Vahid Aref

Vladislav Neskorniuk, Andrea Carnio, Domenico Marsella et al.

Autoencoder-based deep learning is applied to jointly optimize geometric and probabilistic constellation shaping for optical coherent communication. The optimized constellation shaping outperforms the 256 QAM Maxwell-Boltzmann probabilistic distribution with extra 0.05 bits/4D-symbol mutual information for 64 GBd transmission over 170 km SMF link.

Vahid Aref

Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete spectral amplitudes), we use the Darboux Transform. We explain how to the norming factors must be set in order to have the desired discrete spectrum. To derive these norming factors, we study the evolution of nonlinear spectrum by adding a new eigenvalue and its spectral amplitude. We further simplify the Darboux transform algorithm. We propose a novel algorithm (to the best of our knowledge) to numerically compute the nonlinear Fourier Transform (NFT) of a given pulse. The NFT algorithm, called forward-backward method, is based on splitting the signal into two parts and computing the nonlinear spectrum of each part from boundary ($\pm\infty$) inward. The nonlinear spectrum (discrete and continuous) derived from efficiently combining both parts has a promising numerical precision. This method can use any of one-step discretization NFT methods, e.g. Crank-Nicolson, as an NFT kernel for the forward or backward part. Using trapezoid rule of integral, we use an NFT kernel (we called here Trapezoid discretization NFT) in forward-backward method which results discrete spectral amplitudes with a very good numerical precision. These algorithms, forward-backward method and Darboux transform, are used in [1],[2] for design and detection of phase-modulated 2-soliton pulses, and more recently, in [3] for design and detection of more complex pulses with 7 eigenvalues and modulation of spectral phase. For those soliton pulses, the discrete spectral amplitudes (in particular, phase) of both eigenvalues are quite precisely estimated using the forward-backward method.

Vinod Bajaj, Mathieu Chagnon, Sander Wahls et al.

We present a simple, efficient "direct learning" approach to train Volterra series-based digital pre-distortion filters using neural networks. We show its superior performance over conventional training methods using a 64-QAM 64-GBaud simulated transmitter with varying transmitter nonlinearity and noisy conditions.

Vahid Aref, Mathieu Chagnon

We present a novel autoencoder-based learning of joint geometric and probabilistic constellation shaping for coded-modulation systems. It can maximize either the mutual information (for symbol-metric decoding) or the generalized mutual information (for bit-metric decoding).

Vladislav Neskorniuk, Andrea Carnio, Vinod Bajaj et al.

We present a novel end-to-end autoencoder-based learning for coherent optical communications using a "parallelizable" perturbative channel model. We jointly optimized constellation shaping and nonlinear pre-emphasis achieving mutual information gain of 0.18 bits/sym./pol. simulating 64 GBd dual-polarization single-channel transmission over 30x80 km G.652 SMF link with EDFAs.

Boris Karanov, Mathieu Chagnon, Vahid Aref et al.

We investigate methods for experimental performance enhancement of auto-encoders based on a recurrent neural network (RNN) for communication over dispersive nonlinear channels. In particular, our focus is on the recently proposed sliding window bidirectional RNN (SBRNN) optical fiber autoencoder. We show that adjusting the processing window in the sequence estimation algorithm at the receiver improves the reach of simple systems trained on a channel model and applied "as is" to the transmission link. Moreover, the collected experimental data was used to optimize the receiver neural network parameters, allowing to transmit 42 Gb/s with bit-error rate (BER) below the 6.7% hard-decision forward error correction threshold at distances up to 70km as well as 84 Gb/s at 20 km. The investigation of digital signal processing (DSP) optimized on experimental data is extended to pulse amplitude modulation with receivers performing sliding window sequence estimation using a feed-forward or a recurrent neural network as well as classical nonlinear Volterra equalization. Our results show that, for fixed algorithm memory, the DSP based on deep learning achieves an improved BER performance, allowing to increase the reach of the system.

Boris Karanov, Mathieu Chagnon, Vahid Aref et al.

We investigate end-to-end optimized optical transmission systems based on feedforward or bidirectional recurrent neural networks (BRNN) and deep learning. In particular, we report the first experimental demonstration of a BRNN auto-encoder, highlighting the performance improvement achieved with recurrent processing for communication over dispersive nonlinear channels.

Boris Karanov, Mathieu Chagnon, Vahid Aref et al.

We perform an experimental end-to-end transceiver optimization via deep learning using a generative adversarial network to approximate the test-bed channel. Previously, optimization was only possible through a prior assumption of an explicit simplified channel model.

Mohamad Dia, Vahid Aref, Laurent Schmalen

In this work, we formulate the fixed-length distribution matching as a Bayesian inference problem. Our proposed solution is inspired from the compressed sensing paradigm and the sparse superposition (SS) codes. First, we introduce sparsity in the binary source via position modulation (PM). We then present a simple and exact matcher based on Gaussian signal quantization. At the receiver, the dematcher exploits the sparsity in the source and performs low-complexity dematching based on generalized approximate message-passing (GAMP). We show that GAMP dematcher and spatial coupling lead to asymptotically optimal performance, in the sense that the rate tends to the entropy of the target distribution with vanishing reconstruction error in a proper limit. Furthermore, we assess the performance of the dematcher on practical Hadamard-based operators. A remarkable feature of our proposed solution is the possibility to: i) perform matching at the symbol level (nonbinary); ii) perform joint channel coding and matching.