On a Class of High-Girth LDPC Codes Based on Finite Multidimensional Lattices

An LDPC code construction technique is proposed based on the structural properties of finite m-dimensional lattices. The Tanner graph of any code from this class is shown to have a girth of eight, and the number of proper eight-cycles in the graph is enumerated. The minimum distance of the codes is shown to be lower bounded by 2m. The codes are also shown to be highly flexible in terms of code length and rate, and compatible with a low-complexity serial-parallel decoder implementation based on the turbo-decoding message passing algorithm. Finally, simulation results over the AWGN channel demonstrate that these codes have good error-correcting performance.