Rates Achievable on a Fiber-Optical Split-Step Fourier Channel

TL;DR

This paper derives bounds on the capacity of a fiber-optical split-step Fourier channel, showing how capacity saturation depends on the number of segments and power, with implications for nonlinear fiber optics.

Contribution

It introduces new lower bounds on channel capacity, including a simple closed-form expression, and analyzes how capacity saturation scales with segment count.

Findings

Saturation point increases with the number of segments.

A simple closed-form lower bound is provided.

Capacity saturation grows unbounded as segments increase.

Abstract

A lower bound on the capacity of the split-step Fourier channel is derived. The channel under study is a concatenation of smaller segments, within which three operations are performed on the signal, namely, nonlinearity, linearity, and noise addition. Simulation results indicate that for a fixed number of segments, our lower bound saturates in the high-power regime and that the larger the number of segments is, the higher is the saturation point. We also obtain an alternative lower bound, which is less tight but has a simple closed-form expression. This bound allows us to conclude that the saturation point grows unbounded with the number of segments. Specifically, it grows as $c+(1/2)\log(K)$, where $K$ is the number of segments and $c$ is a constant. The connection between our channel model and the nonlinear Schr\"odinger equation is discussed.