Constructive spherical codes on layers of flat tori
Abstract
A new class of spherical codes is constructed by selecting a finite subset of flat tori from a foliation of the unit sphere S2L-1 of R2L and designing a structured codebook on each torus layer. The resulting spherical code can be the image of a lattice restricted to a specific hyperbox in RL in each layer. Group structure and homogeneity, useful for efficient storage and decoding, are inherited from the underlying lattice codebook. A systematic method for constructing such codes are presented and, as an example, the Leech lattice is used to construct a spherical code in R48. Upper and lower bounds on the performance, the asymptotic packing density and a method for decoding are derived.
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