Generalization Bounds for Neural Belief Propagation Decoders
This work addresses the need for theoretical guarantees in machine learning-based decoders for communication systems, providing foundational insights into generalization performance, which is incremental as it builds on existing NBP methods.
The paper tackles the problem of understanding the generalization capabilities of neural belief propagation (NBP) decoders in communication systems, presenting theoretical bounds on the generalization gap that depend on decoder complexity and training dataset size, with experimental results showing this dependence for various codes.
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.