Near-ellipsoidal voronoi coding
Stéphane Ragot, Minjie Xie, Rémi Lefebvre · IEEE Transactions on Information Theory · 2003
We consider a special case of Voronoi coding, where a lattice /spl Lambda/ in /spl Ropf//sup n/ is shaped (or truncated) using a lattice /spl Lambda/'={(m/sub 1/x/sub 1/,...,m/sub n/x/sub n/)|(x/sub 1/,...,x/sub n/)/spl isin//spl Lambda/} for a fixed m_=(m/sub 1/,...,m/sub n/)/spl isin/(/spl Nopf//spl bsol/{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 /spl Lambda/' is a sublattice of /spl Lambda/. 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 A/sub 2/, D/sub n/ (n/spl ges/2) and 2D/sub n//sup +/ (n even /spl ges/4).