Variable-length coding for performance improvement of asymptotically optimal unrestricted polar quantization of bivariate Gaussian source

This paper considers the application of variable-length coding using two unrestricted polar quantizers (UPQs) for performance improvement of unrestricted polar quantization for bivariate Gaussian source. We propose the use of two UPQs, both designed for the bivariate Gaussian source of unit variance, having different sizes of codebooks and different optimal compressor functions. We show that the fixed-rate UPQ is a subset of our model, and we perform rigorous optimization procedure in order to obtain optimal parameter values maximizing the signal to quantization noise ratio (SQNR) for the given average bit rate. In addition, we study how gain in SQNR over the fixed-rate UPQ depends on the average bit rate and we show that the gain ranges from 0.619 dB to 0.869 dB depending on the average bit rate. Discussion is also provided about the proposed quantizer complexity and its performance in comparison to Shannon limit. The proposed UPQ provides a sophisticated choice of average bit rate compared to the fixed-rate UPQ. Features of the proposed quantizer indicate that the obtained model should be of high theoretical and practical significance.