Optimal input signal distribution and per-sample mutual information for nondispersive nonlinear optical fiber channel at large SNR

TL;DR

This paper derives the optimal input signal distribution for a nondispersive nonlinear optical fiber channel at high SNR, enhancing capacity estimates and demonstrating superior mutual information compared to Gaussian inputs.

Contribution

First to find the optimal input distribution for this channel using Feynman path-integral, improving capacity bounds and analyzing different input distributions.

Findings

Optimal input distribution maximizes per-sample mutual information.

Optimal distribution outperforms Gaussian and half-Gaussian inputs.

Explicit calculations of entropy and mutual information for various inputs.

Abstract

We consider a model nondispersive nonlinear optical fiber channel with additive white Gaussian noise at large $\mathrm{SNR}$ (signal-to-noise ratio) in the intermediate power region. Using Feynman path-integral technique we for the first time find the optimal input signal distribution maximizing the channel's per-sample mutual information. The finding of the optimal input signal distribution allows us to improve previously known estimates for the channel capacity. The output signal entropy, conditional entropy, and per-sample mutual information are calculated for Gaussian, half-Gaussian and modified Gaussian input signal distributions. We explicitly show that in the intermediate power regime the per-sample mutual information for the optimal input signal distribution is greater than the per-sample mutual information for the Gaussian and half-Gaussian input signal distributions.