Revisiting Multi-Step Nonlinearity Compensation with Machine Learning

For the efficient compensation of fiber nonlinearity, one of the guiding principles appears to be: fewer steps are better and more efficient. We challenge this assumption and show that carefully designed multi-step approaches can lead to better performance-complexity trade-offs than their few-step counterparts.Comment: 4 pages, 3 figures, This is a preprint of a paper submitted to the 2019 European Conference on Optical Communicatio

Predicting nonlinear dynamics of optical solitons in optical fiber via the SCPINN

The strongly-constrained physics-informed neural network (SCPINN) is proposed by adding the information of compound derivative embedded into the soft-constraint of physics-informed neural network(PINN). It is used to predict nonlinear dynamics and the formation process of bright and dark picosecond optical solitons, and femtosecond soliton molecule in the single-mode fiber, and reveal the variation of physical quantities including the energy, amplitude, spectrum and phase of pulses during the soliton transmission. The adaptive weight is introduced to accelerate the convergence of loss function in this new neural network. Compared with the PINN, the accuracy of SCPINN in predicting soliton dynamics is improved by 5-11 times. Therefore, the SCPINN is a forward-looking method to study the modeling and analysis of soliton dynamics in the fiber

Optical nonlinear impairment compensation based on Deep Neural Network (DNN) for coherent modulation systems

One and most important of the intrinsic challenges facing the optical fibers communication systems and main restriction to limited the system capacity is the fiber nonlinearity impairments. Classical Nonlinear Impairments Compensation (NLC) techniques are widely used and exist on the basis of the approximate Nonlinear Schrodinger Equation (NLSE) solution, their use and requires excessive signal resources, and high-level knowledge accuracy. In addition, their parameterizations can be numerically unstable. Algorithms of Artificial Intelligence (AI) are utilized to determine and resolve the deficiencies by learning from the receiving information itself. To the best of our knowledge, this novel approach is implemented. Therefore, this article proposes a system nonlinearity and single-step compensation algorithm according to a Deep Neural Network (DNN) as a new alternative framework for future optical communications. So, we proposed to use the DNN to compensation the nonlinearity impairments in optical communication systems. The suggested DNN is accessible to higher-order QAM modulations with achieving greater gain in nonlinear impairments compensation compare to classical NLC techniques based on Digital Back Propagation (DBP). Its performance is evaluated experimentally on coherent 65536-bit sequence length with 25 Gbaud single polarization 4-16-64 QAM with 50 and 120 Gb/s back-to-back measurements through using pre-distort symbols at the transmitter for showing Q factor development after 5000 km standard single-mode fiber transmission link. The DNN's weights are to train data with the intrachannel cross-phase modulation (XPM) and self-phase modulation (SPM) that used as input features

DOSnet as a Non-Black-Box PDE Solver: When Deep Learning Meets Operator Splitting

Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers utilize the representation power of DNNs to approximate the input-output relations in an automated manner. However, the lack of physics-in-the-loop often makes it difficult to construct a neural network solver that simultaneously achieves high accuracy, low computational burden, and interpretability. In this work, focusing on a class of evolutionary PDEs characterized by having decomposable operators, we show that the classical ``operator splitting'' numerical scheme of solving these equations can be exploited to design neural network architectures. This gives rise to a learning-based PDE solver, which we name Deep Operator-Splitting Network (DOSnet). Such non-black-box network design is constructed from the physical rules and operators governing the underlying dynamics contains learnable parameters, and is thus more flexible than the standard operator splitting scheme. Once trained, it enables the fast solution of the same type of PDEs. To validate the special structure inside DOSnet, we take the linear PDEs as the benchmark and give the mathematical explanation for the weight behavior. Furthermore, to demonstrate the advantages of our new AI-enhanced PDE solver, we train and validate it on several types of operator-decomposable differential equations. We also apply DOSnet to nonlinear Schr\"odinger equations (NLSE) which have important applications in the signal processing for modern optical fiber transmission systems, and experimental results show that our model has better accuracy and lower computational complexity than numerical schemes and the baseline DNNs

Voronoi Constellations for Coherent Fiber-Optic Communication Systems

The increasing demand for higher data rates is driving the adoption of high-spectral-efficiency (SE) transmission in communication systems. The well-known 1.53 dB gap between Shannon\u27s capacity and the mutual information (MI) of uniform quadrature amplitude modulation (QAM) formats indicates the importance of power efficiency, particularly in high-SE transmission scenarios, such as fiber-optic communication systems and wireless backhaul links. Shaping techniques are the only way to close this gap, by adapting the uniform input distribution to the capacity-achieving distribution. The two categories of shaping are probabilistic shaping (PS) and geometric shaping (GS). Various methods have been proposed for performing PS and GS, each with distinct implementation complexity and performance characteristics. In general, the complexity of these methods grows dramatically with the SE and number of dimensions.Among different methods, multidimensional Voronoi constellations (VCs) provide a good trade-off between high shaping gains and low-complexity encoding/decoding algorithms due to their nice geometric structures. However, VCs with high shaping gains are usually very large and the huge cardinality makes system analysis and design cumbersome, which motives this thesis.In this thesis, we develop a set of methods to make VCs applicable to communication systems with a low complexity. The encoding and decoding, labeling, and coded modulation schemes of VCs are investigated. Various system performance metrics including uncoded/coded bit error rate, MI, and generalized mutual information (GMI) are studied and compared with QAM formats for both the additive white Gaussian noise channel and nonlinear fiber channels. We show that the proposed methods preserve high shaping gains of VCs, enabling significant improvements on system performance for high-SE transmission in both the additive white Gaussian noise channel and nonlinear fiber channel. In addition, we propose general algorithms for estimating the MI and GMI, and approximating the log-likelihood ratios in soft-decision forward error correction codes for very large constellations

Constellation Shaping in Optical Communication Systems

Exploiting the full-dimensional capacity of coherent optical communication systems is needed to overcome the increasing bandwidth demands of the future Internet. To achieve capacity, both coding and shaping gains are required, and they are, in principle, independent. Therefore it makes sense to study shaping and how it can be achieved in various dimensions and how various shaping schemes affect the whole performance in real systems. This thesis investigates the performance of constellation shaping methods including geometric shaping (GS) and probabilistic shaping (PS) in coherent fiber-optic systems. To study GS, instead of considering machine learning approaches or optimization of irregular constellations in two dimensions, we have explored multidimensional lattice-based constellations. These constellations provide a regular structure with a fast and low-complexity encoding and decoding. In simulations, we show the possibility of transmitting and detecting constellation with a size of more than 10^{28} points which can be done without a look-up table to store the constellation points. Moreover, improved performance in terms of bit error rate, symbol error rate, and transmission reach are demonstrated over the linear additive white Gaussian noise as well as the nonlinear fiber channel compared to QAM formats.Furthermore, we investigate the performance of PS in two separate scenarios, i.e., transmitter impairments and transmission over hybrid systems with on-off keying channels. In both cases, we find that while PS-QAM outperforms the uniform QAM in the linear regime, uniform QAM can achieve better performance at the optimum power in the presence of transmitter or channel nonlinearities

Antialiased transmitter-side digital backpropagation

Digital backpropagation (DBP) is an electronic scheme for compensating nonlinear distortions in fiber transmission systems. Due to the nonlinearity-induced spectral broadening, the data must be oversampled to avoid aliasing, which increases the complexity and power consumption of the scheme. In this work, we show that aliasing can alternatively be prevented by distributed antialiasing filters, at a lower complexity. We proposed a new modified split-step Fourier method (SSFM) with easy-To-implement low-pass filters (LPFs) in the linear steps to avoid aliasing due to spectral broadening. Both the forward fiber propagation and a transmitter-side DBP are simulated using the modified SSFM. High-order modulation formats such as 256-Ary quadrature-Amplitude-modulation (256-QAM) and 1024-QAM transmissions at 28 Gbaud and 64 Gbaud over 1000 km fiber are considered, and our results show that the complexity of the DBP can be reduced by up to 50%. The optimal bandwidth of the LPFs is studied for both forward propagation and the DBP