---
abstract: 'We consider a -based transmission scheme, where data is embedded into the imaginary part of the nonlinear discrete spectrum. Inspired by probabilistic amplitude shaping, we propose a scheme as a means to increase the data rate of the system. We exploit the fact that for an -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 scheme shapes the information symbols according to the capacity-achieving distribution and transmits them together with the parity symbols at the output of a encoder, suitably modulated, via time-sharing. We furthermore derive an achievable rate for the proposed scheme. We verify our results with simulations of the discrete-time model as well as with simulations.'
author:
- |
    Andreas Buchberger, Alexandre Graell i Amat, \
    Vahid Aref,  and Laurent Schmalen,  [^1][^2][^3][^4]
title: |
    Probabilistic Eigenvalue Shaping for\
    Nonlinear Fourier Transform Transmission
---

Discrete spectrum, nonlinear Fourier transform (NFT), probabilistic shaping, soliton communication.

Introduction {#sec:introduction}
============

propagation in optical fibers is severely impaired by nonlinear effects that should be either compensated or utilized for the design of the communication system. The  [@yousefi2014nftI-III] provides a method to transform a 