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A deep learning assisted sum-product detection algorithm (DL-SPDA) for faster-than-Nyquist (FTN) signaling is proposed in this paper. The proposed detection algorithm works on a modified factor graph which concatenates a neural network function node to the variable nodes of the conventional FTN factor graph to approach the maximum a posterior probabilities (MAP) error performance. In specific, the neural network performs as a function node in the modified factor graph to deal with the residual intersymbol interference (ISI) that is not considered by the conventional detector with a limited complexity. 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 receiver. Furthermore, we propose a compatible training technique to improve the detection performance of the proposed DL-SPDA with turbo equalization. In particular, the neural network is optimized in terms of the mutual information between the transmitted sequence and the extrinsic information. We also investigate the maximum-likelihood bit error rate (BER) performance of a finite length coded FTN system. Simulation results show that the error performance of the proposed algorithm approaches the MAP performance, which is consistent with the analytical BER.

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., 5 pages, 7 figures, accepted by IEEE ITW 2019