Circulant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-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...

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.