Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2405.13413 · IEEE Journal on Selected Areas in Communications

Boosted Neural Decoders: Achieving Extreme Reliability of LDPC Codes for 6G Networks

Hee-Youl Kwak, Dae-Young Yun, Yongjune Kim, Sang‐Hyo Kim, Jong‐Seon No

Published Jan 20, 2025• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/jsac.2025.3531553

Related papers

Boosting Learning for LDPC Codes to Improve the Error-Floor Performance

Hee-Youl Kwak, Dae-Young Yun, Yongjune Kim +2 more

Low-density parity-check (LDPC) codes have been successfully commercialized in communication systems due to their strong error correction capabilities and simple decoding process. However, the error-floor phenomenon of LDPC codes, in which the error rate stops decreasing rapidly at a certain level, presents challenges for achieving extremely low error rates and deploying LDPC codes in scenarios demanding ultra-high reliability. In this work, we propose training methods for neural min-sum (NMS) decoders to eliminate the error-floor effect. First, by leveraging the boosting learning technique of ensemble networks, we divide the decoding network into two neural decoders and train the post decoder to be specialized for uncorrected words that the first decoder fails to correct. Secondly, to address the vanishing gradient issue in training, we introduce a block-wise training schedule that locally trains a block of weights while retraining the preceding block. Lastly, we show that assigning different weights to unsatisfied check nodes effectively lowers the error-floor with a minimal number of weights. By applying these training methods to standard LDPC codes, we achieve the best error-floor performance compared to other decoding methods. The proposed NMS decoder, optimized solely through novel training methods without additional modules, can be integrated into existing LDPC decoders without incurring extra hardware costs. The source code is available at https://github.com/ghy1228/LDPC_Error_Floor .

arXiv:2310.07194•neural information processing systems•Jan 1, 2023•11 citations

Neural Self-Corrected Min-Sum Decoder for NR LDPC Codes

Taehyun Kim, Joo Sung Park

In this letter, a neural self-corrected min-sum (NSCMS) decoder is proposed for 5G new radio (NR) low-density parity-check (LDPC) codes. Training in real-time on a rapidly changing channel requires low latency and minimal resource utilization. Unfortunately, typical neural decoders for LDPC codes use large and deep neural networks proportional to the code length, leading to latency and resource problems. In the network of NSCMS similar to network model pruning, certain nodes meeting the self correction condition are deleted and excluded from learning. This reduces the computational complexity of learning, compared to conventional networks. Thus, the NSCMS decoder has high practicality in real-time training using machine learning. Furthermore, self-correction allows for more reliable message-based learning and significantly improves performance. Simulation results demonstrate that NSCMS decoders exhibit lower error rates than previously proposed min-sum decoders.

IEEE Communications Letters•May 22, 2024•7 citations

Neural-Network-Optimized Degree-Specific Weights for LDPC MinSum Decoding

Linfang Wang, Sean Chen, Jonathan Nguyen +2 more

Neural Normalized MinSum (N-NMS) decoding delivers better frame error rate (FER) performance on linear block codes than conventional Normalized MinSum (NMS) by assigning dynamic multiplicative weights to each check-to-variable node message in each iteration. Previous N-NMS efforts primarily investigated short block codes (N < 1000), because the number of N-NMS parameters required to be trained scales proportionately to the number of edges in the parity check matrix and the number of iterations. This imposes an impractical memory requirement for conventional tools such as Pytorch and Tensorflow to create the neural network and store gradients. This paper provides efficient methods of training the parameters of N-NMS decoders that support longer block lengths. Specifically, this paper introduces a family of Neural 2-dimensional Normalized (N-2D-NMS) decoders with various reduced parameter sets and shows how performance varies with the parameter set selected. The N-2D-NMS decoders share weights with respect to check node and/or variable node degree. Simulation results justify a reduced parameter set, showing that the trained weights of N- NMS have a smaller value for the neurons corresponding to larger check/variable node degree. Further simulation results on a (3096,1032) Protograph-Based Raptor-Like (PBRL) code show that the N-2D-NMS decoder can achieve the same FER as N- NMS while also providing at least a 99.7% parameter reduction. Furthermore, the N-2D-NMS decoder for the (16200,7200) DVBS- 2 standard LDPC code shows a lower error floor than belief propagation. Finally, this paper proposes a hybrid decoder training structure that utilizes a neural network which combines a feedforward module with a recurrent module. The decoding performance and parameter reduction of the hybrid training depends on the length of recurrent module of the neural network.

arXiv:2107.04221•International Symposium on Turbo Codes and Iterative Information Processing•Aug 30, 2021•22 citations

Performance Enhancement of Low-Density Parity-Check Decoder Using Neural Network Optimized Parameters

Amany Sabah Hassan, Mohammed Abdullah Hussein ElSheikh

Low-density parity-check (LDPC) codes are of prime importance in achieving near-Shannon capacity in current communication systems. However, the optimal decoding process for LDPC codes is computationally intensive. This paper presents a neural normalized min-sum (NNMS) decoding network that improves error correction capabilities with minimal computational overhead. A weight-sharing approach is adopted in the NNMS model, in which the correction factors (α, β) are shared across nodes within a single layer. This approach decreases the total number of parameters in the model compared to traditional neural decoders, making it easier for hardware implementation. The NNMS model is tested using a (576, 432) LDPC code for an additive white Gaussian noise channel with binary phase shift keying modulation. Simulation results show that the NNMS model outperforms traditional normalized min-sum (NMS) decoders. At a signal-to-noise ratio of 5 dB, the NNMS model has a bit-error rate (BER) of 1.0 × 10−7, whereas traditional NMS models have a less steep slope. In particular, the NNMS model has a coding gain of 1.25 dB compared to the traditional NMS model at a BER threshold of 1.0 × 10−3. This shows that the NNMS model is an efficient solution for high-performance, real-time digital communication systems.

UHD Journal of Science and Technology•Jul 5, 2026•0 citations

Learning About Syndrome Awareness and WMS Algorithm for Adaptive Neural Decoding for 6G LDPC Base Graph Enhancement

Noor Salih Mohammed, Ahmed Ghanim Wadday, Bashar Jabbar Hamza

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.

The Eurasia Proceedings of Science Technology Engineering and Mathematics•Nov 30, 2025•0 citations

Normalized Min-Sum Neural Network for LDPC Decoding

Qing Wang, Qing Liu, Shunfu Wang +5 more

The success of deep learning has encouraged its applications in decoding error-correcting codes, e.g., LDPC decoding. In this paper, we propose a model-driven deep learning method for normalized min-sum (NMS) low-density parity-check (LDPC) decoding, namely neural NMS (NNMS) LDPC decoding network. By unfolding the iterative decoding progress between checking nodes (CNs) and variable nodes (VNs) into a feed-forward propagation network, we can harvest the benefits of both the model-driven deep learning and the conventional normalized min-sum (NMS) LDPC decoding method. In addition, we proposed a shared parameters NNMS with the LeakyReLU and a 12-bit quantizer (SNNMS-LR-Q) which reduces the number of required multipliers and correction factors by sharing parameters, increasing the nonlinear fitting ability by adding LeakyReLU. By utilizing the 12-bit quantizer, we can improve the confrontation ability. Thorough experiments with different code lengths, code rates, channel conditions, and check matrices are implemented to demonstrate the advantages and robustness of our proposed networks. The BER performance of the proposed NNMS is 1.5 dB better than the NMS, using fewer iterations. Meanwhile, The SNNMS-LR-Q outperforms the NNMS regarding the BER performance and efficiency.

IEEE Transactions on Cognitive Communications and Networking•Oct 6, 2022•31 citations
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.
Low-density parity-check (LDPC) codes have been successfully commercialized in communication systems due to their strong error correction capabilities and simple decoding process. However, the error-floor phenomenon of LDPC codes, in which the error rate stops decreasing rapidly at a certain level, presents challenges for achieving extremely low error rates and deploying LDPC codes in scenarios demanding ultra-high reliability. In this work, we propose training methods for neural min-sum (NMS) decoders to eliminate the error-floor effect. First, by leveraging the boosting learning technique of ensemble networks, we divide the decoding network into two neural decoders and train the post decoder to be specialized for uncorrected words that the first decoder fails to correct. Secondly, to address the vanishing gradient issue in training, we introduce a block-wise training schedule that locally trains a block of weights while retraining the preceding block. Lastly, we show that assigning different weights to unsatisfied check nodes effectively lowers the error-floor with a minimal number of weights. By applying these training methods to standard LDPC codes, we achieve the best error-floor performance compared to other decoding methods. The proposed NMS decoder, optimized solely through novel training methods without additional modules, can be integrated into existing LDPC decoders without incurring extra hardware costs. The source code is available at https://github.com/ghy1228/LDPC_Error_Floor .
In this letter, a neural self-corrected min-sum (NSCMS) decoder is proposed for 5G new radio (NR) low-density parity-check (LDPC) codes. Training in real-time on a rapidly changing channel requires low latency and minimal resource utilization. Unfortunately, typical neural decoders for LDPC codes use large and deep neural networks proportional to the code length, leading to latency and resource problems. In the network of NSCMS similar to network model pruning, certain nodes meeting the self correction condition are deleted and excluded from learning. This reduces the computational complexity of learning, compared to conventional networks. Thus, the NSCMS decoder has high practicality in real-time training using machine learning. Furthermore, self-correction allows for more reliable message-based learning and significantly improves performance. Simulation results demonstrate that NSCMS decoders exhibit lower error rates than previously proposed min-sum decoders.
Neural Normalized MinSum (N-NMS) decoding delivers better frame error rate (FER) performance on linear block codes than conventional Normalized MinSum (NMS) by assigning dynamic multiplicative weights to each check-to-variable node message in each iteration. Previous N-NMS efforts primarily investigated short block codes (N < 1000), because the number of N-NMS parameters required to be trained scales proportionately to the number of edges in the parity check matrix and the number of iterations. This imposes an impractical memory requirement for conventional tools such as Pytorch and Tensorflow to create the neural network and store gradients. This paper provides efficient methods of training the parameters of N-NMS decoders that support longer block lengths. Specifically, this paper introduces a family of Neural 2-dimensional Normalized (N-2D-NMS) decoders with various reduced parameter sets and shows how performance varies with the parameter set selected. The N-2D-NMS decoders share weights with respect to check node and/or variable node degree. Simulation results justify a reduced parameter set, showing that the trained weights of N- NMS have a smaller value for the neurons corresponding to larger check/variable node degree. Further simulation results on a (3096,1032) Protograph-Based Raptor-Like (PBRL) code show that the N-2D-NMS decoder can achieve the same FER as N- NMS while also providing at least a 99.7% parameter reduction. Furthermore, the N-2D-NMS decoder for the (16200,7200) DVBS- 2 standard LDPC code shows a lower error floor than belief propagation. Finally, this paper proposes a hybrid decoder training structure that utilizes a neural network which combines a feedforward module with a recurrent module. The decoding performance and parameter reduction of the hybrid training depends on the length of recurrent module of the neural network.
Low-density parity-check (LDPC) codes are of prime importance in achieving near-Shannon capacity in current communication systems. However, the optimal decoding process for LDPC codes is computationally intensive. This paper presents a neural normalized min-sum (NNMS) decoding network that improves error correction capabilities with minimal computational overhead. A weight-sharing approach is adopted in the NNMS model, in which the correction factors (α, β) are shared across nodes within a single layer. This approach decreases the total number of parameters in the model compared to traditional neural decoders, making it easier for hardware implementation. The NNMS model is tested using a (576, 432) LDPC code for an additive white Gaussian noise channel with binary phase shift keying modulation. Simulation results show that the NNMS model outperforms traditional normalized min-sum (NMS) decoders. At a signal-to-noise ratio of 5 dB, the NNMS model has a bit-error rate (BER) of 1.0 × 10−7, whereas traditional NMS models have a less steep slope. In particular, the NNMS model has a coding gain of 1.25 dB compared to the traditional NMS model at a BER threshold of 1.0 × 10−3. This shows that the NNMS model is an efficient solution for high-performance, real-time digital communication systems.
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.
The success of deep learning has encouraged its applications in decoding error-correcting codes, e.g., LDPC decoding. In this paper, we propose a model-driven deep learning method for normalized min-sum (NMS) low-density parity-check (LDPC) decoding, namely neural NMS (NNMS) LDPC decoding network. By unfolding the iterative decoding progress between checking nodes (CNs) and variable nodes (VNs) into a feed-forward propagation network, we can harvest the benefits of both the model-driven deep learning and the conventional normalized min-sum (NMS) LDPC decoding method. In addition, we proposed a shared parameters NNMS with the LeakyReLU and a 12-bit quantizer (SNNMS-LR-Q) which reduces the number of required multipliers and correction factors by sharing parameters, increasing the nonlinear fitting ability by adding LeakyReLU. By utilizing the 12-bit quantizer, we can improve the confrontation ability. Thorough experiments with different code lengths, code rates, channel conditions, and check matrices are implemented to demonstrate the advantages and robustness of our proposed networks. The BER performance of the proposed NNMS is 1.5 dB better than the NMS, using fewer iterations. Meanwhile, The SNNMS-LR-Q outperforms the NNMS regarding the BER performance and efficiency.