We propose a new machine-learning approach for fiber-optic communication
systems whose signal propagation is governed by the nonlinear Schr\"odinger
equation (NLSE). Our main observation is that the popular split-step method
(SSM) for numerically solving the NLSE has essentially the same functional form
as a deep multi-layer neural network; in both cases, one alternates linear
steps and pointwise nonlinearities. We exploit this connection by
parameterizing the SSM and viewing the linear steps as general linear
functions, similar to the weight matrices in a neural network. The resulting
physics-based machine-learning model has several advantages over "black-box"
function approximators. For example, it allows us to examine and interpret the
learned solutions in order to understand why they perform well. As an
application, low-complexity nonlinear equalization is considered, where the
task is to efficiently invert the NLSE. This is commonly referred to as digital
backpropagation (DBP). Rather than employing neural networks, the proposed
algorithm, dubbed learned DBP (LDBP), uses the physics-based model with
trainable filters in each step and its complexity is reduced by progressively
pruning filter taps during gradient descent. Our main finding is that the
filters can be pruned to remarkably short lengths-as few as 3 taps/step-without
sacrificing performance. As a result, the complexity can be reduced by orders
of magnitude in comparison to prior work. By inspecting the filter responses,
an additional theoretical justification for the learned parameter
configurations is provided. Our work illustrates that combining data-driven
optimization with existing domain knowledge can generate new insights into old
communications problems.

我们提出一种基于物理的机器学习模型来处理光纤通信中的非线性斯格明子方程，这个模型可以用于数字反传播（DBP），可以有效地逆转非线性方程，而且使用可训练的过滤器可以极大地降低其复杂性。

基于物理的深度学习在光纤通信系统中的应用

Physics-Based Deep Learning for Fiber-Optic Communication Systems

We propose a low-complexity sub-banded DSP architecture for digital
backpropagation where the walk-off effect is compensated using simple delay
elements. For a simulated 96-Gbaud signal and 2500 km optical link, our method
achieves a 2.8 dB SNR improvement over linear equalization.

提出了一种低复杂度的分频数字信号处理架构，用简单的延迟元件来补偿行走效应，针对 96G 波特率信号和 2500 公里光传输距离，采用该方法相比于线性均衡可实现 2.8 分贝的信噪比提高。

基于子带处理和深度学习的宽带时域数字反传播

Wideband Time-Domain Digital Backpropagation via Subband Processing and  Deep Learning

A neural-network-based approach is presented to efficiently implement digital
backpropagation (DBP). For a 32x100 km fiber-optic link, the resulting
"learned" DBP significantly reduces the complexity compared to conventional DBP
implementations.

该研究提出了一种基于神经网络的方法来实现数字反向传播，针对 32x100 公里的光纤链路，所得到的 “学习” 数字反向传播相对于传统实现方法大大降低了复杂性。