Near-ellipsoidal Voronoi coding
In this correspondence, we consider a special case of Voronoi coding, where a lattice A in R-n is shaped (or truncated) using a lattice Lambda' = {(m(1)x(1),...,m(n)x(n))\(x(1),...x(n)) is an element of Lambda} for a fixed (m) under bar = (m(1),...,m(n)) is an element of (N \ {0, 1})(n). Using this technique, the shaping boundary is near-ellipsoidal. It is shown that the resulting codes can be indexed by standard Voronoi indexing algorithms plus a conditional modification step, as far as Lambda' is a sublattice of Lambda. We derive the underlying conditions on (m) under bar and present generic near-ellipsoidal Voronoi indexing algorithms. Examples of constraints on (m) under bar and conditional modification are provided for the lattices A(2), D-n (n greater than or equal to 2) and 2D(n)(+) (n even greater than or equal to 4).
voronoi coding lattice lattice codes lattice indexing