

Hossein Falsafain, Morteza Esmaeili

A new combinatorial technique for constructing girth-6 structured binary regular low-density parity-check (LDPC) codes based on special types of t-designs is given. A very large number of well-known t-designs can be used by this method for code construction. Based on this method, a t-(v,k,λ) design D=(X,B) can be exploited for code construction if it satisfies the following three conditions: 1) |B1 ∩ B2|≤ t for any two blocks B1,B2∈ B and B1≠ B2; 2) λ>1; and 3) k>t. Though the technique works for any t-design satisfying these conditions, we focus only on the utilization of simple triple systems, super-simple BIBDs, Steiner systems, and large sets (LSs) of t-designs. We also construct binary and non-binary girth-6 QC-LDPC codes from the t-designs satisfying these conditions by using matrix dispersion method. Experimental results show that the constructed non-binary QC-LDPC codes can provide good practical performance under iterative decoding using the fast Fourier transform based q-ary sum-product algorithm (FFT-QSPA) and they can achieve acceptable coding gains over random-like codes of comparable parameters decoded with sum-product algorithm (SPA).

IEEE Transactions on Communications•May 1, 2013•8 citations

Large Girth Non-Binary LDPC Codes Based on Finite Fields and Euclidean Geometries

Xueqin Jiang, Moon Ho Lee

This letter presents an approach to the construction of non-binary low-density parity-check (LDPC) codes based on alpha-multiplied circulant permutation matrices and hyperplanes of two different dimensions in Euclidean geometries. Codes constructed by this method have large girth and high binary column weight when the order of Galois field is high. Simulation results show that these codes perform very well with fast Fourier transform (FFT) based sum-product algorithm (SPA).

IEEE Signal Processing Letters•Apr 24, 2009•20 citations

FFT based sum product decoding algorithm of LDPC coder for GF(q)

Jigisha N. Patel, Neeta Chapatwala, Mrugesh Patel

Low Density Parity Check (LDPC) codes have excellent error correcting performance. LDPC codes are one of the block coding techniques and it performs near Shannon limit and recommended for many practical applications. Non-binary LDPC codes extension of binary LDPC in error correcting property especially for short and moderate block length. In many digital communication systems these codes have strong competitors of turbo codes for error control. Low Density Parity Check as it name is suggests that in a parity check matrix (H) consists of very small number of non-zero elements comparing with zero elements. The strength of the LDPC code defines Parity Check Matrix (PCM). LDPC code contains two types of decoding algorithms hard and soft decision algorithm. By comparing with other traditional decoding algorithm FFT based sum product algorithm reduced computation complexity with better decoding performance. In this paper, LDPC codes for FFT based sum product decoding algorithm performances are analysed for various order of Galois Field GF(q) using AWGN channel. Decoding performance measured in terms of symbol error rate which improve with increasing order of Galois field.

International Conference on Emerging Technology Trends in Electronics, Communication and Networking (ET2ECN)•Dec 1, 2014•3 citations

Nonbinary LDPC Codes

W.E. Ryan, Shu Wen Lin

Although a great deal of research effort has been expended on the design, construction, encoding, decoding, performance analysis, and applications of binary LDPC codes in communication and storage systems, very little has been done on nonbinary LDPC codes in these respects. The first study of nonbinary LDPC codes was conducted by Davey and MacKay in 1998. In their paper, they generalized the SPA for decoding binary LDPC codes to decode q -ary LDPC codes, called QSPA . Later, in 2000, MacKay and Davey introduced a fast-Fourier-transform (FFT)-based QSPA to reduce the decoding computational complexity of QSPA. This decoding algorithm is referred to as FFT-QSPA. MacKay and Davey's work on FFT-QSPA was further improved by Barnault and Declercq in 2003 and Declercq and Fossorier in 2007. Significant works on the design, construction and analysis of nonbinary LDPC codes didn't appear until the middle of 2000. Results in these works are very encouraging. They show that nonbinary LDPC codes have a great potential to replace widely used RS codes in some applications in communication and storage systems. This chapter is devoted to nonbinary LDPC codes. Just like binary LDPC codes, nonbinary LDPC codes can be classified into two major categories: (1) random-like nonbinary codes constructed by computer under certain design criteria or rules; and (2) structured nonbinary codes constructed on the basis of algebraic or combinatorial tools, such as finite fields and finite geometries.

Cambridge University Press eBooks•Sep 17, 2009•0 citations

Construction of Nonbinary LDPC Codes Based on BIBD Circulant Permutation Matrices

Jun Gao

The algebraic method for constructing nonbinary quasi-cyclic(QC) low-density parity-check(LDPC) codes based on balanced incomplete block designs(BIBD) is presented.The generalized nonbinary location vector is proposed on constructions.A nonbinary matrix,which consists of nonbinary circulant submatrices,is formed by generalized two-dimensional matrix dispersion considering the generalized nonbinary location vector and BIBD method.The codes constructed by this method have girths at least 6.Experimental results show that significant coding gains are achieved over Reed-Solomon codes of the same parameters under the Additive White Gaussian Noise(AWGN) channel with iterative decoding Fast Fourier Transform based q-ary Sum-Product Algorithm(FFT-QSPA).And a good performance is also achieved over nonbinary Mackay LDPC codes with almost the same conditions.

Telecommunication Engineering•Jan 1, 2011•0 citations

Performance evaluation of regular cycle non-binary LDPC codes in AWGN channel

Ameenudeen Pe, Anchare V. Babu

Low Density Parity Check Codes (LDPC) are a group of channel codes which can be decoded using a graph. LDPC codes are known to give near Shannon limit performance in Additive White Gaussian Channel (AWGN), but for large block-lengths and irregular construction. To overcome this limitation, it has been proposed to define codes over a higher order Galois Field. In this paper,we construct a regular cycle non binary LDPC code over GF(q), where q=2p.We use a Fast Fourier Transform (FFT) based low complexity algorithm to decode the LDPC code defined over a large Galois Field. We evaluate the performance of these codes in AWGN channel using computer simulations and show that they are giving excellent BER performance.

International Conference on Advances in Computing, Communications and Informatics (ICACCI)•Aug 3, 2012•0 citations
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.
A new combinatorial technique for constructing girth-6 structured binary regular low-density parity-check (LDPC) codes based on special types of t-designs is given. A very large number of well-known t-designs can be used by this method for code construction. Based on this method, a t-(v,k,λ) design D=(X,B) can be exploited for code construction if it satisfies the following three conditions: 1) |B1 ∩ B2|≤ t for any two blocks B1,B2∈ B and B1≠ B2; 2) λ>1; and 3) k>t. Though the technique works for any t-design satisfying these conditions, we focus only on the utilization of simple triple systems, super-simple BIBDs, Steiner systems, and large sets (LSs) of t-designs. We also construct binary and non-binary girth-6 QC-LDPC codes from the t-designs satisfying these conditions by using matrix dispersion method. Experimental results show that the constructed non-binary QC-LDPC codes can provide good practical performance under iterative decoding using the fast Fourier transform based q-ary sum-product algorithm (FFT-QSPA) and they can achieve acceptable coding gains over random-like codes of comparable parameters decoded with sum-product algorithm (SPA).
Low Density Parity Check (LDPC) codes have excellent error correcting performance. LDPC codes are one of the block coding techniques and it performs near Shannon limit and recommended for many practical applications. Non-binary LDPC codes extension of binary LDPC in error correcting property especially for short and moderate block length. In many digital communication systems these codes have strong competitors of turbo codes for error control. Low Density Parity Check as it name is suggests that in a parity check matrix (H) consists of very small number of non-zero elements comparing with zero elements. The strength of the LDPC code defines Parity Check Matrix (PCM). LDPC code contains two types of decoding algorithms hard and soft decision algorithm. By comparing with other traditional decoding algorithm FFT based sum product algorithm reduced computation complexity with better decoding performance. In this paper, LDPC codes for FFT based sum product decoding algorithm performances are analysed for various order of Galois Field GF(q) using AWGN channel. Decoding performance measured in terms of symbol error rate which improve with increasing order of Galois field.
Although a great deal of research effort has been expended on the design, construction, encoding, decoding, performance analysis, and applications of binary LDPC codes in communication and storage systems, very little has been done on nonbinary LDPC codes in these respects. The first study of nonbinary LDPC codes was conducted by Davey and MacKay in 1998. In their paper, they generalized the SPA for decoding binary LDPC codes to decode q -ary LDPC codes, called QSPA . Later, in 2000, MacKay and Davey introduced a fast-Fourier-transform (FFT)-based QSPA to reduce the decoding computational complexity of QSPA. This decoding algorithm is referred to as FFT-QSPA. MacKay and Davey's work on FFT-QSPA was further improved by Barnault and Declercq in 2003 and Declercq and Fossorier in 2007. Significant works on the design, construction and analysis of nonbinary LDPC codes didn't appear until the middle of 2000. Results in these works are very encouraging. They show that nonbinary LDPC codes have a great potential to replace widely used RS codes in some applications in communication and storage systems. This chapter is devoted to nonbinary LDPC codes. Just like binary LDPC codes, nonbinary LDPC codes can be classified into two major categories: (1) random-like nonbinary codes constructed by computer under certain design criteria or rules; and (2) structured nonbinary codes constructed on the basis of algebraic or combinatorial tools, such as finite fields and finite geometries.
The algebraic method for constructing nonbinary quasi-cyclic(QC) low-density parity-check(LDPC) codes based on balanced incomplete block designs(BIBD) is presented.The generalized nonbinary location vector is proposed on constructions.A nonbinary matrix,which consists of nonbinary circulant submatrices,is formed by generalized two-dimensional matrix dispersion considering the generalized nonbinary location vector and BIBD method.The codes constructed by this method have girths at least 6.Experimental results show that significant coding gains are achieved over Reed-Solomon codes of the same parameters under the Additive White Gaussian Noise(AWGN) channel with iterative decoding Fast Fourier Transform based q-ary Sum-Product Algorithm(FFT-QSPA).And a good performance is also achieved over nonbinary Mackay LDPC codes with almost the same conditions.
Low Density Parity Check Codes (LDPC) are a group of channel codes which can be decoded using a graph. LDPC codes are known to give near Shannon limit performance in Additive White Gaussian Channel (AWGN), but for large block-lengths and irregular construction. To overcome this limitation, it has been proposed to define codes over a higher order Galois Field. In this paper,we construct a regular cycle non binary LDPC code over GF(q), where q=2p.We use a Fast Fourier Transform (FFT) based low complexity algorithm to decode the LDPC code defined over a large Galois Field. We evaluate the performance of these codes in AWGN channel using computer simulations and show that they are giving excellent BER performance.