Nonlinear Fourier transform for optical data processing and transmission: Advances and perspectives

Fiber-optic communication systems are nowadays facing serious challenges due to fast growing demand on capacity from various new applications and services. It is now well recognised that nonlinear effects limit the spectral efficiency and transmission reach of modern fiber-optic communications. Nonlinearity compensation is therefore widely believed to be of paramount importance for increasing the capacity of future optical networks. Recently, there has been a steadily growing interest in the application of a powerful mathematical tool the nonlinear Fourier transform (NFT) in the development of fundamentally novel nonlinearity mitigation tools for fiber-optic channels. It has been recognized that, within this paradigm, nonlinear cross-talk is effectively absent and that the fiber nonlinearity can enter as a constructive element rather than a degrading factor. The novelty and the mathematical complexity of the NFT, the versatility of the proposed system designs, and the lack of a unified vision of an optimal NFT-type communication system however constitute significant difficulties for communication researchers. In this paper, we therefore survey the existing approaches in a common framework and review the progress in this area with a focus on practical implementation aspects. First, an overview of existing key algorithms for the efficacious computation of the direct and inverse NFT is given, and the issues of accuracy and numerical complexity are elucidated. We then describe different approaches for the utilization of the NFT in practical transmission schemes. After that we discuss the differences, advantages and challenges of various recently emerged system designs employing the NFT, and the efficiency estimation available up to date. With many practical implementation aspects still being open, our mini-review is aimed at helping researchers to assess the perspectives, understand the bottle-necks, and envision the development paths in the upcoming of NFT-based transmission technologies.