Quasi-Cyclic LDPC Codes: Influence of Proto- and Tanner-Graph Structure on Minimum Hamming Distance Upper Bounds
Quasi-Cyclic LDPC Codes: Influence of Proto- and Tanner-Graph Structure on Minimum Hamming Distance Upper Bounds
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DOI：
10.1109/tit.2011.2173244
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发表时间：
2009-01
影响因子：
2.5
通讯作者：
R. Smarandache;P. Vontobel
中科院分区：
文献类型：
--
作者：
R. Smarandache;P. Vontobel
准循环（QC）低密度奇偶校验（LDPC）码是基于原型图的LDPC码的一个重要实例。在本文中，我们提出了上界的最小汉明距离的QC LDPC码，并研究这些上界如何依赖于图的结构参数（如可变度，校验节点度，周长）的坦纳图和底层的原型图。此外，对于几类原图，我们提出了明确的QC LDPC码的建设，实现（或接近）各自的最小汉明距离上界。由于QC码和卷积码之间的紧密代数联系，我们可以对卷积码的自由汉明距离给出类似的结果。事实上，一些QC码语句是通过首先证明相应的卷积码语句，然后使用坦纳的结果来建立的，该结果表明QC码的最小汉明距离的上限是通过“展开”QC码获得的卷积码的自由汉明距离。
Quasi-cyclic (QC) low-density parity-check (LDPC) codes are an important instance of proto-graph-based LDPC codes. In this paper we present upper bounds on the minimum Hamming distance of QC LDPC codes and study how these upper bounds depend on graph structure parameters (like variable degrees, check node degrees, girth) of the Tanner graph and of the underlying proto-graph. Moreover, for several classes of proto-graphs we present explicit QC LDPC code constructions that achieve (or come close to) the respective minimum Hamming distance upper bounds. Because of the tight algebraic connection between QC codes and convolutional codes, we can state similar results for the free Hamming distance of convolutional codes. In fact, some QC code statements are established by first proving the corresponding convolutional code statements and then using a result by Tanner that says that the minimum Hamming distance of a QC code is upper bounded by the free Hamming distance of the convolutional code that is obtained by “unwrapping” the QC code.