I. Introduction
An -dimensional lattice is a discrete additive subgroup of . Let and be two lattices such that . Then, forms a quotient group. If the coset leaders of this quotient group are chosen from the zero-centered Voronoi region of , this construction is called a nested lattice code. Nested lattice codes are well-suited for channels such as those in wireless communications: the coding lattice provides coding gain; the shaping lattice provides shaping gain; and group properties make a candidate for physical-layer network coding.