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Nearest neighbor algorithm for spherical codes from the Leech lattice

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2 Author(s)
Adoul, J.-P. ; Dept. of Electr. Eng., Sherbrooke Univ., Que., Canada ; Barth, M.

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

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Information Theory, IEEE Transactions on  (Volume:34 ,  Issue: 5 )