Constructing QC-LDPC codes based on dimension reduction for physical layer security

As a recently proposed physical layer security scheme, the two-dimensional transmission scheme prevents eavesdropping, but the bit error rate (BER) of the receiver becomes high. A new coding scheme for Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes to improve the performance of the receiver is proposed and named as dimension reduction coding. This new scheme constructs the base matrix, which is necessary to obtain the parity check matrix of QC-LDPC codes, from the channel coefficient matrix of two-dimensional transmission scheme. Then, by analyzing the relationship between the base matrix and the parity check matrix of QC-LDPC codes, we find out the conditions that the base matrix must satisfy so that the corresponding parity check matrix has no shortest cycle in Tanner graph. Furthermore, a dimension reduction algorithm is presented to modify the base matrix and obtain parity check matrices with good performance. Finally, simulation results are given and validate the feasibility of this method.