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