Design of non-binary quasi-cyclic LDPC codes based on multiplicative groups and Euclidean geometries

This paper presents an approach to the construction of non-binary quasi-cyclic (QC) low-density parity-check (LDPC) codes based on multiplicative groups over one Galois field GF(q) and Euclidean geometries over another Galois field GF(2^s). Codes of this class are shown to be regular with girth 6 ≤ g ≤ 18 and have low densities. Finally, simulation results show that the proposed codes perform very well with the iterative decoding.