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Voronoi Cells of Lattices and Quantization Errors

  • J. H. Conway
  • N. J. A. Sloane
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 290)

Abstract

In n-dimensional space, what is the average squared distance of a random point from the closest point of the lattice A n (or D n , E n , A * n or D * n )? If a point is picked at random inside a regular simplex, octahedron, 600-cell or other polytope, what is its average squared distance from the centroid? The answers are given here, together with a description of the Voronoi cells of the above lattices. The results have applications to quantization and to the design of codes for a bandlimited channel. For example, a quantizer based on the eight-dimensional lattice E 8 has a mean squared error per symbol of 0.0717... when applied to uniformly distributed data, compared with 0.08333... for the best one-dimensional quantizer.

Keywords

Root Lattice Weyl Group Quantization Error Voronoi Cell Voronoi Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • J. H. Conway
  • N. J. A. Sloane

There are no affiliations available

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