A necessary and sufficient condition for determining the girth of quasi-cyclic LDPC codes
Xiaofu Wu, Xiaohu You, Chunming Zhao · IEEE Transactions on Communications · 2008
The parity-check matrix of a quasi-cyclic low- density parity-check (QC-LDPC) code can be compactly represented by a polynomial parity-check matrix. By using this compact representation, we derive a necessary and sufficient condition for determining the girth of QC-LDPC codes in a systematic way. The new condition avoids an explicit enumeration of cycles for determining the girth of codes, and thus can be well employed to generate QC-LDPC codes with large girth.