Optimizing LDPC Decoding with Machine Learning Using Learnable Weights: A Hybrid Framework Integrating Neural Networks with Iterative Message-Passing for Enhanced Error-Correction in 5G Systems
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.
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.
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.
Wireless communication is rapidly evolving, and this evolution has led to increasing demands for better error correction, lower latency, and higher adaptability, particularly in Beyond 5G (B5G) networks. Traditional channel coding methods like Low-density Parity-check (LDPC) and Turbo codes often struggle to meet these advanced requirements. To address this challenge, we explore the use of Graph Neural Networks (GNNs) to enhance LDPC decoding. By imposing the structured nature of the Tanner graph, GNNs improve decoding accuracy, optimize bit error rate (BER), and adapt to changing signal conditions in real-time. We implement and evaluate our approach using MATLAB and Python, training our ML-based decoder on varying SNR levels to ensure robustness. The results show that integrating machine learning into LDPC decoding significantly enhances error correction and communication reliability. This work highlights the potential of ML-driven techniques in shaping the future of wireless networks.
Low-density parity-check (LDPC) codes have been one of the most popular error correction candidates in modern communication and data storage systems for the past three decades due to their capacity-approaching error correction capability under the Belief Propagation (BP) decoding algorithms. In this dissertation, we investigate three topics related to efficient and effective decoding algorithms and the code design of LDPC codes. In the first part of this dissertation, we propose a methodology with the help of artificial intelligence to design Finite Alphabet Iterative Decoders (FAID) for LDPC codes, which are not only of great theoretical but also practical importance. This model-driven neural network (NN) framework unfolds the decoding iterations, introduces quantized neural networks (QNN) to model the FAIDs, and proposes a new cost function, namely, bit error rate (BER), to address the inefficiency in discrete-output channel scenarios. The low precision activations in the QNN and quantization in the cost functions cause a critical issue that their gradients vanish almost everywhere, making it difficult to use classical backward propagation. We design and leverage straight-through estimators as surrogate gradients to tackle this issue and provide a joint training scheme. These QNN-aided FAIDs, are capable of surpassing the floating-point BP algorithms, with much lower complexity and faster convergence. The QNN-aided approach is general, as it can be applied to both continuous and discrete-output channels. In the second part of this dissertation, we propose a new code construction of LDPC codes based on the conventional parity-check matrices of Reed-Solomon (RS) codes. We investigate the girth and cycle structure and introduce an efficient searching algorithm to reduce short cycles in their Tanner graphs and to construct LDPC codes with a girth of at least eight. We use masking to further reduce the number of short cycles and to adjust the column and row weights of the parity-check matrices of the constructed codes for performance improvement. Our designs are systematic and flexible, which balance the requirements of good waterfall performance and low error-floor while maintaining a structure that facilitates implementation. In the third part of this dissertation, we investigate binary quasi-cyclic (QC) LDPC codes and their capability to correct phased bursts of erasures. We prove that the peeling algorithm when applied to such parity-check matrices of column weight two can correct all erasures that can be corrected by a maximum likelihood (ML) decoder. We show that by modifying the parity-check matrices of column weight two and globally coupling them, the erasure correcting capability can be further enhanced. For the Additive White Gaussian Noise (AWGN) channel, we design QC LDPC codes with parity-check matrices of column weight three or more that can correct phased bursts of erasures and perform well over the AWGN channel. Our analysis of QC-LDPC codes with parity-check matrices of column weight two is rather comprehensive as we determine, for all such codes, their dimensions, minimum Hamming distances, and their capabilities to correct phased bursts.
Today's modern wireless communication systems demand extensive quality and computational power with an increase in day-to-day data-rate standards. The latest com-munication standards focus on low latency, high throughput, and reliable error correction capabilities which inspired us to explore the 5G New Generation (NR) technology. Low-Density Parity-Check Codes (LDPC) are known to have error correction capabilities that can achieve Shannon's maximum channel ca-pacity. Encoding of LDPC Codes features a sparse property that enables effortless decoding at the receiver end. Advancements in deep learning have helped in estimating the channel noise more accurately. The Iterative Belief Propagation-Convolutional Neural Network (BP-CNN) architecture involves a CNN block which is trained with a quadratic loss function concatenated to a standard BP Decoder. The proposed Iterative BP-CNN architecture with a Batch Normalization layer results in a better performance compared to the Iterative BP-CNN architecture as it standardizes the input to the CNN block and also solves the problem of vanishing gradients during backpropagation.
With the deployment of 5G networks, the Internet of Things (IoT) has experienced a transformative boost, enabling higher data rates, reduced latency, and the connection of millions of devices across applications like smart cities, healthcare, and industrial automation. However, in real-world scenarios, the performance of Low-Density Parity-Check (LDPC) codes, the preferred channel coding scheme in 5G, is severely affected by noise and fading environments, particularly colored noise, which distorts signals over certain frequency bands. Colored noise introduces correlation in the interference, unlike white noise, thereby posing a challenge in decoding, especially in fading channels such as Rayleigh, Rician, and Nakagami-m. In this work, we propose a novel approach that combines the Iterative Offset Min-Sum (OMS) algorithm with a Convolutional Neural Network (CNN) to enhance LDPC decoding efficiency in 5G-enabled IoT networks. Our proposed OMS-CNN hybrid architecture addresses the limitations imposed by colored noise in fading channels by employing deep learning techniques for accurate noise estimation and mitigation. Furthermore, the OMS algorithm mitigates the overestimation of noise correction, refining the output in iterative decoding steps. Through comprehensive simulations, the OMS-CNN decoder demonstrates substantial improvements over traditional decoding approaches. Specifically, it achieves a performance enhancement of 2.7 dB at a bit error rate (BER) of [Formula: see text] across a range of fading channels. The study examines the decoder's performance in environments characterized by Rayleigh, Rician, and Nakagami-m fading models, highlighting the robustness of the proposed solution under different channel conditions. Additionally, this research explores the influence of parameters such as the correlation coefficient of the noise, the scaling factor in the cost function, and the number of iterations between the CNN and OMS decoding steps.
Machine Learning (ML) has proven to be an effective tool for optimizing several aspects of channel codes in communication systems. In this work, ML-based schemes have been adapted to the 5G New Radio (NR) Low-Density Parity Check (LDPC) codes to help them meet the stringent requirements of ultra-reliable low-latency communications (URLLC) in 5G NR. Furthermore, enhancements to the modulation schemes have also been applied to attempt to outperform the complex and robust Layered Belief Propagation Algorithm (LBPA) using the lower complexity Normalized Min-Sum Algorithm (NMSA) decoder. By combining the ML-based schemes and the enhanced modulation schemes, NMSA effectively provided Eb/N0 gains of up to 1 dB and latency reductions of up to 0.53 ms compared to the conventional Layered Belief Propagation Algorithm.