A receiver configured to receive wave packets encoded with data via a nonlinear channel is disclosed. The receiver includes an input configured to receive the wave packets from the non-linear channel. The receiver also includes a processor configured to generate a transfer matrix from the received wave packets and find the representation of the transfer matrix as ratios of polynomials and compute the non-linear Fourier spectrum in which the data has been embedded. The receiver may also include a demodulator configured to demodulate the non-linear Fourier spectrum to recover the data. Periodic boundary conditions may be selected. Boundary conditions may be selected based on a non-periodic vanishing signal. The received wave packets may be configured as solitons. The nonlinear channel may be an optical channel.