[IEEE Trans. on Information Theory, November 1997, pp. 1786-1798]
Asymptotically Efficient Spherical Codes---Part II:
Laminated Spherical Codes
Jon Hamkins and Kenneth Zeger
Abstract
New spherical codes called laminated spherical codes are
constructed in dimensions 2-49 using a technique similar to the
construction of laminated lattices. Each spherical code is
recursively constructed from existing spherical codes in one lower
dimension. Laminated spherical codes outperform the best known
spherical codes in the minimum distance sense for many code sizes. The
density of a laminated spherical code approaches the density of the
laminated lattice in one lower dimension, as the minimum distance
approaches zero. In particular, the three-dimensional laminated
spherical code is asymptotically optimal, in the sense that its density
approaches the Fejes Tóth upper bound as the minimum distance
approaches zero. Laminated spherical codes perform asymptotically as
well as wrapped spherical codes in those dimensions where laminated
lattices are optimal sphere packings. The laminated spherical codes
are also structured, which leads to an efficient decoding algorithm in
low dimensions.