Path-integral approach to mutual information calculation for nonlinear channel with small dispersion at large signal-to-noise ratio

We consider the information fiber optical channel modeled by the nonlinear Schrodinger equation with additive Gaussian noise. Using path-integral approach and perturbation theory for the small dimensionless parameter of the second dispersion, we calculate the conditional probability density functional in the leading and next-to-leading order in the dimensionless second dispersion parameter associated with the input signal bandwidth. Taking into account the specific filtering of the output signal by the output signal receiver, we calculate the mutual information in the leading and next-to-leading order in the dispersion parameter and at large signal-to-noise ratio (SNR). Further, we find the explicit analytical expression for the mutual information in the case of the modified Gaussian input signal distribution taking into account the limited frequency bandwidth of the input signal. We explain the behavior of the mutual information as a function of the average input signal power and the input signal bandwidth in connection with the frequency broadening in the presence of small dispersion.