Deep Neural Network-aided Soft-Demapping in Optical Coherent Systems: Regression versus Classification

We examine here what type of predictive modelling, classification, or regression, using neural networks (NN), fits better the task of soft-demapping based post-processing in coherent optical communications, where the transmission channel is nonlinear and dispersive. For the first time, we present possible drawbacks in using each type of predictive task in a machine learning context, considering the nonlinear coherent optical channel equalization/soft-demapping problem. We study two types of equalizers based on the feed-forward and recurrent NN, for several transmission scenarios, in linear and nonlinear regimes of the optical channel. We point out that even though from the information theory perspective the cross-entropy loss (classification) is the most suitable option for our problem, the NN models based on the cross-entropy loss function can severely suffer from learning problems. The latter translates into the fact that regression-based learning is typically superior in terms of delivering higher Q-factor and achievable information rates. In short, we show by empirical evidence that loss functions based on cross-entropy (or mutual information) may not be necessarily the most suitable option for training communication systems in practical scenarios when overfitting- and vanishing gradients-related problems come into play

Statistics of a noise-driven Manakov soliton

We investigate the statistics of a vector Manakov soliton in the presence of additive Gaussian white noise. The adiabatic perturbation theory for Manakov soliton yields a stochastic Langevin system which we analyze via the corresponding Fokker-Planck equation for the probability density function (PDF) for the soliton parameters. We obtain marginal PDFs for the soliton frequency and amplitude as well as soliton amplitude and polarization angle. We also derive formulae for the variances of all soliton parameters and analyze their dependence on the initial values of polarization angle and phase.Comment: Submitted to J.Phys.A: Mathematical and Genera

Knowledge Distillation Applied to Optical Channel Equalization: Solving the Parallelization Problem of Recurrent Connection

To circumvent the non-parallelizability of recurrent neural network-based equalizers, we propose knowledge distillation to recast the RNN into a parallelizable feedforward structure. The latter shows 38\% latency decrease, while impacting the Q-factor by only 0.5dB.Comment: Paper Accepted for Oral presentation - OFC 2023 (Optical Fiber Communication Conference

Deep Neural Network-aided Soft-Demapping in Coherent Optical Systems: Regression versus Classification

We examine here what type of predictive modelling, classification, or regression, using neural networks (NN), fits better the task of soft-demapping based post-processing in coherent optical communications, where the transmission channel is nonlinear and dispersive. For the first time, we present possible drawbacks in using each type of predictive task in a machine learning context, considering the nonlinear coherent optical channel equalization/soft-demapping problem. We study two types of equalizers based on the feed-forward and recurrent NNs, for several transmission scenarios, in linear and nonlinear regimes of the optical channel. We point out that even though from the information theory perspective the cross-entropy loss (classification) is the most suitable option for our problem, the NN models based on the cross-entropy loss function can severely suffer from learning problems. The latter translates into the fact that regression-based learning is typically superior in terms of delivering higher Q-factor and achievable information rates. In short, we show by empirical evidence that loss functions based on cross-entropy may not be necessarily the most suitable option for training communication systems in practical scenarios when overfitting- and vanishing gradients-related problems come into play

Polarization-multiplexed nonlinear inverse synthesis with standard and reduced-complexity NFT processing

In this work, we study the performance of polarization division multiplexing nonlinear inverse synthesis transmission schemes for fiber-optic communications, expected to have reduced nonlinearity impact. Our technique exploits the integrability of the Manakov equation—the master model for dual-polarization signal propagation in a single mode fiber—and employs nonlinear Fourier transform (NFT) based signal processing. First, we generalize some algorithms for the NFT computation to the two- and multicomponent case. Then, we demonstrate that modulating information on both polarizations doubles the channel information rate with a negligible performance degradation. Moreover, we introduce a novel dual-polarization transmission scheme with reduced complexity which separately processes each polarization component and can also provide a performance improvement in some practical scenarios

Attention-aided partial bidirectional RNN-based nonlinear equalizer in coherent optical systems

We leverage the attention mechanism to investigate and comprehend the contribution of each input symbol of the input sequence and their hidden representations for predicting the received symbol in the bidirectional recurrent neural network (BRNN)-based nonlinear equalizer. In this paper, we propose an attention-aided novel design of a partial BRNN-based nonlinear equalizer, and evaluate with both LSTM and GRU units in a single-channel DP-64QAM 30Gbaud coherent optical communication systems of 20 × 50 km standard single-mode fiber (SSMF) spans. Our approach maintains the Q-factor performance of the baseline equalizer with a significant complexity reduction of ∼56.16% in the number of real multiplications required to equalize per symbol (RMpS). In comparison of the performance under similar complexity, our approach outperforms the baseline by ∼0.2dB to ∼0.25dB at the optimal transmit power, and ∼0.3dB to ∼0.45dB towards the more nonlinear region

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder

Phase computation for the finite-genus solutions to the focusing nonlinear Schrödinger equation using convolutional neural networks

We develop a method for retrieving a set of parameters of a quasi-periodic finite-genus (finite-gap) solution to the focusing nonlinear Schrödinger (NLS) equation, given the solution evaluated on a finite spatial interval for a fixed time. These parameters (named “phases”) enter the jump matrices in the Riemann-Hilbert (RH) problem representation of finite-genus solutions. First, we detail the existing theory for retrieving the phases for periodic finite-genus solutions. Then, we introduce our method applicable to the quasi-periodic solutions. The method is based on utilizing convolutional neural networks optimized by means of the Bayesian optimization technique to identify the best set of network hyperparameters. To train the neural network, we use the discrete datasets obtained in an inverse manner: for a fixed main spectrum (the endpoints of arcs constituting the contour for the associated RH problem) and a random set of modal phases, we generate the corresponding discretized profile in space via the solution of the RH problem, and these resulting pairs – the phase set and the corresponding discretized solution in a finite interval of space domain – are then employed in training. The method’s functionality is then verified on an independent dataset, demonstrating our method’s satisfactory performance and generalization ability