We propose a systematic design of protograph-based quasi-cyclic (QC) low-density parity-check (LDPC) codes with low error floor. We first characterize the trapping sets of such codes and demonstrate, using edge coloring techniques, that the QC structure of the code eliminates some of the trapping set structures that can exist in a code with the same degree distribution and girth but lacking the QC structure. Based on this characterization, our design aims at eliminating a targeted collection of trapping sets. Considering the parent/child relationship between the trapping sets in the collection, we search for and eliminate those trapping sets that are in the collection but are not a child of any other trapping set in the collection. An efficient layered algorithm is designed for the search of these targeted trapping sets. Compared to the existing codes in the literature, the designed codes are superior in the sense that they are free of the same collection of trapping sets while having a smaller block length, or a larger collection of trapping sets while having the same block length. In addition, the efficiency of the search algorithm makes it possible to design codes with larger degrees which are free of trapping sets within larger ranges compared to the state-of-the-art.

中文翻译：

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通过有效的系统搜索和陷阱集消除来构建低错误层的 QC LDPC 码

我们提出了一种基于原图的准循环 (QC) 低密度奇偶校验 (LDPC) 码的系统设计，具有低错误层。我们首先表征此类代码的诱捕集，并使用边缘着色技术证明代码的 QC 结构消除了一些可能存在于具有相同度数分布和周长但缺乏 QC 结构的代码中的诱捕集结构。基于此特征，我们的设计旨在消除有针对性的诱捕集集合。考虑到集合中陷印集之间的父/子关系，我们搜索并消除那些在集合中但不是集合中任何其他陷印集的子集的陷印集。设计了一种高效的分层算法来搜索这些目标诱捕集。与文献中现有的代码相比，所设计的代码的优越性在于它们没有相同的陷阱集集合而具有较小的块长度，或者具有较大的陷阱集集合而具有相同的块长度。此外，与现有技术相比，搜索算法的效率使得设计具有更大程度的代码成为可能，这些代码在更大范围内没有陷阱集。