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Spherical codes on torus layers

A new class of spherical codes is constructed by selecting a finite subset of flat tori that foliate the unit sphere S2L−1 ⊂ ℝ2L and constructing a structured codebook on each torus in the finite subset. The codebook on each torus is the image of a lattice restricted to a specific hyperbox in ℝL. Group structure and homogeneity, useful for efficient decoding, are inherited from the underlying lattice codebook. Upper and lower bounds on performance are derived and a systematic search algorithm is presented for constructing optimal codebooks. The torus layer spherical codes presented here exhibit good performance when compared to the well known apple-peeling, wrapped and laminated codes.