Integrable Communication Channels and the Nonlinear Fourier Transform

This paper considers the transmission of information over integrable channels, a class of (mainly nonlinear) channels described by a Lax operator-pair. For such channels, the nonlinear Fourier transform, a powerful tool in soliton theory and exactly solvable models, plays the same role in "diagonalizing" the channel that the ordinary Fourier transform plays for linear convolutional channels. A transmission strategy encoding information in the nonlinear Fourier spectrum, termed nonlinear frequency-division multiplexing, is proposed for integrable channels that is the nonlinear analogue of orthogonal frequency-division multiplexing commonly used in linear channels. A central and motivating example is fiber-optic data transmission, for which the proposed transmission technique deals with both dispersion and nonlinearity directly and unconditionally without the need for dispersion or nonlinearity compensation methods.