Lattice codes based on product constructions over F2q with applications to compute-and-forward

A novel construction of lattices is proposed. This construction can be thought of as Construction A with linear codes that can be represented as the Cartesian product of two linear codes over F_q; hence, is referred to as the product construction. The existence of a sequence of Poltyrev-good lattices generated by the product construction under some conditions is shown. This family of lattices is then used to generate signal constellations with q² elements which can be used in conjunction with multilevel coding with channel codes over F_q instead of F_q2 to design good coded modulation schemes for compute-and-forward.