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Nearest neighbor algorithm for spherical codes from the Leech lattice. (English) Zbl 0665.94020

The Leech lattice is a regular arrangement of points in 24-dimensional Euclidean space which yields an extremely dense packing when equal spheres are centered at these points. A subset of the Leech lattice can be used as a signal set for the Gaussian channel or as representative vectors for a vector quantizer. Of particular interest are the spherical codes (or code books) which consist of the points of the Leech lattice which lie on a sphere centered at the origin. The most interesting feature of this approach is that the code points do not have to be stored because they can be obtained from a very small set of basic vectors using permutations of the components in a manner dictated by the words of the extended Golay code. A nearest neighbor algorithm which works on this is developed to determine the point in the code closest to some arbitrary vector in \({\mathbb{R}}^{24}\). The performance of this approach when quantizing independent identically distributed Gaussian samples is reported.

MSC:

94B15 Cyclic codes
94A05 Communication theory
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