  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.
