Quasi-Cyclic Protograph-Based Raptor-Like LDPC Codes With Girth 6 and Shortest Length

We consider multiple-edge QC-LDPC codes with a base matrix of large size. We propose a new method, the degree reduction method, to obtain exponent matrices of these codes which considerably reduces the complexity of the search algorithm. We also provide a necessary and sufficient condition to avoid 4-cycles from occurrence in the Tanner graph of codes obtained using our method. Then, we apply our ...