Rotation-Distance Analysis of QC-LDPC Code Based on Circulant Permutation Matrices
Douglas J. Leith · Journal of Jilin University · 2011
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 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.