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.
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.
The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with the codelength, thus they can only support short to moderate codelengths. From the point view of practicality, we propose a high-performance neural min-sum (MS) decoding method that makes full use of the lifting structure of protograph low-density parity-check (LDPC) codes. By this means, the size of the parameter array of each layer in the neural decoder only equals the number of edge-types for arbitrary codelengths. In particular, for protograph LDPC codes, the proposed neural MS decoder is constructed in a special way such that identical parameters are shared by a bundle of edges derived from the same edge-type. To reduce the complexity and overcome the vanishing gradient problem in training the proposed neural MS decoder, an iteration-by-iteration (i.e., layer-by-layer in neural networks) greedy training method is proposed. With this, the proposed neural MS decoder tends to be optimized with faster convergence, which is aligned with the early termination mechanism widely used in practice. To further enhance the generalization ability of the proposed neural MS decoder, a codelength/rate compatible training method is proposed, which randomly selects samples from a set of codes lifted from the same base code. As a theoretical performance evaluation tool, a trajectory-based extrinsic information transfer (T-EXIT) chart is developed for various decoders. Both T-EXIT and simulation results show that the optimized MS decoding can provide faster convergence and up to 1dB gain compared with the plain MS decoding and its variants with only slightly increased complexity. In addition, it can even outperform the sum-product algorithm for some short codes.
The min-sum (MS) decoding for low-density parity-check codes, though less complex than the sum–product algorithm, suffers from worse error-correcting performance. For enhancement, neural MS decoders leveraging deep learning have recently been introduced, but how to train them has not been sufficiently discussed. In this paper, we propose a novel dataset construction method and also propose systematic learning strategies by finding a good combination of dataset composition, loss functions, weight sharing, weight assignment , and weight update method. Simulations demonstrate that the proposed method achieves better error-correcting performance than other works, especially in the error floor region, within a limited number of iterations.
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 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.
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.
In this paper, layered min-sum (MS) iterative decoding is formulated as a customized neural network following the sequential scheduling of check node (CN) updates. By virtue of the lifting structure of protograph low-density parity-check (LDPC) codes, identical network parameters are shared among all derived edges originating from the same edge in the protograph, which makes the number of learn- able parameters manageable. The proposed neural layered MS decoder can support arbitrary codelengths consequently. Moreover, an iteration-wise greedy training method is proposed to tune the parameters such that it avoids the vanishing gradient problem and accelerates the decoding convergence.