Probabilistic Eigenvalue Shaping for Nonlinear Fourier Transform Transmission

TL;DR

This paper introduces a probabilistic eigenvalue shaping scheme for nonlinear Fourier transform-based transmission, enhancing data rates by optimizing symbol distributions and leveraging dynamic symbol intervals.

Contribution

It proposes a novel probabilistic eigenvalue shaping method for NFT-based systems, including capacity analysis and practical implementation with LDPC encoding and time-sharing.

Findings

Achieves higher data rates through optimized eigenvalue distribution.

Derives an achievable rate for the proposed shaping scheme.

Validates results with discrete-time and split-step Fourier simulations.

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.