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A necessary and sufficient condition for determining the girth of quasi-cyclic LDPC codes

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3 Author(s)
Xiaofu Wu ; Nanjing Inst. of Commun. Eng., Nanjing ; Xiaohu You ; Chunming Zhao

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.

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Communications, IEEE Transactions on  (Volume:56 ,  Issue: 6 )