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.