Achievable Rates of Multidimensional Rotationally Invariant Distributions

TL;DR

This paper derives a simple expression for the maximum mutual information of multidimensional rotationally invariant distributions in Gaussian noise, demonstrating that 4-dimensional multisphere distributions outperform 2-dimensional ones in fiber-optic channels at high SNR.

Contribution

It provides a new analytical expression for mutual information of multidimensional rotationally invariant distributions, highlighting the advantages of 4D multisphere distributions in fiber-optic communications.

Findings

4D multisphere distributions achieve higher rates than 2D ones at high SNR.

4D distributions are invariant under nonlinear fiber transmission.

Derived a simple mutual information expression for these distributions.

Abstract

The maximum achievable rate or mutual informa- tion of multidimensional rotationally invariant distributions in the presence of additive white Gaussian noise is analyzed. A simple expression for the special case of multisphere distributions is derived. Such distributions consist of points in a multidimensional Euclidean space that are uniformly distributed over several multidimensional concentric hyperspheres. For the 2-dimensional case, such distributions have been previously considered in order to reduce the computational complexity of finding a bound on the channel capacity of fiber-optic channels. These distributions take advantage of the statistical rotational invariance of the noise and nonlinear distortions in fiber-optic channels. Using the derived mutual information expression, 2- and 4-dimensional multisphere distributions are compared for fiber-optic dual-polarization channels dominated by linear noise. At high signal-to-noise ratios, 4-dimensional multisphere distributions offer higher achievable rates than 2-dimensional ones transmitted on each of the two polarizations of the optical carrier. Such 4-dimensional multisphere distributions are also shown to be statistically invariant under 4-dimensional nonlinear transmission in fibers.