Inverse scattering transform via affine map: applications to high-speed nonlinear optical communications

TL;DR

This paper introduces an affine map method for efficiently solving the inverse scattering problem in nonlinear optical communications, enabling accurate bit recovery by focusing on the continuous spectrum and reducing computational complexity.

Contribution

The paper proposes a novel affine map approximation for the inverse scattering transform, simplifying the process by using only the continuous spectrum and deriving a reduced order model.

Findings

Accurate bit sequence recovery using only the continuous spectrum.

Rank of affine map matrix equals number of bits per sequence.

Reduced order affine map maintains high accuracy with lower complexity.

Abstract

This work present an affine map approximation for solving the inverse scattering problem related to the nonlinear Schr\"odinger model of signal propagation in high-speed coherent optical communication. Numerical simulations indicate that accurate recovery of the transmitted bit sequence can be achieved using only the continuous part of the Lax spectrum at the fiber output, thereby allowing the discrete (soliton) spectrum to be disregarded. We observed that the numerically evaluated rank of the resulting affine map matrix equals the number of bits per transmitted sequence, and we utilize this to derive a reduced order affine map.