Detecting cycles of length 8 in the Tanner graph of a QC-LDPC code based on protograph analysis

For cycles of length 8 in a Tanner graph, we propose an identification procedure based on the analysis of paths in a protograph. We formulate and prove a number of theorems that introduce identification rules for cycles and restrict the number of subgraphs to be analyzed. To distinguish between them, we propose a number of parameters that uniquely determine the group of analyzed paths in the protograph.