Channel model and the achievable information rates of the optical nonlinear frequency division-multiplexed systems employing continuous b-modulation

Following the rise in interest in transmission systems employing the nonlinear Fourier transform (NFT) for the nonlinearity mitigation, we present the theoretical analysis of the achievable information rates in these systems, addressing the case of continuous b-modulated systems. Using adiabatic perturbation theory and the asymptotic analysis by means of Riemann-Hilbert problem, we obtain a remarkably simple input-output relation for arbitrary b-modulated transmission. Based on this model, we estimated the spectral efficiency for various single polarization (scaled and unscaled) b-modulated systems and observed an excellent agreement between our theory and the numerical results in the regime when the inline amplifier noise is the dominant source of spectral distortion.