Asymptotic performance of unrestricted polar quantizers (Corresp.)

Abstract

Unrestricted polar quantizers (UPQ's) were previously introduced to overcome the weak mean-squared error performance of polar coordinate quantizers for the independent bivariate Gaussian source when the number of levels was small ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&lt; 3</tex> bits /dimension). An asymptotic ntean-squared error analysis of the UPQ's with a general circularly symmetric source is presented. The performance of the UPQ's is shown to be asymptotically within <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.17</tex> dB of that of the optimum bivariate quantizer. The results are extended to dimensions greater than two. Examples for the independent Gaussian source are included.