Construction of irregular quasi-cyclic LDPC codes based on Euclidean geometries

This paper presents a method to the construction of irregular low-density parity-check (LDPC) codes based on Euclidean geometries over the Galois field. Codes constructed by this method are quasi-cyclic (QC) and have large girths. The proposed irregular LDPC codes having flexible column/row weights are obtained with a hyperplane decomposing method in Euclidean geometries. Therefore, the degree distributions of proposed irregular LDPC codes can be optimized by technologies like the curve fitting approach in the extrinsic information transfer (EXIT) charts. Simulation results show that these codes perform very well with an iterative decoding over the AWGN channel.