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ASYMPTOTIC ANALYSIS OF PIECE – WISE UNIFORM PRODUCT POLAR QUANTIZERS

In this paper, simple and complete asymptotical analysis is given for a piecewise uniform product polar quantizer (PUPPQ) with respect to mean-square error (mse). PUPPQ is based on uniform product polar quantizers. Polar quantizer optimality conditions and all main equations for the number of phase divisions and optimal number of levels for each partition are presented. PUPPQ has complexity implementation between optimal nonuniform polar quantization (NPQ) and uniform product polar quantization (UPPQ). These systems, although not optimal, may have asymptotic performance arbitrarily close to the optimum. The gain of PUPPQ over the optimum uniform product polar quantization is obtained.