Upper Bound on the Capacity of the Nonlinear Schrödinger Channel

Abstract

It is shown that the capacity of the channel modeled by (a discretized version of) the stochastic nonlinear Schrödinger (NLS) equation is upper-bounded by $\log(1+\text{SNR})$ with $\text{SNR}=\mathcal P_0/σ^2(z)$, where $\mathcal P_0$ is the average input signal power and $σ^2(z)$ 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.

To be presented at the 14th Canadian Workshop on Information Theory (CWIT), St. John's, NL, Canada, July 6-9, 2015. This is the final version submitted to the CWIT 2015