Cireulant矩阵构造准循环LDPC码的旋转环长分析法

低密度奇偶检验（QC-LDPC：Quasi-CyclicLow-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。

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

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.