Communication Using Eigenvalues of Higher Multiplicity of the Nonlinear Fourier Transform

TL;DR

This paper introduces a generalized Nonlinear Fourier Transform (GNFT) incorporating higher multiplicity eigenvalues, demonstrating its robustness and potential for improved fiber optic communication through numerical analysis and comparison with traditional NFT-based methods.

Contribution

The paper develops numerical algorithms for the GNFT with higher multiplicity eigenvalues and demonstrates its advantages over traditional NFT in fiber optic communication scenarios.

Findings

GNFT is more robust than NFT to practical impairments.

Numerical demonstration of communication using a soliton with a double eigenvalue.

Comparison shows potential for higher information rates with GNFT.

Abstract

A generalized Nonlinear Fourier Transform (GNFT), which includes eigenvalues of higher multiplicity, is considered for information transmission over fiber optic channels. Numerical algorithms are developed to compute the direct and inverse GNFTs. For closely-spaced eigenvalues, examples suggest that the GNFT is more robust than the NFT to the practical impairments of truncation, discretization, attenuation and noise. Communication using a soliton with one double eigenvalue is numerically demonstrated, and its information rates are compared to solitons with one and two simple eigenvalues.