Upper bound on the capacity of the 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 log(l + SNR) with SNR = P0/σ²(z), where P0 is the average input signal power and σ²(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.