  A deep learning assisted sum-product detection algorithm (DL-SPA) for
faster-than-Nyquist (FTN) signaling is proposed in this paper. The proposed
detection algorithm concatenates a neural network to the variable nodes of the
conventional factor graph of the FTN system to help the detector converge to
the a posterior probabilities based on the received sequence. More
specifically, the neural network performs as a function node in the modified
factor graph to deal with the residual intersymbol interference (ISI) that is
not modeled by the conventional detector with a limited number of ISI taps. We
modify the updating rule in the conventional sum-product algorithm so that the
neural network assisted detector can be complemented to a Turbo equalization.
Furthermore, a simplified convolutional neural network is employed as the
neural network function node to enhance the detector's performance and the
neural network needs a small number of batches to be trained. Simulation
results have shown that the proposed DL-SPA achieves a performance gain up to
2.5 dB with the same bit error rate compared to the conventional sum-product
detection algorithm under the same ISI responses.
