Periodic Reporting for period 3 - FRECOM (Nonlinear-Distortion Free Communication over the Optical Fibre Channel) Reporting period: 2021-03-01 to 2022-08-31 Summary of the context and overall objectives of the project The enormous growth in the Internet of Things and server farms for cloud services has increased the strain on the optical communication infrastructure. By 2025, our society will require data rates that are physically impossible to implement using current state-of-the-art optical communication technologies. This is because fibre-optic communication systems are rapidly approaching their fundamental capacity limits imposed by the Kerr nonlinearity of the fibre. Nonlinear distortion limits the ability to transport and detect the information stream. This is a very critical problem for increasing the data rates of any optical fibre communication system. The main objective of the project is to explore machine learning to devise novel optical communication systems that are robust to optical fibre nonlinearities and realize nonlinear-distortion free communication systems. Therefore, novel methodologies and concepts for the design of an optical transmission links, noise mitigating receiver and a noise robust transmitter are explored in the project. We are exploring optical communication systems that employ eigenvalues for data transmission. Moreover, we are looking into machine learning techniques that would be able to learn the best strategies to communicate over the nonlinear fibre-optic channel. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far So far, some of the major achievements of the project have been on the experimental demonstration of modulating both the continuous and discrete spectrum of the Nonlinear Fourier Transform (NFT) as a well as joint optimization of transmitter and receiver using machine learning. The reason behind this was to increase an overall spectral efficiency times transmission distance product of the NFT based optical communication systems. For the first time, we have introduced a framework for dual-polarization NFDM systems which allows encoding data on both continuous and discrete spectral components. The dual-polarization joint continuous and discrete spectral modulated NFDM system has then been experimentally demonstrated in a transmission scenario using distributed Raman amplification. A transmission reach of 3200 km was achieved for a 8.4-Gb/s net rate NFDM signal. This work demonstrates the use of all the degrees of freedom available for NFDM-based transmission over standard single mode fibres. More specifically, joint optimization of transmitter and receiver was performed using a machine learning approach of end-to-end learning. We proposed for the first time an auto-encoder scheme for coherent fiber-optic communications considering the accurate model of a nonlinear dispersive fiber channel. The system uses an NFDM transmitter that performs the symbol to-waveform encoding and an NN-based receiver that performs the waveform-to-symbol decoding. The chosen transmitter constraints the solutions space of the generated time-domain waveforms to solitonic pulse-shapes, facilitating the optimization of the AE. Moreover the minimal dispersion of the solitons, even in the presence of losses, allows to use a memoryless receiver implemented with a low-complexity NN. The full optical nonlinear channel model has been implemented using the SSFM. Compared to the state-of-the-art NFDM communication system, the proposed proof-of-concept system allowed extending the transmission reach from 2000 to 6640 km at the HD-FEC threshold. These results of this work have been published in Journal of Lightwave Technology. Secondly, we have proposed a novel machine learning based framework for design of Raman amplifiers which can have a large impact on the NFT based optical communication system. More specifically, a low–complexity and low–latency framework, based on machine learning, has been demonstrated for the inverse system design. The framework consists of two stages: 1) a multi-layer neural network employed to learn the inverse mapping and 2) a multi-layer neural network, representing the forward mapping, in combination with the gradient descent algorithm for fine–adjustments. The first stage can also be used in combination with various optimization algorithms to provide a qualified set of initial conditions. The framework has been demonstrated, using numerical simulations, to provide highly-accurate pump power and wavelength configurations for the design of C and C+L–band Raman amplifiers with arbitrary, flat and tilted gain profiles. Moreover, the corresponding experimental verification has been presented for the design of C–band Raman amplifiers. The experimental results demonstrate that highly–accurate pump power allocations for arbitrary, flat and tilted gains are feasible using the proposed framework. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) A significant progress beyond the-state-of-the art has been demonstrated which is documented by the following publications:1. F. Da Ros, S. Civelli, S. Gaiarin, E.P. da Silva, N. De Renzis, M. Secondini, D. Zibar, “Dual-polarization NFDM transmission with continuous and discrete spectral modulation,” Journal of Lightwave Technology, vol. 37, no. 10, 2019 In this paper, we demonstrate for the first time dual polarization joint modulation of discrete and continues spectra NFT communication system. The proposed dual-polarization joint modulation schemes enables to exploit all the degrees of freedom for modulation (both polarizations and both spectra) provided by a single-mode fiber (SMF).2. D. Zibar, H. –M. Chin, Y. Tong, N. Jain, J. Guo, L. Chang, T. Gehring, J. E. Bowers, U. L. Andersen, “Highly-sensitive phase and frequency noise measurement technique using Bayesian filtering,” IEEE Photonics Technology Letters, vol. 31, no. 23, pp: 1866 – 1869, 2019 (Google Scholar citations: 3) Measuring optical phase is instrumental in many scientific areas ranging from fiber-optic communication, spectroscopy, gravitational wave detection and quantum metrology. This paper demonstrates a method that enables record sensitive and accurate optical phase measurements. It solves a 50 years old problem and is changing the way optical phase is measured. 3. D. Zibar, A. M. Rosa Brusin, U. C. de Moura, F. Da Ros, V. Curri, Andrea Carena, “Inverse system design using machine learning: The Raman amplifier case,” Journal of Lightwave Technology, vol. 38, no. 4, 2020 (Google Scholar citations: 10) This paper demonstrated the benefits of using machine learning in realizing worlds-first programmable gain optical amplifier. Such an amplifier has a potential to significantly improve energy efficiency of fiber-optic networks. Many groups are now following this line of research. 4. S. Gaiarin, F. Da Ros, N. De Renzis, R. T. Jones, D. Zibar, “End-to-end optimization of coherent optical communications over the split-step Fourier method guided by the nonlinear Fourier transform theory,” Journal of Lightwave Technology, accepted for publication, 2020This paper is a first demonstration of how machine learning can be used to design optimum communication strategies over the nonlinear fiber-optic channel and enable robust transmission. By employing automatic differentiation we shows that joint optimization of transmitter and receiver is feasible. cover-image.jpg
