Student: Jon Hamkins

Advisor: Ken Zeger

School: University of Illinois, Urbana-Champaign
Date of PhD: October 1996

A spherical code is a finite set of points on the surface of a multidimensional unit radius sphere. This thesis gives two constructions for large spherical codes that may be used for channel coding and for source coding. The first construction ``wraps'' a finite subset of any sphere packing onto the unit sphere in one higher dimension. The second construction is analogous to the recursive construction of laminated lattices. Both constructions result in codes that are asymptotically optimal with respect to minimum distance, and the first construction can be efficiently used as part of a vector quantizer for a memoryless Gaussian source. Both constructions are structured so that codepoints may be identified without having to store the entire codebook. For several different rates, the distortion performance of the proposed quantizer is superior than previously published results of quantizers with equivalent complexities.

The construction techniques are motivated by the relationship between asymptotically large spherical codes and sphere packings in one lower dimension. It is shown that the asymptotically maximum density of a k-dimensional spherical code equals the maximum density of a sphere packing in tex2html_wrap_inline10