An efficient iterative algorithm for designing an asymptotically optimal modified unrestricted uniform polar quantization of bivariate Gaussian random variables

In this paper, a more efficient and a more accurate algorithm is developed for designing asymptotically optimal unrestricted uniform polar quantization (UUPQ) of bivariate Gaussian random variables compared to the existing algorithms on this subject. The proposed algorithm is an iterative one defining the analytical model of asymptotically optimal UUPQ in only a few iterations. The UUPQ model is also improved via optimization of the last magnitude reconstruction level so that the mean squared error (MSE) is minimal. Moreover, for the straightforward performance assessment of our analytical UUPQ model an asymptotic formula for signal to quantization noise ratio (SQNR) is derived, which is reasonably accurate for any rate (R) greater than or equal to 2.5 bits/sample. It is demonstrated empirically that our asymptotically optimal UUPQ model outperforms the previous UUPQ models in terms of SQNR. Eventually, the transition from the analytical to the practically designed UUPQ model, as an important aspect in quantizer design, is considered in the paper and, as a result, a novel method to achieve this is provided. The proposed method is applicable to the practical design of any unrestricted polar quantization.