Protograph design with multiple edges for regular QC LDPC codes having large girth

In this paper, all subgraph patterns of protographs which prevent quasi-cyclic (QC) low-density parity-check (LDPC) codes from having large girth are searched in allowance with multiple edges based on graph theoretic approach. A systematic construction of protographs with multiple edges using combinatorial design is proposed for designing QC LDPC codes with girth greater than or equal to 14.