Mutual information in nonlinear communication channel: Analytical results in large SNR limit

I. S. Terekhov, A. V. Reznichenko, S. K. Turitsyn

Published 2014-11-27Version 1

Applying quasi-classical perturbation theory in the corresponding Feynman's path-integral representation, we derive in the limit of the large signal-to-noise ratio the analytical expression for the mutual information of the nonlinear communication channel described by the nonlinear Shr\"{o}dinger equation (NLSE) with the additive Gaussian noise. The NLSE is one of the fundamental models in nonlinear physics and has a broad range of applications, including fibre-optic communications --- the backbone of the Internet. Our analytical result demonstrates that the corrections to the mutual information in the leading nonlinearity order are positive. This result is somewhat counterintuitive, that is, that the impact of nonlinearity may increase the Shannon capacity above the capacity of a corresponding linear channel.