论文标题
通过差异三角集建设速率（N-1）/N非二元LDPC卷积代码
Construction of Rate (n-1)/n Non-Binary LDPC Convolutional Codes via Difference Triangle Sets
论文作者
论文摘要
本文提供了非二元LDPC卷积代码的构造，该代码概括了鲁滨逊和伯恩斯坦的工作。形成$（n-1，w）$ - 差异三角集的整数集用作速率$ $（n-1）/n $卷积代码的支持。如果场大小足够大，则与代码的滑动奇偶校验检查矩阵相关的坦纳图将从$ 4 $和6美元的$ 6 $ -CYCLE中免费，无法满足完整的排名条件。这对于改善代码的性能并避免存在低重量的代码字和吸收套件很重要。卷积代码的参数被证明是由基础差异三角集的参数确定的。特别是，代码的自由距离与$ w $有关，并且代码的程度链接到差异三角集的“范围”。因此，找到具有最小范围的差异三角形的家族的问题相当于找到少量程度的卷积代码。
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.
