Asymptotic performance of unrestricted polar quantizers (Corresp.)

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 ( 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 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.