Deep Learning of the Nonlinear Schrödinger Equation in Fiber-Optic Communications
Paper in proceeding, 2018

An important problem in fiber-optic communications is to invert the nonlinear Schrödinger 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.


Christian Häger

Duke University

Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks

Henry D. Pfister

Duke University

IEEE International Symposium on Information Theory - Proceedings

21578095 (ISSN)

Vol. 2018-June 1590-1594 8437734
978-153864780-6 (ISBN)

2018 IEEE International Symposium on Information Theory, ISIT 2018
Vail, USA,

Coding for terabit-per-second fiber-optical communications (TERA)

European Commission (EC) (EC/H2020/749798), 2017-01-01 -- 2019-12-31.

Subject Categories

Computational Mathematics

Control Engineering

Signal Processing



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