Deep Learning of Geometric Constellation Shaping including Fiber Nonlinearities

A new geometric shaping method is proposed, leveraging unsupervised machine learning to optimize the constellation design. The learned constellation mitigates nonlinear effects with gains up to 0.13 bit/4D when trained with a simplified fiber channel model.Comment: 3 pages, 6 figures, submitted to ECOC 201

End-to-end Learning for GMI Optimized Geometric Constellation Shape

Autoencoder-based geometric shaping is proposed that includes optimizing bit mappings. Up to 0.2 bits/QAM symbol gain in GMI is achieved for a variety of data rates and in the presence of transceiver impairments. The gains can be harvested with standard binary FEC at no cost w.r.t. conventional BICM.Comment: submitted to ECOC 201

Machine learning-based EDFA Gain Model Generalizable to Multiple Physical Devices

We report a neural-network based erbium-doped fiber amplifier (EDFA) gain model built from experimental measurements. The model shows low gain-prediction error for both the same device used for training (MSE $\leq$ 0.04 dB$^2$) and different physical units of the same make (generalization MSE $\leq$ 0.06 dB$^2$)

Power Evolution Prediction and Optimization in a Multi-span System Based on Component-wise System Modeling

Cascades of a machine learning-based EDFA gain model trained on a single physical device and a fully differentiable stimulated Raman scattering fiber model are used to predict and optimize the power profile at the output of an experimental multi-span fully-loaded C-band optical communication system

Geometric Constellation Shaping for Fiber-Optic Channels via End-to-End Learning

End-to-end learning has become a popular method to optimize a constellation shape of a communication system. When the channel model is differentiable, end-to-end learning can be applied with conventional backpropagation algorithm for optimization of the shape. A variety of optimization algorithms have also been developed for end-to-end learning over a non-differentiable channel model. In this paper, we compare gradient-free optimization method based on the cubature Kalman filter, model-free optimization and backpropagation for end-to-end learning on a fiber-optic channel modeled by the split-step Fourier method. The results indicate that the gradient-free optimization algorithms provide a decent replacement to backpropagation in terms of performance at the expense of computational complexity. Furthermore, the quantization problem of finite bit resolution of the digital-to-analog and analog-to-digital converters is addressed and its impact on geometrically shaped constellations is analysed. Here, the results show that when optimizing a constellation with respect to mutual information, a minimum number of quantization levels is required to achieve shaping gain. For generalized mutual information, the gain is maintained throughout all of the considered quantization levels. Also, the results implied that the autoencoder can adapt the constellation size to the given channel conditions

End-to-end Learning of a Constellation Shape Robust to Channel Condition Uncertainties

Vendor interoperability is one of the desired future characteristics of optical networks. This means that the transmission system needs to support a variety of hardware with different components, leading to system uncertainties throughout the network. For example, uncertainties in signal-to-noise ratio and laser linewidth can negatively affect the quality of transmission within an optical network due to e.g. mis-parametrization of the transceiver signal processing algorithms. In this paper, we propose to geometrically optimize a constellation shape that is robust to uncertainties in the channel conditions by utilizing end-to-end learning. In the optimization step, the channel model includes additive noise and residual phase noise. In the testing step, the channel model consists of laser phase noise, additive noise and blind phase search as the carrier phase recovery algorithm. Two noise models are considered for the additive noise: white Gaussian noise and nonlinear interference noise model for fiber nonlinearities. The latter models the behavior of an optical fiber channel more accurately because it considers the nonlinear effects of the optical fiber. For this model, the uncertainty in the signal-to-noise ratio can be divided between amplifier noise figures and launch power variations. For both noise models, our results indicate that the learned constellations are more robust to uncertainties in channel conditions compared to a standard constellation scheme such as quadrature amplitude modulation and standard geometric constellation shaping techniques

Optimization of Raman amplifiers: a comparison between black-, grey- and white-box modeling

Designing and optimizing optical amplifiers to maximize system performance is becoming increasingly important as optical communication systems strive to increase throughput. Offline optimization of optical amplifiers relies on models ranging from white-box models deeply rooted in physics to black-box data-driven physics-agnostic models. Here, we compare the capabilities of white-, grey- and black-box models to achieve a target frequency-distance amplification in a bidirectional Raman amplifier. We show that any of the studied methods can achieve down to 1 dB of frequency-distance flatness over the C-band in a 100-km span. Then, we discuss the models' applicability, advantages, and drawbacks based on the target application scenario, in particular in terms of optimization speed and access to training data