  In this work, we propose a fully differentiable graph neural network
(GNN)-based architecture for channel decoding and showcase a competitive
decoding performance for various coding schemes, such as low-density
parity-check (LDPC) and BCH codes. The idea is to let a neural network (NN)
learn a generalized message passing algorithm over a given graph that
represents the forward error correction (FEC) code structure by replacing node
and edge message updates with trainable functions. Contrary to many other deep
learning-based decoding approaches, the proposed solution enjoys scalability to
arbitrary block lengths and the training is not limited by the curse of
dimensionality. We benchmark our proposed decoder against state-of-the-art in
conventional channel decoding as well as against recent deep learning-based
results. For the (63,45) BCH code, our solution outperforms weighted belief
propagation (BP) decoding by approximately 0.4 dB with significantly less
decoding iterations and even for 5G NR LDPC codes, we observe a competitive
performance when compared to conventional BP decoding. For the BCH codes, the
resulting GNN decoder can be fully parametrized with only 9640 weights.
