To appear in IEEE/OSA Journal of Lightwave Technology

A. Buchberger, A. Graell i Amat, V. Aref, and L. Schmalen, "Probabilistic Eigenvalue Shaping for Nonlinear Fourier Transform Transmission," IEEE/OSA Journal of Lightwave Technology, to appear. The paper can be found in [arXiv]

Abstract: We consider a nonlinear Fourier transform (NFT)- based transmission scheme, where data is embedded into the imaginary part of the nonlinear discrete spectrum. Inspired by probabilistic amplitude shaping, we propose a probabilistic eigenvalue shaping (PES) scheme as a means to increase the data rate of the system. We exploit the fact that for an NFT- based transmission scheme, the pulses in the time domain are of unequal duration by transmitting them with a dynamic symbol interval and find a capacity-achieving distribution. The PES scheme shapes the information symbols according to the capacity-achieving distribution and transmits them together with the parity symbols at the output of a low-density parity-check encoder, suitably modulated, via time-sharing. We furthermore derive an achievable rate for the proposed PES scheme. We verify our results with simulations of the discrete-time model as well as with split-step Fourier simulations.