Circulant矩阵构造准循环LDPC码的旋转环长分析法(英文)

Rotation-Distance Analysis of QC-LDPC Code Based on Circulant Permutation Matrices

低密度奇偶检验(QC-LDPC:Quasi-Cyclic Low-Density Parity-Check)码的环长分布影响决定着LDPC码的解码效果和编码复杂度,但其分析较困难。为此,首次提出旋转距离分析法,用于分析基于Circulant矩阵构造的准循环低密度奇偶校验码(QC-LDPC码)的环分布,并给出了任何一个基于Circulant矩阵构造出的QC-LDPC码中的最小环长(girth)的上限(12)。同时,运用该方法,分析出一种权重为(3,5)的QC-LD-PC码的译码效果与该码环分布的关系。由于LDPC码奇偶校验矩阵中的Circulant子矩阵,可以被当成1个矩阵节点的单一节点看待,从而简化了整个码的特纳图,使寻找QC-LDPC码中闭环的方法变得简单。

Cycle distribution of LDPC （Low-Density Parity-Check） codes affects the codes ＇decoding performance and encoding complexity, however it is commonly NP hard to analyse. We propose the rotation-distance for analysis of QC-LDPC （ Quasi-Cyclic Low-Density Parity-Check） code based on circulant matrices. The circulant sub-matrices within the parity-check matrix are treated as a ＂matrix node＂ to simplify theTanner graphs of the codes. Thus cycles of QC-LDPC codes can be found efficiently, and we demonstrate the usefulness of the new method by a simple proof of the known result that 12 is an upper limit of the girth of the QC-LDPC codes we considered. Moreover, the cycle analysis based on the new method also reveals relations between decoding performance and the cycle distribution of the code.