Integrable communication channels and the nonlinear fourier transform
Mansoor Yousefi Frank R. Kschischang
Proceedings of the IEEE International Symposium on Information Theory, Istanbul, Turkey, July 2013

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.