The Golden Quantizer: The Complex Gaussian Random Variable Case

TL;DR

This paper introduces a novel quantizer design for complex Gaussian variables using spiral packing principles, achieving lower distortion and comparable performance to trained vector quantizers with a structured, flexible approach.

Contribution

It presents a new quantizer based on spiral packing for complex Gaussian variables, offering lower distortion and a natural ordering, unlike traditional methods.

Findings

Lower mean-square error distortion compared to existing quantizers

Performance close to trained vector quantizers

Flexible design allowing any number of centroids

Abstract

The problem of quantizing a circularly-symmetric complex Gaussian random variable is considered. For this purpose, we design two non-uniform quantizers, a high-rate-, and a Lloyd-Max-, quantizer that are both based on the (golden angle) spiral-phyllotaxis packing principle. We find that the proposed schemes have lower mean-square error distortion compared to (non)-uniform polar/rectangular-quantizers, and near-identical to the best performing trained vector quantizers. The proposed quantizer scheme offers a structured design, a simple natural index ordering, and allow for any number of centroids.