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

Problems of Information Transmission

Low-density parity-check codes based on steiner systems and permutation matrices

Fedor I. Ivanov, Victor Zyablov

Published Oct 1, 2013• 3 citations
Publisher

Abstract

An algorithm for generating parity-check matrices of regular low-density paritycheck codes based on permutation matrices and Steiner triple systems S(v, 3, 2), v = 2 m − 1, is proposed. Estimations of the rate, minimum distance, and girth for obtained code constructions are presented. Results of simulation of the obtained code constructions for an iterative “belief propagation” (Sum-Product) decoding algorithm applied in the case of transmission over a binary channel with additive Gaussian white noise and BPSK modulation are presented.

DOI
10.1134/s0032946013040042

Related papers

Comparison of various constructions of binary LDPC codes based on permutation matrices

Victor Zyablov, Fedor I. Ivanov, В. Г. Потапов

Ensembles of low-density parity check codes based on permutation matrices are considered. Algorithms for generation of check matrices of such codes are proposed. The results of simulation of the obtained code constructions for an iterative belief propagation (sum-product) decoding algorithm applied in the case of transmission of a code word via a binary channel with an additive Gaussian white noise are presented.

Journal of Communications Technology and Electronics•Aug 1, 2012•3 citations

A special class of quasi-cyclic low-density parity-check codes based on repetition codes and permutation matrices

Fedor I. Ivanov

We propose a new ensemble of binary low-density parity-check codes with paritycheck matrices based on repetition codes and permutation matrices. The proposed class of codes is a subensemble of quasi-cyclic codes. For the constructed ensemble, we obtain minimum distance estimates. We present simulation results for the proposed code constructions under the (Sum-Product) iterative decoding algorithm for transmission over an additive white Gaussian noise channel using binary phase-shift keying.

Problems of Information Transmission•Feb 27, 2017•0 citations

Low-density parity-check codes based on Galois fields

Fedor I. Ivanov, Victor Zyablov, В. Г. Потапов

Methods for constructing a mapping of the elements of a multiplicative group of a Galois field onto a symmetric group of permutation matrices are proposed. A technique minimizing the order of the symmetric group is suggested. The results are used for constructing an ensemble of low-density parity-check codes. The obtained code constructions are tested on an iterative belief propagation (sum-product) decoding algorithm on transmission of a code word through a binary channel with an additive Gaussian white noise.

Journal of Communications Technology and Electronics•Aug 1, 2012•3 citations

Алгоритм декодирования кодов с малой плотностью проверок на четность с большим распараллеливанием

Fedor I. Ivanov, Igor V. Zhilin, Victor Zyablov

Modification of the belief propagation decoding algorithm for low-density parity check codes based on permutation matrices is proposed. The given algorithm has vector implementation. Computer simulation results for this algorithm using transfer of a code word with binary phase-shift keying and additive white gaussian noise are given.

Информационно-управляющие системы•Jan 1, 2012•0 citations

Structured LDPC codes from permutation matrices free of small trapping sets

Dung Viet Nguyen, Bane V. Vasic, Michael W. Marcellin +1 more

This paper introduces a class of structured low-density parity-check (LDPC) codes whose parity check matrices are arrays of permutation matrices. The permutation matrices are obtained from Latin squares and form a finite field under some matrix operations. They are chosen so that the Tanner graphs do not contain subgraphs harmful to iterative decoding algorithms. The construction of column-weight-three codes is presented. Although the codes are optimized for the Gallager A/B algorithm over the binary symmetric channel (BSC), their error performance is very good on the additive white Gaussian noise channel (AWGNC) as well.

arXiv:1004.1198•IEEE Information Theory Workshop (ITW)•Aug 1, 2010•25 citations

Performance Analysis and Design of (3,ρ) — Regular Quasi Cyclic LDPC Codes

Xu Xia, Moon Ho Lee, Choi Seung Je +1 more

In this paper we construct a novel family of (3,rho)-regular quasi-cyclic (QC) low-density parity-check (LDPC) codes, derived from permutation theorem for Latin squares, when used over binary input additive white Gaussian noise (BIAWGN) channel. The codes have high code rate, girth absence of 4, good minimum distance, and sparse parity check matrices. They are designed to perform well when iteratively decoding with sum-product decoding algorithm and to allow low complexity encoding

•Dec 10, 2005•0 citations
An algorithm for generating parity-check matrices of regular low-density paritycheck codes based on permutation matrices and Steiner triple systems S(v, 3, 2), v = 2 m − 1, is proposed. Estimations of the rate, minimum distance, and girth for obtained code constructions are presented. Results of simulation of the obtained code constructions for an iterative “belief propagation” (Sum-Product) decoding algorithm applied in the case of transmission over a binary channel with additive Gaussian white noise and BPSK modulation are presented.
Methods for constructing a mapping of the elements of a multiplicative group of a Galois field onto a symmetric group of permutation matrices are proposed. A technique minimizing the order of the symmetric group is suggested. The results are used for constructing an ensemble of low-density parity-check codes. The obtained code constructions are tested on an iterative belief propagation (sum-product) decoding algorithm on transmission of a code word through a binary channel with an additive Gaussian white noise.
This paper introduces a class of structured low-density parity-check (LDPC) codes whose parity check matrices are arrays of permutation matrices. The permutation matrices are obtained from Latin squares and form a finite field under some matrix operations. They are chosen so that the Tanner graphs do not contain subgraphs harmful to iterative decoding algorithms. The construction of column-weight-three codes is presented. Although the codes are optimized for the Gallager A/B algorithm over the binary symmetric channel (BSC), their error performance is very good on the additive white Gaussian noise channel (AWGNC) as well.