Communication Using Eigenvalues of Higher Multiplicity of the Nonlinear Fourier Transform

A generalized Nonlinear Fourier Transform (GNFT), which includes eigenvalues of higher multiplicity, is considered for information transmission over fiber optic channels. Numerical algorithms are developed to compute the direct and inverse GNFTs. For closely spaced eigenvalues, examples suggest that the GNFT is more robust than the Nonlinear Fourier Transform to the practical impairments of truncation, discretization, attenuation, and noise. Communication using a soliton with one double eigenvalue is numerically demonstrated and its information rates are compared to solitons with one and two simple eigenvalues.