Four and Six-Dimensional Signal Constellations From Algebraic Lattices

In this work we describe a procedure to construct finite signal constellations from lattices associated to rings of algebraic integers and their ideals. The procedure provides a natural way to label the constellation points by elements of a finite field. The labeling is proven to be linear which allows, at the receiver, a fast way to map a constellation point into a field element. The performance of four and six-dimensional constellations are determined in terms of minimum squared Euclidean distance and average energy, for rates from 1 up to 3.