Alternative Decoding Methods for Optical Communications Based on Nonlinear Fourier Transform

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 λ ∈ C ⁺ , information are encoded and decoded in the spectral amplitudes q(λ) = b(λ)/(da(λ)/dλ) at the root λ _rt where a(λ _rt ) = 0. In this paper, we propose two alternative decoding methods using a(λ) and b(λ) instead of q(λ) as decision metrics. For discrete eigenvalue modulation systems, we show that symbol decisions usinga(λ) at a prescribed set of λ values perform similarly to conventional methods using q(λ) 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 b(λ) after for symbol detection and show that the noise in da(λ)/dλ and λ _rt after transmission is all correlated with that in b(λ _rt ). A linear minimum mean square error estimator of the noise in b(λ _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.