  Remarkable mathematical properties of the integrable nonlinear Schr\"odinger
equation (NLSE) can offer advanced solutions for the mitigation of nonlinear
signal distortions in optical fibre links. Fundamental optical soliton,
continuous and discrete eigenvalues of the nonlinear spectrum have already been
considered for transmission of information in fibre-optic channels. Here we
propose to apply signal modulation to the kernel of the
Gelfand-Levitan-Marchenko equations (GLME) that offers the advantage of a
relatively simple decoder design. First, we describe an approach based on
exploiting the general N-soliton solution of the NLSE for simultaneous coding
of $N$ symbols involving $4\times N$ coding parameters. As a specific elegant
sub-class of the general schemes we introduce a soliton orthogonal frequency
division multiplexing (SOFDM) method. This method is based on the choice of
identical imaginary parts of the N-soliton solution eigenvalues, corresponding
to equidistant soliton frequencies making it similar to the conventional OFDM
scheme, thus, allowing use of the efficient fast Fourier transform algorithm to
recover the data. Then, we demonstrate how to use this new approach to control
signal parameters in the case of the continuous spectrum.
