Counting number of girth 6 for sparse quasi cyclic low density parity check codes using gallager approach

Abstract

This manuscript presents two approaches for counting the number of girth 6, these are based on Gallager construction of sparse QC-LDPC (Quasi Cyclic Low Density Parity Check codes). The Sparse QC-LDPC matrix has been constructed through counter shifting, permutation, circulant shifting, creates generator matrix, sub-matrix and basic construction of Gallager technique. It performs the 6 cycles check algorithm with constant row weight 3 and column weight 6 on various codes of half code rate. Simulation results show that the constructed sparse regular QC-LDPC codes outperforms to number of girth 6 counting using these two approaches that compared to Existing results.