Tight lower bound of consecutive lengths for QC-LDPC codes with girth at least ten |
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Authors: | GuoHua Zhang JuHua Wang XueYuan Li XinMei Wang |
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Affiliation: | (1) State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, 710071, China;(2) China Academy of Space Technology (Xi’an), Xi’an, 710100, China |
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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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Keywords: | low-density parity-check code quasi-cyclic girth consecutive |
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