The $\log\log$ growth of channel capacity for nondispersive nonlinear optical fiber channel in intermediate power range. Extension of the model

TL;DR

This paper extends a nonlinear optical fiber channel model to include time dependence and detection procedures, revealing a logarithmic growth of channel capacity in the intermediate power range.

Contribution

It introduces a more realistic model with time-dependent initial signals and detection, and analyzes the channel capacity growth in the intermediate power range.

Findings

Channel capacity grows as log(log(P)) in the intermediate power range.

Derived analytical and numerical correlators of the output signal.

Identified optimal input signal distribution for maximum mutual information.

Abstract

In our previous paper [Phys. Rev. E 95, 062122 (2017)] we considered the optical channel modelled by the nonlinear Schr\"odinger equation with zero dispersion and additive Gaussian noise. We found per-sample channel capacity rof this model. In the present paper we extend per-sample model by introducing the initial signal dependence on time and the output signal detection procedure. The proposed model is a closer approximation of the realistic communication link than the per-sample model where there is no dependence of the initial signal on time. For the proposed model we found the correlators of the output signal both analytically and numerically. Using these correlators we built the conditional probability density function. Then we calculated an entropy of the output signal, a conditional entropy, and the mutual information. Maximizing the mutual information we found the optimal input signal distribution, channel capacity? and their dependence on the shape or the initial signal in the time domain for the intermediate power range.