Finite-Genus Solutions-based Optical Communication with the Riemann-Hilbert Problem Transmitter and a Convolutional Neural Network Receiver

In the study, we develop a new optical communication system based on the nonlinear Fourier transform for generic (quasiperiodic) finite-genus solutions to the nonlinear Schrödinger equation. At the transmitter, the finite-genus solutions of a generic type, which are not subject to any periodicity constraint, are generated by means of the Riemann-Hilbert problem (RHP) approach and utilized as the data carriers. Data encoding is achieved by modulating the phases of these solutions (as defined by the RHP), whereas the main spectrum determines signal parameters such as duration, bandwidth, and power. To decode the phases and compensate for their evolution, we propose a receiver that employs a convolutional neural network (CNN). CNN helps us overcome the lack of a complete theoretical framework for generic finite-genus solutions. We carry out the numerical simulations of a communication system that utilizes the phases of finite-genus solutions as data carriers with a CNN-based receiver. We present an analysis of the system's performance in terms of bit error ratio (BER) in dependence on signal power, propagation distance, and sampling rate. Additionally, we investigate the ability of the CNN-based receiver to process signals with a truncated linear spectrum to provide higher spectral efficiency, attaining ${4.28\,\mathrm{bits/s/Hz}}$ (for a single polarization) at ${\text{1040}\,\text{km}}$ transmission distance.