Upper Bound on the Capacity of the Single-User Nonlinear Schrödinger Channel

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 logp1` SNRq with SNR “ P0{σ pzq, where P0 is the average input signal power and σpzq is the total noise power up to distance z. This implies that the capacity of this model of the single-user optical fiber channel is below the capacity of the corresponding additive white Gaussian noise channel. The result is a consequence of the fact that the deterministic NLS equation is a Hamiltonian energy-preserving dynamical system.