Scale-recursive lattice-based multiple-access symbol constellations
IEEE Transactions on Information Theory
| Hi-index | 754.90 |
We consider a special case of Voronoi coding, where a lattice Λ in Rn is shaped (or truncated) using a lattice Λ'={(m1x1,...,mnxn)|(x1,...,xn)∈Λ} for a fixed m_=(m1,...,mn)∈(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 Λ' is a sublattice of Λ. We derive the underlying conditions on m_ and present generic near-ellipsoidal Voronoi indexing algorithms. Examples of constraints on m_ and conditional modification are provided for the lattices A2, Dn (n≥2) and 2Dn+ (n even ≥4).