Diversity of low-density lattices

We describe full-diversity constructions of real lattices defined by their integer-check matrix, i.e. the inverse of their generator matrix. In the first construction suited to maximum-likelihood decoding, these lattices are defined by sparse (low-density) or non-sparse integer-check matrices. Based on a special structure of the lattice binary image, a second full-diversity lattice construction is described for sparse integer-check matrices in the context of iterative probabilistic decoding. Full diversity is theoretically proved in both cases. Computer simulation results also confirm that the proposed low-density lattices attain the maximal diversity order.