Rates Achievable on a Fiber-Optical Split-Step Fourier Channel

A lower bound on the capacity of the split-step Fourier channel is derived. The channel under study is a concatenation of smaller segments, within which three operations are performed on the signal, namely, nonlinearity, linearity, and noise addition. Simulation results indicate that for a fixed number of segments, our lower bound saturates in the high-power regime and that the larger the number of segments is, the higher is the saturation point. We also obtain an alternative lower bound, which is less tight but has a simple closed-form expression. This bound allows us to conclude that the saturation point grows unbounded with the number of segments. Specifically, it grows as $c+(1/2)\log(K)$, where $K$ is the number of segments and $c$ is a constant. The connection between our channel model and the nonlinear Schr\"odinger equation is discussed.