[IEEE Trans. on Information Theory, November 1997, pp. 1774-1785]
Asymptotically Efficient Spherical Codes---Part I:
Wrapped Spherical Codes
Jon Hamkins and Kenneth Zeger
Abstract
A new class of spherical codes called wrapped spherical codes is
constructed by ``wrapping'' any sphere packing Λ in Euclidean
space onto a finite subset of the unit sphere in one higher dimension.
The mapping preserves much of the structure of Λ, and unlike
previously proposed maps, the density of wrapped spherical codes
approaches the density of Λ, as the minimum distance
approaches zero. In particular, wrapped spherical codes are
asymptotically optimal as the minimum distance shrinks, whenever the
packing Λ is optimal. Additionally, wrapped spherical codes
can be effectively decoded using a decoding algorithm for Λ.
Click here to see a Wrapped Spherical Code in 3 dimensions.