Mutual information in nonlinear communication channel. Preliminary   analytical results in large SNR and small nonlinearity limit
  Applying perturbation theory to the path-integral representation for the mutual information of the nonlinear communication channel described by the nonlinear Shr\"{o}dinger equation (NLSE) with the additive Gaussian noise we analyze the analytical expression for the mutual information at large signal-to-noise ratio ($\mathrm{SNR}$) and small nonlinearity. We classify all possible corrections to the mutual information in nonlinearity parameter and demonstrate that all singular in $\mathrm{SNR}$ terms vanish in the final result. Furthermore our analytical result demonstrates that the corrections to Shannon's contribution to the mutual information in the leading order in $\mathrm{SNR}$ are of order of squared nonlinearity parameter. We outline the way for the calculation of these corrections in the further investigations. 
I. S. Terekhov, A. V. Reznichenko, and S. K. Turitsyn
cs.IT math.IT