A Quasi-cyclic LDPC Codes Construction Scheme Based on Pseudo-cyclic MDS Codes

This paper proposes a construction scheme of girth-6 quasi-cyclic Low-Density Check-Parity (LDPC) codes based on pseudo-cyclic Maximum Distance Separable (MDS) codes with two information symbols. The parity-check matrix of an quasi-cyclic LDPC code in GF(q) can be constructed by calculating the generator polynomials of pseudo-cyclic MDS code with length q+1 directly. It utilizes mainly the special characteristic of the circularity of pseudo-cyclic MDS codes with two information symbols. Also the distance between arbitrary two codes is not less than q. Therefore, it guarantees no cycles-4 in the construction of the quasi-cyclic LDPC codes. Simulation results show that the quasi-cyclic LDPC codes based on pseudo-cyclic MDS codes perform well in an AGWN channel.