Path-integral approach to mutual information calculation for nonlinear communication channel with small second dispersion at large signal-to-noise power ratio

TL;DR

This paper develops a path-integral method to compute mutual information in nonlinear optical fiber channels modeled by the nonlinear Schrödinger equation, considering small second dispersion and high SNR, with explicit formulas for different input signals.

Contribution

It introduces a perturbative path-integral approach to calculate mutual information in nonlinear fiber channels with small second dispersion, including explicit expressions for various input distributions.

Findings

Derived mutual information expressions up to next-to-leading order in dispersion.

Accounted for specific output filtering effects on mutual information.

Provided explicit formulas for Gaussian input signals with bandwidth limitations.

Abstract

We consider the information fiber optical channel modeled by the nonlinear Schrodinger equation with additive Gaussian noise. Using path-integral approach and perturbation theory for the small dimensionless parameter of the second dispersion, we calculate the conditional probability density functional in the leading and next-to-leading order in the dimensionless second dispersion parameter associated with the input signal bandwidth. Taking into account specific filtering of the output signal by the output signal receiver, we calculate the mutual information in the leading and next-to-leading order in the dispersion parameter and in the leading order in the parameter signal-to-noise ratio (SNR). Further, we find the explicit expression for the mutual information in case of the modified Gaussian input signal distribution taking into account the limited frequency bandwidth of the input signal.