2020/01/22 by Gianira N. Alfarano, Alfarano, Gianira N., Julia Lieb +3
Computer Science · Engineering · #Combinatorics (math.CO) #Cooperative Communication and Network Coding #Error Correcting Code Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Telecommunications and Broadcasting Technologies
paper · pdf · doi:10.48550/arxiv.2001.07969
openalex publication_date 2020/01/22 · openalex created_date 2022/07/18 · openalex updated_date 2026/07/28
This paper provides a construction of non-binary LDPC convolutional codes,\nwhich generalizes the work of Robinson and Bernstein. The sets of integers\nforming an (n-1,w)-difference triangle set are used as supports of the\ncolumns of rate (n-1)/n convolutional codes. If the field size is large\nenough, the Tanner graph associated to the sliding parity-check matrix of the\ncode is free from 4 and 6-cycles not satisfying the full rank condition.\nThis is important for improving the performance of a code and avoiding the\npresence of low-weight codewords and absorbing sets. The parameters of the\nconvolutional code are shown to be determined by the parameters of the\nunderlying difference triangle set. In particular, the free distance of the\ncode is related to w and the degree of the code is linked to the "scope" of\nthe difference triangle set. Hence, the problem of finding families of\ndifference triangle set with minimum scope is equivalent to find convolutional\ncodes with small degree.\n