Abstract
For an arbitrary (3,L) quasi-cyclic(QC) low-density parity-check (LDPC) code with girth at least ten, a tight lower bound of the consecutive lengths is presented. For an arbitrary length above the bound the corresponding LDPC code necessarily has a girth at least ten, and for the length equal to the bound, the resultant code inevitably has a girth smaller than ten. This new conclusion can be well applied to some important issues, such as the proofs of the existence of large girth QC-LDPC codes, the construction of large girth QC-LDPC codes based on the Chinese remainder theorem, as well as the construction of LDPC codes with the guaranteed error correction capability.
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Zhang, G., Wang, J., Li, X. et al. Tight lower bound of consecutive lengths for QC-LDPC codes with girth at least ten. Chin. Sci. Bull. 56, 1272–1277 (2011). https://doi.org/10.1007/s11434-010-4049-8
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DOI: https://doi.org/10.1007/s11434-010-4049-8