Channel capacity and simple correlators for nonlinear communication channel at large SNR and small dispersion

We consider the optical fiber channel modelled by the nonlinear Schrodinger equation with additive white Gaussian noise. Using Feynman path-integral approach for the model with small dispersion we find the estimations for the first nonzero corrections to the conditional probability density function, to the optimal input signal distribution, and to the channel capacity at large signal-to-noise ratio. On the base of the factorization assumption of the conditional probability density function we demonstrate that the correction to the channel capacity in small dimensionless dispersion parameter is quadratic and positive therefore increasing the earlier calculated capacity for a nondispersive nonlinear optical fiber channel in the intermediate power regime. To illustrate our approach we also find the analytical expressions for simple correlators of the output signal in our noisy channel with small dispersion.