End-to-End Optimization of Coherent Optical Communications Over the Split-Step Fourier Method Guided by the Nonlinear Fourier Transform Theory

Optimizing modulation and detection strategies for a given channel is critical to maximizing the throughput of a communication system. Such an optimization can be easily carried out analytically for channels that admit closed-form analytical models. However, this task becomes extremely challenging for nonlinear dispersive channels such as the optical fiber. End-to-end optimization through autoencoders (AEs) can be applied to define symbol-to-waveform (modulation) and waveform-to-symbol (detection) mappings, but so far it has been mainly shown for systems relying on approximate channel models. Here, for the first time, we propose an AE scheme applied to the full optical channel described by the nonlinear Schrödinger equation (NLSE). Transmitter and receiver are jointly optimized through the split-step Fourier method (SSFM) which accurately models an optical fiber. In this first numerical analysis, the detection is performed by a neural network (NN), whereas the symbol-to-waveform mapping is aided by the nonlinear Fourier transform (NFT) theory in order to simplify and guide the optimization on the modulation side. This proof-of-concept AE scheme is thus benchmarked against a manually-optimized NFT-based system and a three-fold increase in achievable distance (from 2000 to 6640 km) is demonstrated.

[1]  M. Ablowitz,et al.  Integrable Nonlinear Schrodinger Systems and their Soliton Dynamics , 2004 .

[2]  Francesco Da Ros,et al.  End-to-End Optimized Nonlinear Fourier Transform-Based Coherent Communications , 2020, 2020 Conference on Lasers and Electro-Optics (CLEO).

[3]  Francesco Da Ros,et al.  Dual polarization nonlinear Fourier transform-based optical communication system , 2018, ArXiv.

[4]  Mansoor I. Yousefi.  Information Transmission using the Nonlinear Fourier Transform , 2013 .

[5]  Polina Bayvel,et al.  End-to-End Deep Learning of Optical Fiber Communications , 2018, Journal of Lightwave Technology.

[6]  Leif K. Oxenløwe,et al.  Constellation Shaping for WDM Systems Using 256QAM/1024QAM With Probabilistic Optimization , 2016, Journal of Lightwave Technology.

[7]  Henk Wymeersch,et al.  Achievable Information Rates for Nonlinear Fiber Communication via End-to-end Autoencoder Learning , 2018, 2018 European Conference on Optical Communication (ECOC).

[8]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

[9]  Jakob Hoydis,et al.  An Introduction to Deep Learning for the Physical Layer , 2017, IEEE Transactions on Cognitive Communications and Networking.

[10]  A. Carena,et al.  Suppression of spurious tones induced by the split-step method in fiber systems simulation , 2000, IEEE Photonics Technology Letters.

[11]  Yuji Kodama,et al.  Solitons in optical communications , 1995 .

[12]  Francesco Da Ros,et al.  Dual-Polarization NFDM Transmission With Continuous and Discrete Spectral Modulation , 2019, Journal of Lightwave Technology.

[13]  Georg Böcherer,et al.  Experimental Comparison of Probabilistic Shaping Methods for Unrepeated Fiber Transmission , 2017, Journal of Lightwave Technology.

[14]  Patrick Schulte,et al.  Rate Adaptation and Reach Increase by Probabilistically Shaped 64-QAM: An Experimental Demonstration , 2016, Journal of Lightwave Technology.

[15]  Francesco Da Ros,et al.  Experimental Demonstration of Nonlinear Frequency Division Multiplexing Transmission With Neural Network Receiver , 2020, Journal of Lightwave Technology.

[16]  W. Marsden.  I and J , 2012 .

[17]  Mansoor I. Yousefi,et al.  Nonlinear Frequency Division Multiplexed Transmissions Based on NFT , 2015, IEEE Photonics Technology Letters.

[18]  Sepp Hochreiter,et al.  Self-Normalizing Neural Networks , 2017, NIPS.

[19]  V. Aref,et al.  Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit , 2017, Nature Photonics.

[20]  Polina Bayvel,et al.  End-to-End Optimized Transmission over Dispersive Intensity-Modulated Channels Using Bidirectional Recurrent Neural Networks , 2019, Optics express.

[21]  Barak A. Pearlmutter,et al.  Automatic differentiation in machine learning: a survey , 2015, J. Mach. Learn. Res..

[22]  Benjamin J. Puttnam,et al.  Geometric Constellation Shaping for Fiber Optic Communication Systems via End-to-end Learning , 2018, ArXiv.

[23]  Yoshua Bengio,et al.  Understanding the difficulty of training deep feedforward neural networks , 2010, AISTATS.

[24]  Chao Lu,et al.  An Optical Communication's Perspective on Machine Learning and Its Applications , 2019, Journal of Lightwave Technology.

[25]  Sander Wahls,et al.  Generation of Time-Limited Signals in the Nonlinear Fourier Domain via b-Modulation , 2017, 2017 European Conference on Optical Communication (ECOC).

[26]  Tianqi Chen,et al.  Training Deep Nets with Sublinear Memory Cost , 2016, ArXiv.

[27]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[28]  Timothy Dozat,et al.  Incorporating Nesterov Momentum into Adam , 2016 .

[29]  V. Matveev,et al.  Darboux Transformations and Solitons , 1992 .

[30]  Frank R. Kschischang,et al.  Information Transmission Using the Nonlinear Fourier Transform, Part II: Numerical Methods , 2012, IEEE Transactions on Information Theory.

[31]  Hao Li,et al.  Visualizing the Loss Landscape of Neural Nets , 2017, NeurIPS.

[32]  Alex Alvarado,et al.  Regular perturbation on the group-velocity dispersion parameter for nonlinear fibre-optical communications , 2020, Nature Communications.

[33]  Francesco Da Ros,et al.  Dual-Polarization NFDM Transmission Using Distributed Raman Amplification and NFT-Domain Equalization , 2018, IEEE Photonics Technology Letters.

[34]  Sergei K. Turitsyn,et al.  Nonlinear Fourier Transform for Optical Data Processing and Transmission: Advances and Perspectives , 2017, 2018 European Conference on Optical Communication (ECOC).

[35]  Metodi P. Yankov,et al.  Time-Domain Neural Network Receiver for Nonlinear Frequency Division Multiplexed Systems , 2018, IEEE Photonics Technology Letters.

[36]  Hermann A. Haus,et al.  Solitons in optical communications , 1996 .

[37]  Marco Ruffini,et al.  An Overview on Application of Machine Learning Techniques in Optical Networks , 2018, IEEE Communications Surveys & Tutorials.

[38]  Frank R. Kschischang,et al.  Information Transmission Using the Nonlinear Fourier Transform, Part I: Mathematical Tools , 2012, IEEE Transactions on Information Theory.

[39]  Tobias A. Eriksson,et al.  Deep Learning of Geometric Constellation Shaping Including Fiber Nonlinearities , 2018, 2018 European Conference on Optical Communication (ECOC).