Deep Learning of the Nonlinear Schr\"odinger Equation in Fiber-Optic Communications

TL;DR

This paper introduces a deep learning approach to efficiently invert the nonlinear Schr"odinger equation in fiber-optic communications, significantly reducing computational complexity compared to traditional methods while maintaining accuracy.

Contribution

It demonstrates that jointly optimizing filters with deep learning can drastically lower complexity in fiber-optic channel equalization.

Findings

Optimized 5-tap and 3-tap filters achieve near-linear equalization complexity.

Deep learning reduces the number of filter taps needed for accurate inversion.

Complexity is decreased to 2-6 times that of linear equalization.

Abstract

An important problem in fiber-optic communications is to invert the nonlinear Schr\"odinger equation in real time to reverse the deterministic effects of the channel. Interestingly, the popular split-step Fourier method (SSFM) leads to a computation graph that is reminiscent of a deep neural network. This observation allows one to leverage tools from machine learning to reduce complexity. In particular, the main disadvantage of the SSFM is that its complexity using M steps is at least M times larger than a linear equalizer. This is because the linear SSFM operator is a dense matrix. In previous work, truncation methods such as frequency sampling, wavelets, or least-squares have been used to obtain "cheaper" operators that can be implemented using filters. However, a large number of filter taps are typically required to limit truncation errors. For example, Ip and Kahn showed that for a 10 Gbaud signal and 2000 km optical link, a truncated SSFM with 25 steps would require 70-tap filters in each step and 100 times more operations than linear equalization. We find that, by jointly optimizing all filters with deep learning, the complexity can be reduced significantly for similar accuracy. Using optimized 5-tap and 3-tap filters in an alternating fashion, one requires only around 2-6 times the complexity of linear equalization, depending on the implementation.