Generalization Bounds for Neural Belief Propagation Decoders

Machine learning based approaches are being increasingly used for designing decoders for next generation communication systems. One widely used framework is neural belief propagation (NBP), which unfolds the belief propagation (BP) iterations into a deep neural network and the parameters are trained in a data-driven manner. NBP decoders have been shown to improve upon classical decoding algorithms. In this paper, we investigate the generalization capabilities of NBP decoders. Specifically, the generalization gap of a decoder is the difference between empirical and expected bit-error-rate(s). We present new theoretical results which bound this gap and show the dependence on the decoder complexity, in terms of code parameters (blocklength, message length, variable/check node degrees), decoding iterations, and the training dataset size. Results are presented for both regular and irregular parity-check matrices. To the best of our knowledge, this is the first set of theoretical results on generalization performance of neural network based decoders. We present experimental results to show the dependence of generalization gap on the training dataset size, and decoding iterations for different codes.