Convolutional long short-term memory neural network equalizer for nonlinear Fourier transform-based optical transmission systems

Kotlyar, Oleksandr; Kamalian-Kopae, Morteza; Pankratova, Maryna; Vasylchenkova, Anastasiia; Prilepsky, Jaroslaw E.; Turitsyn, Sergei K.

doi:10.1364/oe.419314

Cited by 36 publications

(13 citation statements)

References 36 publications

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“…1. We chose this architecture because it delivers the best performance for impairments mitigation in long-haul coherent optical systems when compared to several alternative NN structures, provided that the computational complexity is not restricted [11,32].…”

Section: B Application Of Transfer Learning To Nonlinearity Mitigationmentioning

confidence: 99%

Transfer Learning for Neural Networks-Based Equalizers in Coherent Optical Systems

Freire

Abode

Prilepsky

et al. 2021

J. Lightwave Technol.

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In this work, we address the question of the adaptability of artificial neural networks (NNs) used for impairments mitigation in optical transmission systems. We demonstrate that by using well-developed techniques based on the concept of transfer learning, we can efficaciously retrain NN-based equalizers to adapt to the changes in the transmission system, using just a fraction (down to 1%) of the initial training data or epochs. We evaluate the capability of transfer learning to adapt the NN to changes in the launch power, modulation format, symbol rate, or even fiber plants (different fiber types and lengths). The numerical examples utilize the recently introduced NN equalizer consisting of a convolutional layer coupled with bi-directional long-short term memory (biLSTM) recurrent NN element. Our analysis focuses on long-haul coherent optical transmission systems for two types of fibers: the standard single-mode fiber (SSMF) and the TrueWave Classic (TWC) fiber. We underline the specific peculiarities that occur when transferring the learning in coherent optical communication systems and draw the limits for the transfer learning efficiency. Our results demonstrate the effectiveness of transfer learning for the fast adaptation of NN architectures to different transmission regimes and scenarios, paving the way for engineering flexible and universal solutions for nonlinearity mitigation.

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Section: B Application Of Transfer Learning To Nonlinearity Mitigationmentioning

confidence: 99%

Transfer Learning for Neural Networks-Based Equalizers in Coherent Optical Systems

Freire

Abode

Prilepsky

et al. 2021

J. Lightwave Technol.

Self Cite

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“…As was noted before, the NNs have already demonstrated their decent potential in optical signal processing and channel equalization tasks, 42 and, in particular, in the NFT-based systems. [35][36][37][38][39]…”

Section: Benefits Of Using Neural Network In Nonlinear Signal Processingmentioning

confidence: 99%

“…[35][36][37] For the systems based on the continuous NFT spectrum, the NNs were used at the post-processing equalization stage . 38,39 There has been just one very recent work where a simple NN was used for the processing of continuous nonlinear spectrum: 40 actually, the Matlab routine for the recognition of the hand-written digit was adapted there for the classification of constellation points, which brings about essential limitations for such an approach usage. In our work, we propose to implement a more advanced regression approach: we compute the continuous NFT spectrum using a special NN, and also restore the initial optical field (i.e.…”

Section: Introductionmentioning

confidence: 99%

Computing continuous nonlinear Fourier spectrum of optical signal with artificial neural networks

Sedov

Prylepskiy

Chekhovskoy

et al. 2021

Applications of Machine Learning 2021

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In this work, we demonstrate that the high-accuracy computation of the continuous nonlinear spectrum can be performed by using artificial neural networks. We propose the artificial neural network (NN) architecture that can efficiently perform the nonlinear Fourier (NF) optical signal processing. The NN consists of sequential convolution layers and fully connected output layers. This NN predicts only one component of the continuous NF spectrum, such that two identical NNs have to be used to predict the real and imaginary parts of the reflection coefficient. To train the NN, we precomputed 94035 optical signals. 9403 signals were used for validation and excluded from training. The final value of the relative error for the entire validation dataset was less than 0.3%. Our findings highlight the fundamental possibility of using the NNs to analyze and process complex optical signals when the conventional algorithms can fail to deliver an acceptable result.

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“…A regression neural network receiver in TD for QAM of spectral amplitude, which has the robustness to laser phase noise, was also proposed [18]. As an improved approach, a bidirectional long short-term memory gated recurrent neural network equalizer has been proposed and shown to outperform a feed-forward ANN equalizer at a spectral amplitude of 64-QAM of spectral amplitude [19]. However, these ANN-based receivers have been demonstrated only with a small static CFO ≤ 100 MHz generated by simulation or using acousto-optic modulator in experiment.…”

Section: Introductionmentioning

confidence: 99%

Combining IST-Based CFO Compensation and Neural Network-Based Demodulation for Eigenvalue-Modulated Signal

Mishina

Maeda

Hisano

et al. 2021

J. Lightwave Technol.

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Eigenvalue-based communication technologies using inverse scattering transform (IST) have gained attention as a new transmission strategy in optical fiber communications. In recent years, several studies on artificial neural network (ANN)based equalization and demodulation schemes for eigenvaluemodulated signal have been conducted to enhance the receiver sensitivity. However, in the case of a presence of a carrier frequency offset (CFO) at receiver, the effects of the CFO on ANN receiver of eigenvalue-modulated signal is yet to be reported. In this study, we numerically and experimentally investigated the generalization performances of eigenvalue domain ANN-based demodulator on CFO. Furthermore, we propose to combine an ANN-based demodulator with a CFO compensation method based on IST and a relation between frequency and eigenvalue shifts. The proposed method, based on an appropriate soliton pulse, achieves a high CFO estimation accuracy of submegahertz order even if the CFO reaches ± 2.5 GHz under the noiseless condition. In the presence of noise and a large CFO of 2.5 GHz, the method attains a CFO estimation accuracy below 60 MHz for OSNR=10 dB with a low pilot pulse rate, such as 0.064%. We show the simulation results obtained after applying the proposed CFO compensation to the ANN demodulator, which is valid for 2.5 GHz CFO and long-haul transmission over 5000 km. Experiments performed in this study demonstrate successful demodulation of an eigenvalue-modulated signal with OSNR penalty < 1 dB in the presence of CFO within 1 GHz at 2.5 Gb/s.

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Convolutional long short-term memory neural network equalizer for nonlinear Fourier transform-based optical transmission systems

Cited by 36 publications

References 36 publications

Transfer Learning for Neural Networks-Based Equalizers in Coherent Optical Systems

Transfer Learning for Neural Networks-Based Equalizers in Coherent Optical Systems

Computing continuous nonlinear Fourier spectrum of optical signal with artificial neural networks

Combining IST-Based CFO Compensation and Neural Network-Based Demodulation for Eigenvalue-Modulated Signal

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