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 fiber 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 single- and dual-polarisation cases, respectively. In this paper, we study the capacity lower bounds of this channel under an average power constraint in bits per channel use. We develop an asymptotic semi-analytic approximation for a capacity lower bound for arbitrary n and a Rayleigh input distribution. It is shown that this lower bound grows logarithmically with signal-to-noise ratio (SNR), independently of the value of n. Numerical results for other continuous 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 SNR of 25 dB, the best lower bounds we developed are approximately 3.68 bit per channel use. The practically relevant case of amplitude shift-keying (ASK) constellations is also numerically analyzed. For the same SNR of 25 dB, a 16-ASK constellation yields a rate of approximately 3.45 bit per channel use.