Design of Asymptotically Optimal Unrestricted Polar Quantizer for Gaussian Source

In this letter, in order to outperform the existing method for unrestricted polar quantizer (UPQ) design in terms of signal to quantization noise ratio, the asymptotic approximations of Rayleigh distributed function are applied to all magnitude regions of the UPQ, except to the last one. Given the constraint, the UPQ is designed to provide the minimum of the asymptotic mean-squared error distortion for the Gaussian source of unit variance. The effects of this constraint are studied for different bit rates R. The accuracy of the derived formulas is assessed and the reasonable accuracy is observed for R ≥ 2.5 bit/sample.