Full-spectrum periodic nonlinear Fourier transform optical communication through solving the Riemann-Hilbert problem

Morteza Kamalian Kopae, Anastasiia Vasylchenkova, Dmitry Shepelsky, Jaroslaw E. Prilepsky, Sergei K. Turitsyn

Research output: Contribution to journalArticlepeer-review


In this article, for the first time, a full-spectrum periodic nonlinear Fourier transform (NFT)-based communication system with the inverse transformation at the transmitter performed by using the solution of Riemann-Hilbert problem (RHP), is proposed and studied. The entire control over the nonlinear spectrum rendered by our technique, where we operate with two qualitatively different components of this spectrum represented, correspondingly, in terms of the main spectrum and the phases, allows us to design a time-domain signal tailored to the characteristics of the transmission channel. In the heart of our system is the RHP-based signal processing utilised to generate the time-domain signal from the modulated nonlinear spectrum. This type of NFT processing leads to a computational complexity that scales linearly with the number of time-domain samples, and we can process signal samples in parallel. In this article, we suggest the way of getting an exactly periodic signal through the correctly formulated RHP, and present evidence of the analogy between band-limited (in ordinary Fourier sense) signals and finite-band (in RHP sense) signals. Also, for the first time, we explain how to modulate the phases of individual periodic nonlinear modes. The performance of our transmission system is evaluated through numerical simulations in terms of bit error rate and Q$^2$-factor dependencies on the transmission distance and power, and the results demonstrate the good potential of the approach.

Original languageEnglish
Article number9027900
Pages (from-to)3602-3615
Number of pages14
JournalJournal of Lightwave Technology
Issue number14
Early online date10 Mar 2020
Publication statusPublished - 15 Jul 2020

Bibliographical note

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.

Funding: Leverhulme Trust and EPSRC


  • Fibre-optic communications
  • Riemann-Hilbert problem
  • coherent communications
  • inverse scattering
  • nonlinear Fourier transform


Dive into the research topics of 'Full-spectrum periodic nonlinear Fourier transform optical communication through solving the Riemann-Hilbert problem'. Together they form a unique fingerprint.

Cite this