Modulation on Discrete Nonlinear Spectrum: Perturbation Sensitivity and Achievable Rates

Multi-soliton pulses are studied under small perturbations. By means of mutual information, we show that the nonlinear spectrum becomes correlated when a 64-PSK modulated 2-eigenvalues soliton is perturbed by a small additive white Gaussian noise (AWGN). Transmission over two channels are considered: an AWGN channel (back-to-back scenario) and an ideal optical fiber link with distributed noise. We numerically show that the Jost coefficients <inline-formula> <tex-math notation="LaTeX">${b}({\lambda }_{k})$ </tex-math></inline-formula> are less correlated than the discrete spectral amplitudes <inline-formula> <tex-math notation="LaTeX">${q}_{d}({\lambda }_{k})$ </tex-math></inline-formula> while either of them can be alternatively used for modulation. In both channels, we compare the achievable information rates (AIRs) of joint detection and separate detection if the modulation is over either <inline-formula> <tex-math notation="LaTeX">${q}_{d}({\lambda }_{k})$ </tex-math></inline-formula> or <inline-formula> <tex-math notation="LaTeX">${b}({\lambda }_{k})$ </tex-math></inline-formula>. We show that if the length of the link is relatively short, the separate detection of <inline-formula> <tex-math notation="LaTeX">${b}({\lambda }_{k})$ </tex-math></inline-formula> gives almost the same total information rate as the joint detection of <inline-formula> <tex-math notation="LaTeX">${b}({\lambda }_{k})$ </tex-math></inline-formula> or <inline-formula> <tex-math notation="LaTeX">${q}_{d}({\lambda }_{k})$ </tex-math></inline-formula>. Moreover, the AIRs are compared with one of a first-order soliton with the same modulation.