Name
Abstract | ||
|---|---|---|
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). |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1109/TIT.2003.813484 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
present generic near-ellipsoidal voronoi,special case,lattices a2,conditional modification step,near-ellipsoidal voronoi coding,fixed m,underlying condition,indexing algorithm,conditional modification,voronoi coding,standard voronoi indexing algorithm,set theory,indexation,algorithm design and analysis,gaussian mixture model,speech coding,indexing,vectors,lattices | Discrete mathematics,Ellipsoid,Combinatorics,Lattice (order),Algebraic codes,Voronoi diagram,Mathematics,Lambda | Journal |
Volume | Issue | ISSN |
49 | 7 | 0018-9448 |
Citations | PageRank | References |
3 | 0.46 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| S. Ragot | 1 | 18 | 2.17 |
| Minjie Xie | 2 | 36 | 4.82 |
| R. Lefebvre | 3 | 3 | 0.46 |