Nearest neighbor algorithm for spherical codes from the Leech lattice

The Leech lattice is a regular arrangement of points in 24-dimensional Euclidean space that 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) that consist of the points of the Leech lattice which lie on a sphere centered at the origin. 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 that works on this is developed to determine the point in the code closet to some arbitrary vector in R²⁴. The performance of this approach when quantizing independent identically distributed Gaussian samples is reported