On the Capacity of b-Modulated Nonlinear Frequency Division Multiplexing

In this paper, we investigate the capacity of the continuous spectrum of nonlinear frequency division multiplexing (NFDM) systems when data is encoded using b-modulation. Recently, a tractable channel model is proposed for such optical fiber communication systems, describing the received b-modulated signal with an input-dependent complex Gaussian distributed noise. Considering this channel model, we prove that the capacity-achieving distribution is unique and discrete. A search algorithm is proposed to determine the optimal discrete input distribution that maximizes the mutual information. The numerical results show that the optimal input distributions form ring-based constellations. We compare these optimal designs with some conventional ring-based amplitude and phase shift keying (APSK) modulation schemes including 16 APSK, 32 APSK and 64 APSK, to show the achievable performance gains.