A fast searching method for the construction of QC-LDPC codes with large girth

In this paper, we propose an effective and efficient searching method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes with a desired girth g. We begin with an arbitrary QC-LDPC code with girth-4 and we evaluate only the number of cycles with length 4. When all the cycles with length 4 are removed by adjusting the elements of the QC-LDPC code, we form a QC-LDPC code with girth-6. Subsequently, we consider only the numbers of cycles with length 4 and length 6. In general, knowing that the current QC-LDPC code has a girth of g´, we only consider the numbers of cycles with length up to g´ even though g´ may be smaller than the desired girth g. By using an adaptive cost function, which is defined as the number of cycles of length g´, in the optimization/searching process, we are able to reduce the computational effort tremendously compared with Wang´s searching algorithm [1]. Consequently, our proposed method can generate QC-LDPC codes with the desired girth much more efficiently.