In this paper, we review the historical evolution of predictions of the performance of optical communication systems. We will describe how such predictions were made from the outset of research in laser based optical communications and how they have evolved to their present form, accurately predicting the performance of coherently detected communication systems.

Formation of coherent structures and patterns from unstable uniform state or noise is a fundamental physical phenomenon that occurs in various areas of science ranging from biology to astrophysics. Understanding of the underlying mechanisms of such processes can both improve our general interdisciplinary knowledge about complex nonlinear systems and lead to new practical engineering techniques. Modern optics with its high precision measurements offers excellent test-beds for studying complex nonlinear dynamics, though capturing transient rapid formation of optical solitons is technically challenging. Here we unveil the build-up of dissipative soliton in mode-locked fibre lasers using dispersive Fourier transform to measure spectral dynamics and employing autocorrelation analysis to investigate temporal evolution. Numerical simulations corroborate experimental observations, and indicate an underlying universality in the pulse formation. Statistical analysis identifies correlations and dependencies during the build-up phase. Our study may open up possibilities for real-time observation of various nonlinear structures in photonic systems.

We introduce low complexity machine learning method method (based on lasso regression, which promotes sparsity, to identify the interaction between symbols in different time slots and to select the minimum number relevant perturbation terms that are employed) for nonlinearity mitigation. The immense intricacy of the problem calls for the development of "smart" methodology, simplifying the analysis without losing the key features that are important for recovery of transmitted data. The proposed sparse identification method for optical systems (SINO) allows to determine the minimal (optimal) number of degrees of freedom required for adaptive mitigation of detrimental nonlinear effects. We demonstrate successful application of the SINO method both for standard fiber communication links (over 3 dB gain) and for few-mode spatial-division-multiplexing systems.

Since Shannon derived the seminal formula for the capacity of the additive linear white Gaussian noise channel, it has commonly been interpreted as the ultimate limit of error-free information transmission rate. However, the capacity above the corresponding linear channel limit can be achieved when noise is suppressed using nonlinear elements; that is, the regenerative function not available in linear systems. Regeneration is a fundamental concept that extends from biology to optical communications. All-optical regeneration of coherent signal has attracted particular attention. Surprisingly, the quantitative impact of regeneration on the Shannon capacity has remained unstudied. Here we propose a new method of designing regenerative transmission systems with capacity that is higher than the corresponding linear channel, and illustrate it by proposing application of the Fourier transform for efficient regeneration of multilevel multidimensional signals. The regenerative Shannon limit-the upper bound of regeneration efficiency-is derived.

All-optical platforms for recurrent neural networks can offer higher computational speed and energy efficiency. To produce a major advance in comparison with currently available digital signal processing methods, the new system would need to have high bandwidth and operate both signal quadratures (power and phase). Here we propose a fiber echo state network analogue (FESNA)-the first optical technology that provides both high (beyond previous limits) bandwidth and dual-quadrature signal processing. We demonstrate applicability of the designed system for prediction tasks and for the mitigation of distortions in optical communication systems with multilevel dual-quadrature encoded signals.