Transmission of information via the non-linear Scroedinger equation: The random Gaussian input case

TL;DR

This paper analyzes how information can be transmitted through optical fibers modeled by the non-linear Schrödinger equation, showing that Gaussian inputs can outperform traditional WDM in low noise conditions.

Contribution

It demonstrates that under certain conditions, Gaussian input signals yield higher mutual information than WDM, leveraging the integrability of the non-linear Schrödinger equation.

Findings

Gaussian input has higher mutual information than WDM in low noise limit

Non-perturbative treatment of fiber non-linearities is essential at high intensities

Exact integrability of the Schrödinger equation enables new analysis methods

Abstract

The explosion of demand for ultra-high information transmission rates over the last decade has necessitated the usage of increasingly high light intensities for fiber optical transmissions. As a result, the fiber non-linearities need to be treated non-perturbatively. Similar analyses in the past have focused on the effects of non-linearities on existing transmission technologies, e.g. WDM. In this paper we take advantage of the fact that, under certain assumptions, light transmission through optical fibers can be described using the non-linear Schroedinger equation, which is exactly integrable. As a particular example, we show that in the low Gaussian noise limit, the Gaussian input distribution has a higher mutual information than the transmission using WDM over the same available bandwidth.