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

Calculation of mutual information for nonlinear communication channel at large SNR