Design of Irregular Quasi-Cyclic LDPC Codes Based on Euclidean Geometries

This paper presents an approach to the construction of low-density parity-check (LDPC) codes based on hyperplanes (mu-flats) of different dimensions in Euclidean geometries. Codes constructed by this method have quasi-cyclic and irregular structure. The degree distributions of these codes are optimized by the curve fitting approach in the extrinsic information transfer (EXIT) charts. By constraining the fraction of degree-2 nodes, we can lower the error floor at the cost of a small increase in the threshold SNR. Simulation results show that these codes perform very well at both of waterfall region and the error floor region with the iterative decoding.