Upper Bound on the Capacity of the Nonlinear Schrödinger Channel (1502.06455v2)

Abstract: It is shown that the capacity of the channel modeled by (a discretized version of) the stochastic nonlinear Schr\"odinger (NLS) equation is upper-bounded by $\log(1+\text{SNR})$ with $\text{SNR}=\mathcal P_0/\sigma^2(z)$, where $\mathcal P_0$ is the average input signal power and $\sigma^2(z)$ is the total noise power up to distance $z$. The result is a consequence of the fact that the deterministic NLS equation is a Hamiltonian energy-preserving dynamical system.