The Golden Quantizer in Complex Dimension Two

In this letter, we focus on numerical solutions to the problem of quantizing circularly symmetric complex Gaussian random variables from open symmetrized bidiscs in
$\mathbb {C}^{2}$
. To that end, we leverage techniques from the complex variable analysis, especially the symmetrization map. Four novel non-uniform quantizers,
i.e.
Bd1/2-GQ and EC Bd1/2-GQ, are proposed to reduce the mean square error distortion. Compared to the existing high-rate golden quantizer, entropy-coded high-rate golden quantizer, and (non)-uniform polar/rectangular quantizers, Bd1-GQ and EC Bd1-GQ achieve lower mean square error distortion. Moreover, the EC Bd2-GQ reaches better performance than the polar- and rectangular- quantizers.