Universal Gaussian Quantization with Side Information using Polar Lattices

TL;DR

This paper introduces a universal, practical Gaussian quantization scheme with side information using Polar lattices, achieving rate optimality and sub-exponential convergence for all unknown noise variances.

Contribution

It proposes a universally rate optimal quantization scheme with Polar lattices that works for all noise variances and includes a finite blocklength analysis.

Findings

Achieves sub-exponential convergence for distortion

Achieves exponential convergence for rate

Complexity is $O(N^2 ext{log}^2 N)$ for fixed rate

Abstract

We consider universal quantization with side information for Gaussian observations, where the side information is a noisy version of the sender's observation with noise variance unknown to the sender. In this paper, we propose a universally rate optimal and practical quantization scheme for all values of unknown noise variance. Our scheme uses Polar lattices from prior work, and proceeds based on a structural decomposition of the underlying auxiliaries so that even when recovery fails in a round, the parties agree on a common "reference point" that is closer than the previous one. We also present the finite blocklength analysis showing an sub-exponential convergence for distortion and exponential convergence for rate. The overall complexity of our scheme is $O(N^2\log^2 N)$ for any target distortion and fixed rate larger than the rate-distortion bound.