Quantizing Using Lattice Intersections
نویسندگان
چکیده
The usual quantizer based on an n-dimensional lattice Λ maps a point x ∈ Rn to a closest lattice point. Suppose Λ is the intersection of lattices Λ1, . . . ,Λr. Then one may instead combine the information obtained by simultaneously quantizing x with respect to each of the Λi. This corresponds to decomposing Rn into a honeycomb of cells which are the intersections of the Voronoi cells for the Λi, and identifying the cell to which x belongs. This paper shows how to write several standard lattices (the face-centered and body-centered cubic lattices, the root lattices D4, E ∗ 6 , E8, the Coxeter-Todd, Barnes-Wall and Leech lattices, etc.) in a canonical way as intersections of a
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