Near-ellipsoidal Voronoi coding

We consider a special case of Voronoi coding, where a lattice(Lambda) in (R)/sup n/ is shaped (or truncated) using a lattice (Lambda)ʹ={(m/sub 1/x/sub 1/,...,m/sub n/x/sub n/)|(x/sub 1/,...,x/sub n/)(element of)(Lambda)} for a fixed m_=(m/sub 1/,...,m/sub n/)(element of)(N)\{0,1})/sup 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)ʹ is a sublattice of (Lambda). We derive the underlying conditions on m_ and present generic nearellipsoidal Voronoi indexing algorithms. Examples of constraints on m_ and conditional modification are provided for the lattices A/sub 2/, D/sub n/ (n>2) and 2D/sub n//sup +/ (n even >4).