Tight lower bound of consecutive lengths for QC-LDPC codes with girth twelve

2012/04/22 by Guohua Zhang, Xinmei Wang, GuoHua, Zhang +1
Computer Science · Engineering · #Error Correcting Code Techniques #Advanced Wireless Communication Techniques #Advanced Wireless Network Optimization

paper · pdf · doi:10.48550/arxiv.1204.4864

Abstract

For an arbitrary (3,L) QC-LDPC code with a girth of twelve, a tight lower bound of the consecutive lengths is proposed. For an arbitrary length above the bound the resultant code necessarily has a girth of twelve, and for the length meeting the bound, the corresponding code inevitably has a girth smaller than twelve. The conclusion can play an important role in 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, and the construction of LDPC codes with the guaranteed error correction capability.

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