  In this work, we propose a novel decoding algorithm for short block codes
based on an edge-weighted graph neural network (EW-GNN). The EW-GNN decoder
operates on the Tanner graph with an iterative message-passing structure, which
algorithmically aligns with the conventional belief propagation (BP) decoding
method. In each iteration, the "weight" on the message passed along each edge
is obtained from a fully connected neural network that has the reliability
information from nodes/edges as its input. Compared to existing
deep-learning-based decoding schemes, the EW-GNN decoder is characterised by
its scalability, meaning that 1) the number of trainable parameters is
independent of the codeword length, and 2) an EW-GNN decoder trained with
shorter/simple codes can be directly used for longer/sophisticated codes of
different code rates. Furthermore, simulation results show that the EW-GNN
decoder outperforms the BP and deep-learning-based BP methods from the
literature in terms of the decoding error rate.
