Shaping Gain for Optical Fiber Communication Systems Employing the Nonlinear Fourier Transform

We demonstrate the shaping gain of up to 6.4 dB achieved by probabilistic shaping of discrete nonlinear eigenvalues for scalar and vector optical fiber channel respectively. The adopted communication scheme corresponds to the most practical PAM modulation of soliton shapes in these channels. We use the well established channel models available in the literature and used previously to perform a probabilistic shaping for discrete and continuous alphabet and show that the shaping gain for the channels in question is significantly larger than those for additive Gaussian channels for constellations of similar cardinality.