Title :
A counterexample to a Voronoi constellation conjecture
Author :
Headley, Patrick
Author_Institution :
Dept. of Math., Michigan Univ., Ann Arbor, MI, USA
fDate :
11/1/1991 12:00:00 AM
Abstract :
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 Λ/Λs is the set of points in some translate Λ+a that fall within the Voronoi region R(Λs). 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
Keywords :
encoding; information theory; Voronoi constellation conjecture; average signal power; lattice codes; lattice partition; signal constellations; two-dimensional counterexample; Bandwidth; Combinatorial mathematics; Concrete; Constellation diagram; Lattices; Numerical analysis; Partitioning algorithms; Prediction methods; Signal sampling; Stochastic processes;
Journal_Title :
Information Theory, IEEE Transactions on
