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 S^{2L-1} of R^{2L} 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 R^L 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 R^{48}. Upper and lower bounds on the performance, the asymptotic packing density and a method for decoding are derived.
Keywords
Cite
@article{arxiv.1205.5914,
title = {Constructive spherical codes on layers of flat tori},
author = {Cristiano Torezzan and Sueli I. R. Costa and Vinay A. Vaishampayan},
journal= {arXiv preprint arXiv:1205.5914},
year = {2016}
}
Comments
9 pages, 5 figures, submitted to IEEE Transactions on Information Theory