Construction of flexible type II and III QC-LDPC codes

Abstract: Type II and III low-density parity-check codes (QC-LDPC) codes have been shown to have better minimum distance compared to Type I QC-LDPC codes. This article presents a highly flexible method for constructing high-girth type II and III QC-LDPC codes. The proposed algorithm establishes constraints to be observed in creating a bipartite graph of a given girth. The algorithm is by far more flexible in constructing a wide range (rates and lengths) of type II and III QC-LDPC codes compared to existing methods. Although the proposed algorithm uses a search approach to construct codes, it generally successfully constructs a code even at low code lengths. Constructed codes show better bit error rate performances compared to type I codes as expected