Using simulated annealing to design good codes
IEEE Transactions on Information Theory
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Vector quantization and signal compression
Vector quantization and signal compression
Flat tori, lattices and bounds for commutative group codes
Designs, Codes and Cryptography
Asymptotically dense spherical codes. I. Wrapped spherical codes
IEEE Transactions on Information Theory
Asymptotically dense spherical codes .II. laminated spherical codes
IEEE Transactions on Information Theory
Curves on a sphere, shift-map dynamics, and error control for continuous alphabet sources
IEEE Transactions on Information Theory
Graphs, tessellations, and perfect codes on flat tori
IEEE Transactions on Information Theory
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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.