Using a prefix code for addressing the Voronoi constellations based on lattices DN and DN*

In Voronoi constellations, the Voronoi region of a lattice, called the shaping lattice, is used as the boundary of the signal constellation. Some properties of Voronoi constellations based on the shaping lattices D_N and D_N* are discussed. The induced probability distribution on the two-dimensional subspaces is found. A prefix coding scheme as an alternative for the addressing is presented. This code in some sense simulates the effect of the boundary by using the points of the subspaces with nonequal probability. An example of such a coding scheme is presented