Computers & Mathematics with Applications
Locality sensitive hashing: A comparison of hash function types and querying mechanisms
Pattern Recognition Letters
Geometric piecewise uniform lattice vector quantization of the memoryless Gaussian source
Information Sciences: an International Journal
A new approach to the information set decoding algorithm
Computer Communications
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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? Inn-dimensional space, what is the average squared distance of a random point from the closest point of the latticeA_{n}(orD_{n}, E_{n}, A_{n}^{ast} or D_{n}^{ast})?The answers are given here, together with a description of the Voronoi (or nearest neighbor) regions of these lattices. The results have applications to quantization and to the design of signals for the Gaussian channel. For example, a quantizer based on the eight-dimensional lattice E8 has a mean-squared error per symbol of0.0717 cdotswhen applied to uniformly distributed data, compared with0.08333 cdotsfor the best one-dimensional quantizer.