Capacity Lower Bounds of the Noncentral Chi-Channel with Applications to Soliton Amplitude Modulation

The channel law for amplitude-modulated solitons transmitted through a nonlinear optical fibre with ideal distributed amplification and a receiver based on the nonlinear Fourier transform is a noncentral chi distribution with 2n degrees of freedom, where n = 2 and n = 3 correspond to the singleand dual-polarisation cases, respectively. In this paper, we study the capacity of this channel in bits per channel use, and develop a semi-analytic capacity lower bound for arbitrary n and a Rayleigh input distribution. An asymptotic analysis of the bound is also presented, which shows that this lower bound grows logarithmically with signal-to-noise ratio (SNR), independently of the value of n. Numerical results for other input distributions are also provided. A half-Gaussian input distribution is shown to give larger rates than a Rayleigh input distribution for n = 1, 2, 3. At an effective SNR of 30 dB, the obtained lower bounds are approximately 4 bit per channel use.