Multivariate block polar quantization

We introduce multivariate block polar quantization (MBPQ). MBPQ minimizes the weighted squared-error distortion for a set of complex variables representing one block of a signal under a resolution constraint for the entire block. MBPQ performs below the lower bound for classical bivariate quantization, both for Gaussian complex variables and for complex variables found from sinusoidal analysis of audio data. Still, it is of similar complexity as traditional polar quantizers. In the case of audio data, we found a performance gain of about 2.5 dB over the best performing conventional resolution-constrained polar quantization (an extension of unrestricted polar quantization).