论文标题
用弦的短周期构建基于原始的LDPC代码
Construction of protograph-based LDPC codes with chordless short cycles
论文作者
论文摘要
控制小尺寸的陷阱集和短周期可能会导致LDPC代码，最小距离$ d _ {\ min} $。我们证明，带有和弦的短周期是几个陷阱集的根源，消除这些周期增加了$ d _ {\ min} $。我们表明，LDPC代码的$ d _ {\ min} $带有无弦短循环，腰围6（和8）的下限，分别是$2γ$（和10），与现有的binds $γ+1 $（和6）相比，这是一个重大改进。针对任何类型的单块单个边缘和多边缘，正常且不规则的原质仪，提出了基于原质的LDPC代码的指数矩阵的必要条件。我们的方法在GIRTH-6 QC-LDPC代码中的应用表明，这些周期的去除可改善文献中的先前结果。
Controlling small size trapping sets and short cycles can result in LDPC codes with large minimum distance $d_{\min}$. We prove that short cycles with a chord are the root of several trapping sets and eliminating these cycles increases $d_{\min}$. We show that the lower bounds on $d_{\min}$ of an LDPC code with chordless short cycles, girths 6 (and 8), and column weights $γ$ (and 3), respectively, are $2γ$ (and 10), which is a significant improvement compared to the existing bounds $γ+1$ (and 6). Necessary and sufficient conditions for exponent matrices of protograph-based LDPC codes with chordless short cycles are proposed for any type of protographs, single-edge and multiple-edge, regular and irregular. The application of our method to girth-6 QC-LDPC codes shows that the removal of those cycles improves previous results in the literature.
