Gaussian Channel Simulation with Rotated Dithered Quantization

TL;DR

This paper presents a new method for Gaussian channel simulation using rotated dithered quantization, significantly reducing excess information bounds and KL divergence with higher dimensions.

Contribution

It introduces a novel multi-channel simulation technique with dithered quantization that outperforms previous one-dimensional methods in efficiency and accuracy.

Findings

Reduces excess information bound by half in multi-channel simulation.

Achieves up to six times reduction in upper bound with higher-dimensional lattices.

KL divergence decreases at a rate of O(n^{-1}) with increasing dimensions.

Abstract

Channel simulation involves generating a sample $Y$ from the conditional distribution $P_{Y|X}$, where $X$ is a remote realization sampled from $P_X$. This paper introduces a novel approach to approximate Gaussian channel simulation using dithered quantization. Our method concurrently simulates $n$ channels, reducing the upper bound on the excess information by half compared to one-dimensional methods. When used with higher-dimensional lattices, our approach achieves up to six times reduction on the upper bound. Furthermore, we demonstrate that the KL divergence between the distributions of the simulated and Gaussian channels decreases with the number of dimensions at a rate of $O(n^{-1})$.