Construction of Optimal Uniform Polar Switched Quantizer in Wide Volume Range

In this paper we will present a simple and complete asymptotical analysis of optimal uniform quantization of two-dimensional memoryless Gaussian sources with the respect to distortion (D(σ,σ
₀
)) i.e. the mean-square error (MSE). Uniform quantizer optimality conditions and all main equations for phase partitions and optimal number of levels for each partition are presented. We derive the optimal granular distortion Doptg (σ,σ
₀
) in a closed form. Switched quantization is used in order to give higher quality by increasing signal-to-quantization-noise-ratio (SQNR) in a wide range of signal volumes (variances).