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 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 in the leading order in the parameter signal-to-noise ratio (SNR). Further, we find the explicit expression for the mutual information in case of the modified Gaussian input signal distribution taking into account the limited frequency bandwidth of the input signal.

翻译：我们考虑由含加性高斯噪声的非线性薛定谔方程建模的信息光纤信道。利用路径积分方法以及针对二阶色散小无量纲参数的微扰理论，我们计算了与输入信号带宽相关的二阶色散无量纲参数在领头阶和次领头阶条件下的条件概率密度泛函。考虑到输出信号接收器对输出信号的特定滤波处理，我们计算了互信息在色散参数的领头阶和次领头阶以及信噪比参数的领头阶下的表达式。进一步，在考虑输入信号有限频率带宽对修正高斯输入信号分布的影响下，我们给出了互信息的显式表达式。