  Using the path-integral technique we examine the mutual information for the
communication channel modelled by the nonlinear Schr\"odinger equation with
additive Gaussian noise. The nonlinear Schr\"odinger equation is one of the
fundamental models in nonlinear physics, and it has a broad range of
applications, including fiber optical communications --- the backbone of the
Internet. At large signal-to-noise ratio ($\mathrm{SNR}$) we present the mutual
information through the path-integral which is convenient for the perturbative
expansion in nonlinearity. In the limit of small noise and small nonlinearity
we derive analytically the first nonzero nonlinear correction to the mutual
information for the channel.
