Gaussian Channel Simulation with Rotated Dithered Quantization
Szymon Kobus, Lucas Theis, Deniz Gündüz
TL;DR
This work presents rotated dithered quantization as a computationally efficient framework for simulating multivariate Gaussian channels. By combining subtractive dithering with random rotations and lattice quantization, the method achieves rotationally invariant error distributions and matches Gaussian noise through careful moment alignment, yielding an $O(n^{-1})$ decay in KL-divergence to the true Gaussian channel. Excess information overhead is shown to shrink significantly with dimension and lattice choice, with reductions up to six-fold per dimension using high-dimensional lattices like the Leech lattice. The approach offers practical benefits for end-to-end lossy compression, federated learning, and privacy-preserving communication due to its scalability and low complexity.
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 $O(n^{-1})$.