Data Transmission based on Exact Inverse Periodic Nonlinear Fourier Transform, Part I: Theory

TL;DR

This paper develops a complete theoretical framework and algorithm for the inverse periodic nonlinear Fourier transform, enabling new modulation schemes for optical fiber communication that are compatible with nonlinear transmission properties.

Contribution

It introduces a tailored algebrogeometric inverse PNFT algorithm and proposes a novel nonlinear frequency amplitude modulation scheme for optical communications.

Findings

Complete inverse PNFT algorithm derived from algebrogeometric methods

Design of nonlinear frequency amplitude modulation scheme

Foundation for future PNFT-based communication experiments

Abstract

The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission scheme inherently compatible with the nonlinear fiber is obtained. Despite potential advantages, the periodic NFT (PNFT) has been studied less compared to its counterpart based on vanishing boundary conditions, due to the mathematical complexity of the inverse transform. In this paper we extract the theory of the algebrogeometric integration method underlying the inverse PNFT from the literature, and tailor it to the communication problem. We provide a complete algorithm to compute the inverse PNFT. As an application, we employ the algorithm to design a novel modulation scheme called nonlinear frequency amplitude modulation, where four different nonlinear frequencies are modulated independently. Finally we provide two further modulation schemes that may be considered in future research. The algorithm is further applied in Part II of this paper to the design of a PNFT-based communication experiment.