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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.