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 eightcycles in the graph is enumerated. The minimum distance of the codes is shown to be lower bounded by 2 m. 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.