Lifting methods for quasi-cyclic LDPC codes

Abstract

In this paper we present two simple methods to construct a quasi-cyclic LDPC (QC-LDPC) code of larger length by lifting a given QC-LDPC code. We show that its girth is always larger than or equal to that of the given QC-LDPC code. Applying the methods recursively, it is possible to construct a sequence of QC-LDPC codes generated from a single exponent matrix by proper floor or modulo operations. Simulation results show that they have no serious performance degradation, as compared with randomly constructed LDPC codes.