On the Capacity of the Continuous-Space SSFM Model of Optical Fiber

The limit of a discrete-time model of the optical fiber described by the split-step Fourier method (SSFM) when the number of segments in distance K tends to infinity is considered. It is shown that if $K \geq {\mathcal{P}^{2/3}}$ and $\mathcal{P} \to \infty $, where $\mathcal{P}$ is the average input power, the capacity of the resulting continuous-space lossless model is lower bounded by $\frac{1}{2}{\log _2}\left( {1 + {\text{SNR}}} \right) - \frac{1}{2} + o\left( 1 \right)$, where o(1) tends to zero with the signal-to-noise ratio SNR. This implies that at least half of the signal degrees-of-freedom remain asymptotically in this model.