Construct Parity-check Matrix H of QC LDPC Codes via Arithmetic Progression

In this correspondence, the construction of quasi-cyclic low-density parity-check(QC LDPC) codes via Arithmetic Progression(AP) is investigated. A mild necessary and sufficient condition is derived for the QC LDPC code to remove specifically circles whose girth equal to 6. Based on this condition, Arithmetic Progression method for constructing shift value matrix is proposed and it is also proved that the specifically circles do not exist. For given N,K,J and L, a family of QC LDPC code is obtained via AP method. The simulation results illustrate that code constructed via AP method can perform well.