On the Low Complexity Construction of Quasi-Cyclic Low-Density Parity-Check Codes by Progressive-Block Growth

In this paper, we propose a novel method with low complexity for constructing quasi-cyclic LDPC codes. The algorithm chooses every circulant permutation matrix sequentially, and makes sure that the current circulant permutation matrix forms no cycles of length 4 and 6 with the existent matrices, finally a family of (3,L) QC-LDPC codes with girth at least 8 is obtained. The main complexity of the algorithm is checking cycles of length 6, the number of which is no more than L². Simulation results show that, when block length is 1008 and using the iterative belief propagation decoding, the LDPC code constructed by the proposed algorithm out performs the random code about 0.1 dB at the bit-error-rate of 10^-5.