Various embodiments and implementations of graph-neural-network (GNN)-based decoding applications are disclosed. The GNN-based decoding schemes are broadly applicable to different coding schemes, and capable of operating on both binary and non-binary codewords, in different implementations. Advantageously, the inventive GNN-based decoding is scalable, even with arbitrary block lengths, and not subject to typical limits with respect to dimensionality. Decoding performance of the inventive GNN-based techniques demonstrably matches or outpaces BCH and LDPC (both regular and 5G NR) decoding algorithms, while exhibiting improvements with respect to number of iterations required and scalability of the GNN-based approach. These inventive concepts are implemented, according to various embodiments, as methods, systems, and computer program products.