Construction of QC-LDPC codes with girth larger than eight based on GPU

Based on the necessary and sufficient conditions for increasing girth, a shortened cycle elimination algorithm to construct Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes with large girth based on the Graphic Processing Unit (GPU) is presented. Firstly, we propose a cycle statistics algorithm based on GPU to search for the elements of base matrix that satisfies the no-cycle conditions. If the search process fails to find qualified elements, we delete the corresponding column in which this element is located in order to make the algorithm converge. And then, we apply GPU to construct QC-LDPC codes and get base matrices of QC-LDPC codes with girth larger than eight.