Fiber-optic communication using Hirota modulation and neural networks

Light propagation in models of optical fibers subject to the group velocity dispersion and the nonlinear Kerr effect can be described by the nonlinear Schrodinger equation (NLSE). Multi-solitons are solutions of the integrable NLSE obtained from the discrete spectrum in the nonlinear Fourier transform (NFT). While the eigenvalues in NFT are robust to noise, their spectral amplitudes can be sensitive and carry less information without sophisticated signal processing. We consider a mathematical representation of multi-solitons based on the Hirota bilinearization of the NLSE. The advantage of this approach compared to the standard NFT is that all soliton degrees-of-freedom are robust to perturbations. This enables modulation of the full discrete spectrum over longhaul optical fiber links with low error rates (BERs), improving transmission rates compared to existing methods by leveraging all degrees-of-freedom. On the other hand, while NFT algorithms have been extensively studied, there is no straightforward method to demodulate the spectral amplitudes of the Hirota multi-solitons. To recover these parameters, we apply neural networks (NNs). We consider bandlimited long-haul optical fiber transmission. The information bit stream is encoded using the Hirota modulator at the transmitter. For demodulation, a low-complexity feedforward NN is trained at the receiver, that outputs the spectral amplitudes. We demonstrate 1600 km transmission with 5 bits per spectral amplitude per real dimension with BERs between 1e-4 and 1e-2. The results show that the spectral amplitudes of multi-solitons can be accurately modulated and detected using this approach, and used to transport information over long distances.