Next-to-leading-order corrections to capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region

We consider the optical fiber channel modeled by the nonlinear Schrödinger equation with zero dispersion and additive Gaussian noise. Using the Feynman path-integral approach for the model, we find corrections to conditional probability density function, output signal distribution, conditional and output signal entropies, and the channel capacity at large signal-to-noise ratio. We demonstrate that the correction to the channel capacity is positive for large signal power. Therefore, this correction increases the earlier calculated capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region.

Figure 1

The correction $\mathrm{\Delta }{C}^{\prime }$, see Eq. (70), as a function of power $P$ for the parameters $Q=1.5\times {10}^{-7}\mathrm{mW}{\mathrm{km}}^{-1}$, $\gamma =1.31\times {10}^{-3}{\mathrm{mW}}^{-1}{\mathrm{km}}^{-1}$, and $L=1000\mathrm{km}$.

Figure 2

The correction $\mathrm{\Delta }{C}^{\prime }$, see Eq. (70), as a function of power $P$ for the parameters $Q=1.5\times {10}^{-7}\mathrm{mW}{\mathrm{km}}^{-1}$, $\gamma =1.31\times {10}^{-3}{\mathrm{mW}}^{-1}{\mathrm{km}}^{-1}$, and $L=1000\mathrm{km}$. The solid black line corresponds to the exact expression obtained using Eq. (65). The red dashed line corresponds to the asymptotics obtained using Eq. (69).