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

Sergei K. Turitsyn*, Jaroslaw E. Prilepsky, Son Thai Le, Sander Wahls, Leonid L. Frumin, Morteza Kamalian, Stanislav A. Derevyanko

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review


Fiber-optic communication systems are nowadays facing serious challenges due to the fast growing demand on capacity from various new applications and services. It is now well recognized 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 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, the nonlinear crosstalk due to the Kerr effect is effectively absent, and fiber nonlinearity due to the Kerr effect 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, as well as the spectral efficiency estimates available up-to-date. With many practical implementation aspects still being open, our mini-review is aimed at helping researchers assess the perspectives, understand the bottlenecks, and envision the development paths in the upcoming NFT-based transmission technologies.

Original languageEnglish
Pages (from-to)307-322
Number of pages16
Issue number3
Early online date28 Feb 2017
Publication statusPublished - 20 Mar 2017

Bibliographical note

© 2017 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited.

Funding: EPSRC (UNLOC EP/J017582/1); ERC; Ministry of Education and Science
of the Russian Federation (Minobrnauka) (14.B25.31.0003).


  • coherent communications
  • fiber optics communications
  • inverse scattering
  • nonlinear optical signal processing


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