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Construction of rate (n — 1 )/n non-binary LDPC convolutional codes via difference triangle sets


Alfarano, Gianira Nicoletta; Lieb, Julia; Rosenthal, Joachim (2020). Construction of rate (n — 1 )/n non-binary LDPC convolutional codes via difference triangle sets. In: 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 21 June 2020 - 26 June 2020.

Abstract

This paper provides a construction of non-binary LDPC convolutional codes, which generalizes the work of Robinson and Bernstein. The sets of integers forming an (n - 1,w)- difference triangle set are used as supports of the columns of rate (n - 1)/n convolutional codes. If the field size is large enough, the Tanner graph associated to the sliding parity-check matrix of the code is free from 4 and 6-cycles not satisfying the full rank condition. This is important for improving the performance of a code and avoiding the presence of low-weight codewords and absorbing sets. The parameters of the convolutional code are shown to be determined by the parameters of the underlying difference triangle set. In particular, the free distance of the code is related to w and the degree of the code is linked to the "scope" of the difference triangle set. Hence, the problem of finding families of difference triangle set with minimum scope is equivalent to find convolutional codes with small degree.

Abstract

This paper provides a construction of non-binary LDPC convolutional codes, which generalizes the work of Robinson and Bernstein. The sets of integers forming an (n - 1,w)- difference triangle set are used as supports of the columns of rate (n - 1)/n convolutional codes. If the field size is large enough, the Tanner graph associated to the sliding parity-check matrix of the code is free from 4 and 6-cycles not satisfying the full rank condition. This is important for improving the performance of a code and avoiding the presence of low-weight codewords and absorbing sets. The parameters of the convolutional code are shown to be determined by the parameters of the underlying difference triangle set. In particular, the free distance of the code is related to w and the degree of the code is linked to the "scope" of the difference triangle set. Hence, the problem of finding families of difference triangle set with minimum scope is equivalent to find convolutional codes with small degree.

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Additional indexing

Item Type:Conference or Workshop Item (Paper), not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Theoretical Computer Science
Physical Sciences > Information Systems
Physical Sciences > Modeling and Simulation
Physical Sciences > Applied Mathematics
Language:English
Event End Date:26 June 2020
Deposited On:06 Nov 2020 08:18
Last Modified:31 Jan 2021 11:21
ISBN:9781728164328
OA Status:Closed
Publisher DOI:https://doi.org/10.1109/isit44484.2020.9174510

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