A counterexample to a Voronoi constellation conjecture

Voronoi constellations are of interest because it is possible to save on signal power by choosing a lattice for which the second moment of the Voronoi region is close to that of a sphere with the same dimensionality. A Voronoi constellation based on the lattice partition Lambda / Lambda /sub s/ is the set of points in some translate Lambda +a that fall within the Voronoi region R( Lambda /sub s/). G.D. Forney, Jr. (1989) proposed an algorithm for constructing Voronoi constellations and conjectured that this algorithm minimized the average signal power. A two-dimensional counterexample, to Forney's conjecture is presented.<
>