A Fokker-Planck differential equation approach for the zero-dispersion optical fiber channel

Optical fiber channels modeled by the stochastic nonlinear Schrödinger equation and operating at zero dispersion are considered in this paper. As a result of the Kerr nonlinearity and its interaction with amplified spontaneous emission noise, the amplitude and phase channels correlate with each other and the statistics of the received signal are non-Gaussian. In order to find the capacity of such a nonlinear channel, one must find the conditional probability density function (PDF) of the channel output given channel input. The complex zero-dispersion channel (viewed as an instance of the Langevin equation) is transformed to polar coordinates using Itô calculus, where the cubic nonlinearity appears to be more tractable. A method is introduced based on the Fokker-Planck differential equation, known in the statistical physics, to describe the PDF of the received signal.