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 Fq; 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 Fq instead of Fq2 to design good coded modulation schemes for compute-and-forward.
展开▼
