Construction of QC LDPC Codes with Desired Girths

In this paper, a class of Quasi-cyclic (QC) lowdensity parity-check (LDPC) codes, called FSS codes, with large girth and arbitrary column-weight distributions is presented. Especially, column-weight-2 FSS codes reach larger rates than the column-weight-2 geometric and cylinder-type codes with the same girths. To find the maximum girth of FSS codes, we define the inevitable walks, and the maximum girth can be determined by the smallest length of inevitable walks.