A product construction of lattices for bandwidth-limited channels

Lattice-based construction of codes is of theoretical as well as of practical importance, in particular for communications over bandwidth-limited channels. The paper investigates the, so called, product lattice construction. A product lattice is obtained using the Kronecker product of two low-dimensional component lattices. Some fundamental properties of product lattices are derived. It is shown that the product lattice construction may achieve comparable, and potentially better, performance than known good lattices, such as the Leech lattice. Practical issues concerning the encoding and decoding of product lattices are discussed.