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 using a(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.