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

Informatyka Automatyka Pomiary w Gospodarce i Ochronie Środowiska

Multithreshold majority decoding of LDPC-codes

Павел Павлович Урбанович, Романенко Дмитрий Михайлович, D. Shiman, Виткова Марина Федоровна

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

The article deals with the majority decoding LDPC-codes - three-dimensional linear iterative codes. The possibility of correcting different types of multiple errors is analyzed. The expediency of using multithreshold majority decoding with codes, belonging to this class is presented.

Related papers

On the error-correcting capability of LDPC codes

Kamil Sh. Zigangirov, A. E. Pusane, D. K. Zigangirov +1 more

We consider the ensemble of low-density parity-check (LDPC) codes introduced by Gallager [1]. The Zyablov-Pinsker majority-logic iterative algorithm [2] for decoding LDPC codes is analyzed on the binary symmetric channel. An analytical lower bound on the error-correcting capability τ max that grows linearly in the code block length is obtained.

Problems of Information Transmission•Sep 1, 2008•11 citations

Correcting capabilities of binary irregular LDPC code under low-complexity iterative decoding algorithm

Pavel S. Rybin

This paper deals with the irregular binary low-density parity-check (LDPC) codes and two iterative low-complexity decoding algorithms. The first one is the majority error-correcting decoding algorithm, and the second one is iterative erasure-correcting decoding algorithm. The lower bounds on correcting capabilities (the guaranteed corrected error and erasure fraction respectively) of irregular LDPC code under decoding (error and erasure correcting respectively) algorithms with low-complexity were represented. These lower bounds were obtained as a result of analysis of Tanner graph representation of irregular LDPC code. The numerical results, obtained at the end of the paper for proposed lower-bounds achieved similar results for the previously known best lower-bounds for regular LDPC codes and were represented for the first time for the irregular LDPC codes.

Journal of Communications Technology and Electronics•Dec 1, 2016•2 citations

LDPC codes which can correct three errors under iterative decoding

Anantha Raman Krishnan, Bane V. Vasic

Abstract — In this paper, we provide necessary and sufficient conditions for a column-weight-three LDPC code to correct three errors when decoded using Gallager A algorithm. We then provide a construction technique which results in a code satisfying the above conditions. We also provide numerical assessment of code performance via simulation results. I.

•Jan 1, 2008•19 citations

LDPC codes which can correct three errors under iterative decoding

Shashi Kiran Chilappagari, Anantha Raman Krishnan, Bane Vasic

In this paper, we provide necessary and sufficient conditions for a column-weight-three LDPC code to correct all patterns up to three errors when decoded using Gallager A algorithm. We then provide a construction technique which results in a code satisfying the above conditions. We also provide numerical assessment of code performance via simulation results.

arXiv:0801.1282•IEEE Information Theory Workshop (ITW)•May 1, 2008•15 citations

Iterative decoding of a class of cyclic codes

Li Guo Zhang, Qin Huang, Shu Lin

Among the classes of LDPC codes that have been constructed and designed, the only class of LDPC codes that are cyclic is the class of codes constructed based on the incidence vectors of lines of finite geometries, called finite geometry LDPC codes. Cyclic finite geometry LDPC codes are known to have large minimum distances and can provide good error performance with very low error-floors using iterative decoding based on belief propagation. Their cyclic structure allows them to be efficiently and systematically encoded with simple shift-registers in linear time with linear complexity. An obvious question is whether, besides cyclic finite geometry LDPC codes, there are other cyclic codes with large minimum distances that can be efficiently decoded iteratively using channel soft information. In this paper, we present one such class of cyclic codes. Codes in this class are two-step majority-logic decodable and they are also constructed based on finite geometries. Two iterative decoding algorithms are devised for this class of cyclic codes and they provide significant coding gain over the two-step majority-logic decoding of codes in this class.

Information Theory and Applications Workshop (ITA)•Jan 1, 2010•4 citations

A general class of LDPC finite geometry codes and their performance

Jun Jim Xu, Heng Tang, Yu Kou +2 more

We present a general class of finite geometry LDPC codes which perform well with iterative decoding although their Tanner graphs may contain many cycles of length 4. A hybrid two-stage decoding algorithm is proposed that combines iterative and multi-step majority-logic decodings to achieve good performance with low decoding complexity.

IEEE International Symposium on Information Theory (ISIT)•Jun 25, 2003•9 citations
This paper deals with the irregular binary low-density parity-check (LDPC) codes and two iterative low-complexity decoding algorithms. The first one is the majority error-correcting decoding algorithm, and the second one is iterative erasure-correcting decoding algorithm. The lower bounds on correcting capabilities (the guaranteed corrected error and erasure fraction respectively) of irregular LDPC code under decoding (error and erasure correcting respectively) algorithms with low-complexity were represented. These lower bounds were obtained as a result of analysis of Tanner graph representation of irregular LDPC code. The numerical results, obtained at the end of the paper for proposed lower-bounds achieved similar results for the previously known best lower-bounds for regular LDPC codes and were represented for the first time for the irregular LDPC codes.
Among the classes of LDPC codes that have been constructed and designed, the only class of LDPC codes that are cyclic is the class of codes constructed based on the incidence vectors of lines of finite geometries, called finite geometry LDPC codes. Cyclic finite geometry LDPC codes are known to have large minimum distances and can provide good error performance with very low error-floors using iterative decoding based on belief propagation. Their cyclic structure allows them to be efficiently and systematically encoded with simple shift-registers in linear time with linear complexity. An obvious question is whether, besides cyclic finite geometry LDPC codes, there are other cyclic codes with large minimum distances that can be efficiently decoded iteratively using channel soft information. In this paper, we present one such class of cyclic codes. Codes in this class are two-step majority-logic decodable and they are also constructed based on finite geometries. Two iterative decoding algorithms are devised for this class of cyclic codes and they provide significant coding gain over the two-step majority-logic decoding of codes in this class.