6G wireless communication networks require low-latency, ultra-reliable error correction capabilities that adapt to dynamic channel scenarios and block lengths. This study presents a new adaptive neural decoding workflow for 5G-New Radio LDPC base graphs (BG1 and BG2). It combines a weighted Min-Sum (WMS) algorithm with syndrome-aware learning that uses parity-check feedback to guide neural decoding in two key ways: syndrome-based loss and syndrome-conditioned message updates. This approach overcomes the limitations of traditional min-sum (MS) and belief propagation (BP) decoders. To improve message updates among iterations based on real-time parity-check feedback, we first introduce trainable parameters for better training on the most challenging error patterns; a unique data pipeline collects "uncorrected" frame samples at low SNR and generates log-likelihood ratios (LLRs) under the Additive White Gaussian Noise (AWGN) channel and Rayleigh flat-fading channel. The training scheme has two stages: (1) an end-to-end supervised stage focused on minimizing both soft-BER and soft-FER loss across random noisy codewords, and (2) a boosting stage for learning residual corrections using mean-squared error on uncorrected frames. Performance is evaluated across various SNR levels, lifting factors, and code rates. Results show that BG1 outperforms BG2 in the AWGN channel by 1 dB and in the Rayleigh flat-fading channel by 2 dB. To balance reliability and decoding complexity, early convergence is achieved within 10 to 20 iterations. Additionally, lower rates and higher lifting factors produce sharper waterfalls and error floors below 10−7 and 10−8 for AWGN and Rayleigh, respectively. The proposed framework generalizes to different channel types and LDPC designs and offers a 0.3 dB waterfall gain compared to traditional neural Min–Sum decoders. These results demonstrate adaptable, high-performance error correction suitable for various wireless applications, highlighting the practicality of syndrome-aware WMS neural decoding for future 6G standards.
6G wireless communication networks require low-latency, ultra-reliable error correction capabilities that adapt to dynamic channel scenarios and block lengths. This study presents a new adaptive neural decoding workflow for 5G-New Radio LDPC base graphs (BG1 and BG2). It combines a weighted Min-Sum (WMS) algorithm with syndrome-aware learning that uses parity-check feedback to guide neural decoding in two key ways: syndrome-based loss and syndrome-conditioned message updates. This approach overcomes the limitations of traditional min-sum (MS) and belief propagation (BP) decoders. To improve message updates among iterations based on real-time parity-check feedback, we first introduce trainable parameters for better training on the most challenging error patterns; a unique data pipeline collects "uncorrected" frame samples at low SNR and generates log-likelihood ratios (LLRs) under the Additive White Gaussian Noise (AWGN) channel and Rayleigh flat-fading channel. The training scheme has two stages: (1) an end-to-end supervised stage focused on minimizing both soft-BER and soft-FER loss across random noisy codewords, and (2) a boosting stage for learning residual corrections using mean-squared error on uncorrected frames. Performance is evaluated across various SNR levels, lifting factors, and code rates. Results show that BG1 outperforms BG2 in the AWGN channel by 1 dB and in the Rayleigh flat-fading channel by 2 dB. To balance reliability and decoding complexity, early convergence is achieved within 10 to 20 iterations. Additionally, lower rates and higher lifting factors produce sharper waterfalls and error floors below 10−7 and 10−8 for AWGN and Rayleigh, respectively. The proposed framework generalizes to different channel types and LDPC designs and offers a 0.3 dB waterfall gain compared to traditional neural Min–Sum decoders. These results demonstrate adaptable, high-performance error correction suitable for various wireless applications, highlighting the practicality of syndrome-aware WMS neural decoding for future 6G standards.
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.
Ensuring extremely high reliability in channel coding is essential for 6G networks. The next-generation of ultra-reliable and low-latency communications (xURLLC) scenario within 6G networks requires frame error rate (FER) below 10-9. However, low-density parity-check (LDPC) codes, the standard in 5G new radio (NR), encounter a challenge known as the error floor phenomenon, which hinders to achieve such low frame error rates. To tackle this problem, we introduce an innovative solution: boosted neural min-sum (NMS) decoder. This decoder operates identically to conventional NMS decoders, but is trained by novel training methods including: i) boosting learning with uncorrected vectors, ii) block-wise training schedule to address the vanishing gradient issue, iii) dynamic weight sharing to minimize the number of trainable weights, iv) transfer learning to reduce the required sample count, and v) data augmentation to expedite the sampling process. Leveraging these training strategies, the boosted NMS decoder achieves the state-of-the art performance in reducing the error floor as well as superior waterfall performance. Remarkably, we fulfill the 6G xURLLC requirement for 5G LDPC codes without a severe error floor. Additionally, the boosted NMS decoder, once its weights are trained, can perform decoding without additional modules, making it highly practical for immediate application. The source code is available athttps://github.com/ghy1228/LDPC_Error_Floor.
This thesis investigates the optimization of Low-Density Parity-Check (LDPC) decoding through machine learning techniques, with a specific focus on 5G communication systems. Traditional LDPC decoding algorithms face a critical trade-off: Belief Propagation (BP) offers excellent error-correction performance but with high computational complexity, while Min-Sum (MS) reduces complexity at the cost of degraded performance. To address this limitation, a hybrid neural network architecture is proposed that incorporates learnable normalization and offset weights into the message-passing framework of LDPC decoders. This approach integrates multiplicative (normalization) and additive (offset) weights into the Tanner graph structure, allowing the decoder to adapt to specific channel conditions. A novel weighted binary cross-entropy loss function is developed that prioritizes entire block recovery by assigning different importance to information and parity bits during training. Experimental results demonstrate that ML-assisted decoder consistently outperforms conventional Min-Sum decoding, approaching the error-correction capability of Belief Propagation while maintaining comparable computational efficiency to Min-Sum. Comprehensive evaluations across different weight configurations (scalar and vector-based) reveal that increased parametrization generally improves decoding performance. Analysis of the impact of iteration counts shows that the optimal number of decoding iterations varies between different code configurations with studied Basegraph 1 case requiring 15 iterations for optimal performance while studied Basegraph 2 case benefits significantly from 20 iterations. The proposed ML-assisted LDPC decoder represents a significant advancement for 5G systems, offering improved error correction at lower signal strengths while balancing latency and computational requirements. This research contributes to the ongoing evolution of wireless technology by demonstrating how machine learning can effectively enhance traditional decoding algorithms, providing a practical pathway toward more efficient and adaptive error correction in modern communication systems.
Low-density parity-check(LDPC) code has been selected as the channel coding method by 5G NR because of its excellent error-correcting performance. To further improve the performance of LDPC decoding, this paper proposes a neural normalized min-sum(NNMS) algorithm based on multi-edge-type(MET). Based on the LLR convergence analysis of the protograph matrix of 5G NR, the base matrix is divided into several independent regions. Each part is assigned a unique scaling factor at different iterations. To verify the effectiveness of the proposed algorithm, We use two parity-check matrixes(PCM) derived from different base graphs in simulations. The results show that the proposed algorithm performs at most 0.45dB better than BP, 0.37dB better than NMS, and 0.25dB better than OMS, respectively, when the frame error rate (FER) is at 10−5 level over additive white Gaussian noise (AWGN) channels using BPSK modulation.
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.
Recently a number of low-density parity-check (LDPC) decoding algorithms based on deep learning have been proposed in the literature. However, most of the work has been targeted for additive white Gaussian noise (AWGN) channels. For more practical scenarios, in this paper we investigate the neural-network based min-sum (MS) decoding for protograph LDPC codes in fading channels. Since the wireless channel is complex and varying, accurate channel state information (CSI) cannot be always available at the receiver. We classify the scenarios into three cases with perfect CSIs, imperfect CSIs, and no CSIs. By assigning learnable weights on the edges in the iterative decoding, the proposed neural decoder compensates for the performance loss caused by the error/lack of CSIs. The trajectory-based extrinsic information transfer (T-EXIT) chart is employed as a theoretical tool to select the proper training dataset for the neural network and the proper channel initialization scheme for the receiver. Numerical results in terms of block error rates are provided, which agree with the T-EXIT analysis. It can be seen that the proposed neural MS decoder clearly outperforms the traditional MS algorithm in Rayleigh fading channels. Meanwhile, the proposed decoder shows a good compatibility so that it can be applied to the cases with different accuracy of CSIs.