Extension of quasi-cyclic LDPC codes by lifting

In this paper, we analyze some cycle properties of quasi-cyclic low-density parity-check (QC-LDPC) codes and show that the girth of a QC-LDPC code is upper bounded by a certain number introduced by the structure of its mother matrix. We also propose a simple method to extend QC-LDPC codes of large length by lifting QC-LDPC codes of smaller length. In particular, it is possible to generate them from a single exponent matrix by a proper modulo-operation. Simulation results show that the more we apply the lifting to QC-LDPC codes, the more memory efficiency becomes better, but it may induce a little performance degradation.