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Paper IDA.5.2
Paper Title Construction of Rate (n-1)/n Non-Binary LDPC Convolutional Codes via Difference Triangle Sets
Authors Gianira Nicoletta Alfarano, Julia Lieb, Joachim Rosenthal, University of Zurich, Switzerland
Session A.5: Combinatorial Coding Theory II
Presentation Lecture
Track Algebraic and Combinatorial Coding Theory
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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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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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