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

Globecom

Dispersed Reed-Solomon codes for iterative decoding and construction of q-ary LDPC codes

Lingqi Zeng, Lan Lan, Y.Y. Tai, Shu Hwa Lin

Published Jan 1, 2005• 27 citations
Publisher

Abstract

This paper presents three algebraic methods for constructing q-ary LDPC codes. The first method gives a class of dispersed Reed-Solomon codes as LDPC codes. The second method gives a class of q-ary quasi-cyclic LDPC codes. The third method gives two classes of q-ary finite geometry LDPC codes. Codes constructed by these methods perform very well with iterative decoding, even for short codes.

DOI
10.1109/glocom.2005.1577842

Related papers

Construction of Partial Geometries and LDPC codes based on Reed-Solomon Codes

Juane Li, Keke Liu, Shu Lin +1 more

This paper presents a construction of a class of partial geometries based on RS codes of prime lengths and shows that LDPC codes constructed based on Reed-Solomon codes of prime lengths are finite geometry LDPC codes. Furthermore, a new method for design and construction of nonbinary quasi-cyclic LDPC codes based on the conventional parity-check matrices of Reed-Solomon codes is presented. Simulation results show that the constructed nonbinary LDPC codes perform well over the additive white Gaussian channel.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2019•4 citations

On Algebraic Construction of Gallager and Circulant Low-Density Parity-Check Codes

H. Tang, Jun Xu, Y. Kou +2 more

This correspondence presents three algebraic methods for constructing low-density parity-check (LDPC) codes. These methods are based on the structural properties of finite geometries. The first method gives a class of Gallager codes and a class of complementary Gallager codes. The second method results in two classes of circulant-LDPC codes, one in cyclic form and the other in quasi-cyclic form. The third method is a two-step hybrid method. Codes in these classes have a wide range of rates and minimum distances, and they perform well with iterative decoding.

IEEE Transactions on Information Theory•Jun 1, 2004•105 citations

Construction of Quasi-Cyclic LDPC Codes Based on the Primitive Elements of Finite Fields

Shumei Song, Lan Lan, Shu Lin +1 more

This paper presents an algebraic method for constructing quasi-cyclic LDPC codes based on the primitive elements of finite fields. The construction gives a class of efficiently encodable quasi-cyclic LDPC codes. Experimental results show that the constructed codes decoded with iterative decoding using the sum-product algorithm perform well over the AWGN channel.

Conference on Information Sciences and Systems•Mar 1, 2006•11 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

Reed-Solomon Based Quasi-Cyclic LDPC Codes: Designs, Girth, Cycle Structure, and Reduction of Short Cycles

Xin Wei Xiao, Bane V. Vasic, Shu Lin +2 more

Designs and constructions of quasi-cyclic (QC) LDPC codes for the AWGN channel are presented. The codes are constructed based on the conventional parity-check matrices of Reed-Solomon (RS) codes and are referred to as RS-QC-LDPC codes. Several classes of RS-QC-LDPC codes are given. Cycle structural properties of the Tanner graphs of codes in these classes are analyzed and specific methods for constructing codes with girth at least eight and reducing their short cycles are presented. The designed codes perform well in both waterfall and low error-rate regions.

IEEE Transactions on Communications•May 14, 2019•18 citations

Algebraic Constructions of Nonbinary Quasi-Cyclic LDPC Codes

Shu Hwa Lin, Shumei Song, Ying Tai +2 more

In the late 1950's and early 1960's, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for correcting random errors with algebraic decoding, such as Bose-Chaudhuri-Hocqenghem (BCH) and Reed-Solomon (RS) codes. Recently it has been shown that finite fields can also be used successfully to construct binary quasi-cyclic (QC)-LDPC codes that perform very well not only over the AWGN channel but also over the binary erasure channel with iterative decoding, besides being efficiently encodable. This paper is concerned with constructions of nonbinary QC-LDPC codes based on finite fields

International Conference on Communications, Circuits and Systems•Jun 1, 2006•19 citations
This paper presents three algebraic methods for constructing q-ary LDPC codes. The first method gives a class of dispersed Reed-Solomon codes as LDPC codes. The second method gives a class of q-ary quasi-cyclic LDPC codes. The third method gives two classes of q-ary finite geometry LDPC codes. Codes constructed by these methods perform very well with iterative decoding, even for short codes.
This paper presents a construction of a class of partial geometries based on RS codes of prime lengths and shows that LDPC codes constructed based on Reed-Solomon codes of prime lengths are finite geometry LDPC codes. Furthermore, a new method for design and construction of nonbinary quasi-cyclic LDPC codes based on the conventional parity-check matrices of Reed-Solomon codes is presented. Simulation results show that the constructed nonbinary LDPC codes perform well over the additive white Gaussian channel.
This correspondence presents three algebraic methods for constructing low-density parity-check (LDPC) codes. These methods are based on the structural properties of finite geometries. The first method gives a class of Gallager codes and a class of complementary Gallager codes. The second method results in two classes of circulant-LDPC codes, one in cyclic form and the other in quasi-cyclic form. The third method is a two-step hybrid method. Codes in these classes have a wide range of rates and minimum distances, and they perform well with iterative decoding.
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.
Designs and constructions of quasi-cyclic (QC) LDPC codes for the AWGN channel are presented. The codes are constructed based on the conventional parity-check matrices of Reed-Solomon (RS) codes and are referred to as RS-QC-LDPC codes. Several classes of RS-QC-LDPC codes are given. Cycle structural properties of the Tanner graphs of codes in these classes are analyzed and specific methods for constructing codes with girth at least eight and reducing their short cycles are presented. The designed codes perform well in both waterfall and low error-rate regions.
In the late 1950's and early 1960's, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for correcting random errors with algebraic decoding, such as Bose-Chaudhuri-Hocqenghem (BCH) and Reed-Solomon (RS) codes. Recently it has been shown that finite fields can also be used successfully to construct binary quasi-cyclic (QC)-LDPC codes that perform very well not only over the AWGN channel but also over the binary erasure channel with iterative decoding, besides being efficiently encodable. This paper is concerned with constructions of nonbinary QC-LDPC codes based on finite fields