Construction of LDPC Code based on Permutation Matrices Optimization

The presence of circles would lay a great impact on the quasi-cyclic LDPC decoding.Therefore,the parity check matrix with good girth distribution is beneficial to the performance of code.This paper first makes a analysis on girth distribution of the check matrix.Then a reasonable constraint is set between the mother matrix and shift matrix,thus,by this way,the check matrix could maximize the minimum cycle length of the check matrix and the average length of the cycle.Finally,a method to construct QC-LDPC code with high girth is given.Simulation results show that this method for minimizing the short code cycle could construct good practical codes.