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.
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.
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.
Abstract In the evolving landscape of wireless communication, particularly in Beyond 5G (B5G) systems, channel coding must meet increasingly demanding requirements for reliability, adaptability, and low latency. Traditional decoding algorithms such as Belief Propagation (BP), while effective in structured environments, lack the flexibility to adapt to dynamic and noisy channel conditions. This paper presents a novel Graph Neural Network (GNN)-based approach for decoding Low-Density Parity-Check (LDPC) codes, leveraging the inherent bipartite graph structure of Tanner graphs. The proposed decoder learns data-driven message-passing strategies that outperform BP across a wide range of signal-to-noise ratios (SNRs) and block lengths.Our implementation integrates Python-based GNN modeling with MATLAB-based LDPC encoding and benchmarks the decoding performance under additive white Gaussian noise (AWGN) channels. Experimental results demonstrate that the GNN-based decoder achieves significantly lower bit error rates (BER), faster convergence, and superior robustness to noise variability compared to BP, particularly at medium-to-high SNR levels. Furthermore, an ablation study validates the architectural efficiency of shallow GNNs with attention mechanisms and skip connections. This work highlights the potential of machine learning-enhanced decoders in redefining the physical layer of next-generation wireless networks and sets the foundation for scalable, adaptive, and intelligent decoding systems in B5G and 6G architectures.
Next-generation communication systems face challenges in meeting the growing demand of ultra-reliable low-latency communications (URLLC), which require advanced physical-layer designs, especially in channel coding. To satisfy the strict reliability and latency constraints of URLLC in 5G and emerging 6G networks, it is essential to use short codes with robust error-correction capabilities. This thesis explores the application of deep learning methodologies to develop advanced channel coding frameworks for short linear block codes. First, I 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, algorithmically aligning with conventional belief propagation (BP) decoding. The decoder is characterized by scalability, with trainable parameters independent of codeword length, and outperforms BP and existing deep-learning-based methods. I present a novel auto-encoder integrating deep reinforcement learning (DRL) and graph neural networks (GNN) for end-to-end channel coding. Code generation is modeled as a Markov decision process to optimize error rates and algebraic properties. An iterative joint training of the DRL-based code designer and the EW-GNN decoder is performed to optimise the end-to-end encoding and decoding process. Simulation results show significant improvements over traditional coding schemes including LDPC and BCH codes. Finally, I design a supervised learning framework using an integrated auto-encoder architecture with a systematic code generator and matrix-based adaptive double-weighted (MA-DW) decoder. This approach achieves superior performance compared to conventional systems while reducing training complexity through joint optimization of code design and decoding parameters.
In this work, we propose a fully differentiable iterative decoder for quantum low-density parity-check (LDPC) codes. The proposed algorithm is composed of classical belief propagation (BP) decoding stages and intermediate graph neural network (GNN) layers. Both components of the decoder are defined over the same sparse decoding graph enabling a seamless integration and scalability to large codes. The core idea is to use the GNN component between consecutive BP runs so that the knowledge from the previous BP run can be leveraged to better initialize the next BP run. This enables the proposed decoder to learn to compensate for sub-optimal BP decoding graphs that result from the design constraints of quantum LDPC codes. Since the entire decoder remains differentiable, gradient descent-based training is possible. We compare the error rate performance of the proposed decoder against various post-processing methods such as random perturbation, enhanced feedback, augmentation, and ordered-statistics decoding (OSD) and show that a carefully designed training process lowers the error-floor significantly. As a result, our proposed decoder outperforms the former three methods using significantly fewer post-processing attempts. The source code of our experiments is available online.
With changing scenarios in Beyond 5G (B5G) systems, channel coding methods will be faced with stronger requirements for reliability, flexibility, and low latency.Conventional decoding algorithms such as Belief Propagation (BP) are efficient in structured contexts but not sufficiently flexible to respond effectively to dynamic and noisy channel conditions.In this study, we introduces a new Graph Neural Network (GNN)-based solution to decode Low-Density Parity-Check (LDPC) codes by taking advantage of the intrinsic bipartite graph representation of Tanner graphs.The proposed decoder learns a data-driven messagepassing algorithm that performs better than BP over a large range of signal-to-noise ratios (SNRs) and block lengths.The experimental results show that the GNN-based decoder yields much lower bit error rates (BER), faster convergence, and better resistance to noise variability than belief propagation, especially at medium to high SNR levels.Thus, our findings highlight the foundation for scalable, adaptive, and intelligent decoding systems in B5G and 6G architectures.
Quantum computing requires effective error correction strategies to mitigate noise and decoherence. Quantum Low-Density Parity-Check (QLDPC) codes have emerged as a promising solution for scalable Quantum Error Correction (QEC) applications by supporting constant-rate encoding and a sparse parity-check structure. However, decoding QLDPC codes via traditional approaches such as Belief Propagation (BP) suffers from poor convergence in the presence of short cycles. Machine learning techniques like Graph Neural Networks (GNNs) utilize learned message passing over their node features; however, they are restricted to pairwise interactions on Tanner graphs, which limits their ability to capture higher-order correlations. In this work, we propose HyperNQ, the first Hypergraph Neural Network (HGNN)- based QLDPC decoder that captures higher-order stabilizer constraints by utilizing hyperedges-thus enabling highly expressive and compact decoding. We use a two-stage message passing scheme and evaluate the decoder over the pseudo-threshold region. Below the pseudo-threshold mark, HyperNQ improves the Logical Error Rate (LER) up to 84% over BP and 50% over GNN-based strategies, demonstrating enhanced performance over the existing state-of-the-art decoders.