Alternative Decoding Methods for Optical Communications Based on Nonlinear Fourier Transform

Abstract

Long-haul optical communications based on nonlinear Fourier Transform have gained attention recently as a new communication strategy that inherently embrace the nonlinear nature of the optical fiber. For communications using discrete eigenvalues ${\boldsymbol{\lambda }} \in {\mathbb{C}^ + }$ , information are encoded and decoded in the spectral amplitudes ${\boldsymbol{q}}({\boldsymbol{\lambda }}) = {\boldsymbol{b}}({\boldsymbol{\lambda }})/({\frac{{{\boldsymbol{da}}({\boldsymbol{\lambda }})}}{{{\boldsymbol{d\lambda }}}}})$ at the root ${{\boldsymbol{\lambda }}_{{\rm{rt}}}}$ where ${\boldsymbol{a}}({{{\boldsymbol{\lambda }}_{{\rm{rt}}}}}) = 0$ . In this paper, we propose two alternative decoding methods using ${\boldsymbol{a}}({\boldsymbol{\lambda }})$ and ${\boldsymbol{b}}({\boldsymbol{\lambda }})$ instead of ${\boldsymbol{q}}({\boldsymbol{\lambda }})$ as decision metrics. For discrete eigenvalue modulation systems, we show that symbol decisions using ${\boldsymbol{a}}({\boldsymbol{\lambda }})$ at a prescribed set of ${\boldsymbol{\lambda }}$ values perform similarly to conventional methods using ${\boldsymbol{q}}({\boldsymbol{\lambda }})$ but avoid root searching, and, thus, significantly reduce computational complexity. For systems with phase and amplitude modulation on a given discrete eigenvalue, we propose to use ${\boldsymbol{b}}({\boldsymbol{\lambda }})$ after for symbol detection and show that the noise in $\frac{{{\boldsymbol{da}}({\boldsymbol{\lambda }})}}{{{\boldsymbol{d\lambda }}}}$ and ${{\boldsymbol{\lambda }}_{{\rm{rt}}}}$ after transmission is all correlated with that in ${\boldsymbol{b}}({{{\boldsymbol{\lambda }}_{{\rm{rt}}}}})$ . A linear minimum mean square error estimator of the noise in ${\boldsymbol{b}}({{{\boldsymbol{\lambda }}_{{\rm{rt}}}}})$ is derived based on such noise correlation and transmission performance is considerably improved for QPSK and 16-quadratic-amplitude modulation systems on discrete eigenvalues.