Capacity Region Bounds for Optical WDM Channels Based on First-Order Regular Perturbation

It is known that fiber nonlinearities induce crosstalk in a wavelength division multiplexed (WDM) system, which limits the capacity of such systems as the transmitted signal power is increased. A network user in a WDM system is an entity that operates around a given optical wavelength. Traditionally, the channel capacity of a WDM system has been analyzed under different assumptions for the transmitted signals of the other users, while treating the interference arising from these users as noise. In this paper, we instead take a multi-user information theoretic view and treat the optical WDM system impaired by cross-phase modulation and dispersion as an interference channel. We characterize an outer bound on the capacity region of simultaneously achievable rate pairs, assuming a simplified $K$-user perturbative channel model using genie-aided techniques. Furthermore, an achievable rate region is obtained by time-sharing between certain single-user strategies. It is shown that such time-sharing can achieve better rate tuples compared to treating nonlinear interference as noise. The achievable rates using the latter strategy are known to exhibit a maximum for an optimum launch power, beyond which a further increase of power leads to a reduction in achievable rates. For the single-polarization single-span system under consideration and a power 3.5 dB above the optimum launch power, treating nonlinear interference as noise results in a rate of 4.25 b/sym, while time-sharing gives a rate of 7.99 b/sym.