Log-log growth of channel capacity for nondispersive nonlinear optical fiber channel in intermediate power range:...

In our previous paper [Terekhov et al., Phys. Rev. E 95, 062133 (2017)2470-004510.1103/PhysRevE.95.062133] we considered the optical channel modeled by the nonlinear Schrödinger equation with zero dispersion and additive Gaussian noise. We found per-sample channel capacity for this model. In the present paper we extend the per-sample channel model by introducing the initial signal dependence on time and the output signal detection procedure. The proposed model is a closer approximation of the realistic communications link than the per-sample model where there is no dependence of the initial signal on time. For the proposed model we found the correlators of the output signal both analytically and numerically. Using these correlators we built the conditional probability density function. Then we calculated an entropy of the output signal, a conditional entropy, and the mutual information. Maximizing the mutual information we found the optimal input signal distribution, channel capacity, and their dependence on the shape of the initial signal in the time domain for the intermediate power range.