Uniform Spherical Coordinate Quantization of Spherically Symmetric Sources

For signal quantization with the minimum mean square error criterion, optimum spherical coordinate quantizers have been shown to outperform optimum rectangular coordinate qnantizers for many spherically symmetric sources. In this paper, spherical coordinate quantizers are designed and analyzed under the added constraint that each scalar quantizer is a uniform (equal step-size) quantizer. It is shown that for small block length, uniform spherical coordinate quantizers outperform the uniform rectangular coordinate quantizer as well as the uniform qnantizer consisting of a tesselation of the minimum inertia, space filling polytope.