Generalized low-density (GLD) lattices

We propose the construction of a new family of lattice sphere packings. Given a small-dimensional lattice, we start by building a first lattice in a large dimension by the direct sum of the small lattice. Then, the coordinates of the first large lattice are permuted to yield a second large-dimensional lattice. Finally, our generalized low-density (GLD) lattice is the intersection of the first and the second lattice. We restrict our construction in this paper to integer lattices. GLD lattices are the result of mixing classical lattice theory with modern coding theory. They are potential candidates not only for channel coding as coded modulations, but also for physical-layer network coding and for secure digital communications.