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arXiv · 1712.08467

Probabilistic Eigenvalue Shaping for Nonlinear Fourier Transform Transmission

Andreas Buchberger·Alexandre Graell i Amat·Vahid Aref·Laurent Schmalen
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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.

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Andreas Buchberger, Alexandre Graell i Amat, Vahid Aref, Laurent Schmalen. 2018-08-06. Probabilistic Eigenvalue Shaping for Nonlinear Fourier Transform Transmission. https://doi.org/10.1109/jlt.2018.2854760

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