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:2410.11543 · IEEE Communications Letters

Spiking Neural Belief Propagation Decoder for Short Block Length LDPC Codes

Alexander von Bank, Eike-Manuel Edelmann, Sisi Miao, Jonathan Mandelbaum, Laurent Schmalen

Published Nov 6, 2024• 5 citations
arXivHTMLPDF

Abstract

Spiking neural networks (SNNs) are neural networks that enable energy-efficient signal processing due to their event-based nature. This letter proposes a novel decoding algorithm for low-density parity-check (LDPC) codes that integrates SNNs into belief propagation (BP) decoding by approximating the check node update equations using SNNs. For the (273,191) and (1023,781) finite-geometry LDPC code, the proposed decoder outperforms sum-product decoder at high signal-to-noise ratios (SNRs). The decoder achieves a similar bit error rate to normalized sum-product decoding with successive relaxation. Furthermore, the novel decoding operates without requiring knowledge of the SNR, making it robust to SNR mismatch.

DOI
10.1109/lcomm.2024.3492711

Related papers

Spiking Neural Belief Propagation Decoder for LDPC Codes with Small Variable Node Degrees

Alexander von Bank, Eike-Manuel Edelmann, Jonathan Mandelbaum +1 more

Spiking neural networks (SNNs) promise energyefficient data processing by imitating the event-based behavior of biological neurons. In previous work, we introduced the enlarge-likelihood-each-notable-amplitude spiking-neural-network (ELENA-SNN) decoder, a novel decoding algorithm for low-density parity-check (LDPC) codes. The decoder integrates SNNs into belief propagation (BP) decoding by approximating the check node (CN) update equation using SNNs. However, when decoding LDPC codes with a small variable node (VN) degree, the approximation gets too rough, and the ELENASNN decoder does not yield good results. This paper introduces the multi-level ELENA-SNN (ML-ELENA-SNN) decoder, which is an extension of the ELENA-SNN decoder. Instead of a single SNN approximating the CN update, multiple SNNs are applied in parallel, resulting in a higher resolution and higher dynamic range of the exchanged messages. We show that the ML-ELENASNN decoder performs similarly to the ubiquitous normalized min-sum decoder for the$(38400,30720)$regular LDPC code with a VN degree of$d_{v}=3$and a CN degree of$d_{\mathrm{c}}=15$.

arXiv:2412.15897•International ITG Conference on Systems, Communications and Coding (SCC)•Mar 10, 2025•0 citations

A Neuromorphic Approach to LDPC Decoding with Spiking Belief Propagation

Lucas Pelz, Ahsan Javed Awan, Mustafa Özger

The rapid growth of mobile data traffic demands increasingly energy-efficient error correction solutions. Traditional decoding based on Belief Propagation (BP) often relies on the approximate Min-Sum (MS) algorithm for efficiency reasons, leading to performance degradation. While machine learning approaches like Neural Normalized Offset Min-Sum (NNOMS) mitigate this, they also introduce complexity inherent to artificial neural networks (ANNs). To address this trade-off, this paper designs and evaluates a Spiking Normalized Offset Min-Sum (SNOMS), a Spiking Neural Network-based decoder compatible with Digital Neuromorphic Hardware (DNH) such as Intel's Loihi 2. SNOMS translates the parameter-learned decoding of NNOMS into the event-driven domain. Through simulation, SNOMS achieves performance competitive with its NNOMS baseline, incurring a maximum penalty of only 0.05 dB on Low-Density Parity-Check (LDPC) codes when measuring Block Error Rate. These results points us toward both more efficient trainable decoding algorithms and specialized, energyefficient neuromorphic decoding hardware, building a foundation for future sustainable wireless communication.

Joint European Conference on Networks and Communications & 6G Summit (EuCNC/6G Summit)•Jun 2, 2026•0 citations

Graph Neural Network-Based LDPC Decoding for Beyond 5G Communication Systems

Ambar Bajpai

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.

•Jul 28, 2025•0 citations

Intelligent LDPC Decoding Using Graph Neural Networks for Beyond 5G Communication Systems

Ambar Bajpai

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.

Journal of information and communication convergence engineering•Dec 31, 2025•0 citations

Learned Decimation for Neural Belief Propagation Decoders

Andreas Buchberger, Christian Häger, Henry D. Pfister +2 more

We introduce a two-stage decimation process to improve the performance of neural belief propagation (NBP), recently introduced by Nachmani et al., for short low-density parity-check (LDPC) codes. In the first stage, we build a list by iterating between a conventional NBP decoder and guessing the least reliable bit. The second stage iterates between a conventional NBP decoder and learned decimation, where we use a neural network to decide the decimation value for each bit. For a (128,64) LDPC code, the proposed NBP with decimation outperforms NBP decoding by 0.75 dB and performs within 1 dB from maximum-likelihood decoding at a block error rate of $10^{-4}$.

arXiv:2011.02161•Nov 4, 2020•4 citations

Learned Decimation for Neural Belief Propagation Decoders : Invited Paper

Andreas Buchberger, Christian Häger, Henry D. Pfister +2 more

We introduce a two-stage decimation process to improve the performance of neural belief propagation (NBP), recently introduced by Nachmani et al., for short low-density parity-check (LDPC) codes. In the first stage, we build a list by iterating between a conventional NBP decoder and guessing the least reliable bit. The second stage iterates between a conventional NBP decoder and learned decimation, where we use a neural network to decide the decimation value for each bit. For a (128,64) LDPC code, the proposed NBP with decimation outperforms NBP decoding by 0.75dB and performs within 1dB from maximum-likelihood decoding at a block error rate of 10−4.

IEEE International Conference on Acoustics Speech and Signal Processing•May 13, 2021•17 citations
Spiking neural networks (SNNs) are neural networks that enable energy-efficient signal processing due to their event-based nature. This letter proposes a novel decoding algorithm for low-density parity-check (LDPC) codes that integrates SNNs into belief propagation (BP) decoding by approximating the check node update equations using SNNs. For the (273,191) and (1023,781) finite-geometry LDPC code, the proposed decoder outperforms sum-product decoder at high signal-to-noise ratios (SNRs). The decoder achieves a similar bit error rate to normalized sum-product decoding with successive relaxation. Furthermore, the novel decoding operates without requiring knowledge of the SNR, making it robust to SNR mismatch.
Spiking neural networks (SNNs) promise energyefficient data processing by imitating the event-based behavior of biological neurons. In previous work, we introduced the enlarge-likelihood-each-notable-amplitude spiking-neural-network (ELENA-SNN) decoder, a novel decoding algorithm for low-density parity-check (LDPC) codes. The decoder integrates SNNs into belief propagation (BP) decoding by approximating the check node (CN) update equation using SNNs. However, when decoding LDPC codes with a small variable node (VN) degree, the approximation gets too rough, and the ELENASNN decoder does not yield good results. This paper introduces the multi-level ELENA-SNN (ML-ELENA-SNN) decoder, which is an extension of the ELENA-SNN decoder. Instead of a single SNN approximating the CN update, multiple SNNs are applied in parallel, resulting in a higher resolution and higher dynamic range of the exchanged messages. We show that the ML-ELENASNN decoder performs similarly to the ubiquitous normalized min-sum decoder for the(38400,30720)(38400,30720)(38400,30720)regular LDPC code with a VN degree ofdv=3d_{v}=3dv​=3and a CN degree ofdc=15d_{\mathrm{c}}=15dc​=15.
The rapid growth of mobile data traffic demands increasingly energy-efficient error correction solutions. Traditional decoding based on Belief Propagation (BP) often relies on the approximate Min-Sum (MS) algorithm for efficiency reasons, leading to performance degradation. While machine learning approaches like Neural Normalized Offset Min-Sum (NNOMS) mitigate this, they also introduce complexity inherent to artificial neural networks (ANNs). To address this trade-off, this paper designs and evaluates a Spiking Normalized Offset Min-Sum (SNOMS), a Spiking Neural Network-based decoder compatible with Digital Neuromorphic Hardware (DNH) such as Intel's Loihi 2. SNOMS translates the parameter-learned decoding of NNOMS into the event-driven domain. Through simulation, SNOMS achieves performance competitive with its NNOMS baseline, incurring a maximum penalty of only 0.05 dB on Low-Density Parity-Check (LDPC) codes when measuring Block Error Rate. These results points us toward both more efficient trainable decoding algorithms and specialized, energyefficient neuromorphic decoding hardware, building a foundation for future sustainable wireless communication.
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.
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.
We introduce a two-stage decimation process to improve the performance of neural belief propagation (NBP), recently introduced by Nachmani et al., for short low-density parity-check (LDPC) codes. In the first stage, we build a list by iterating between a conventional NBP decoder and guessing the least reliable bit. The second stage iterates between a conventional NBP decoder and learned decimation, where we use a neural network to decide the decimation value for each bit. For a (128,64) LDPC code, the proposed NBP with decimation outperforms NBP decoding by 0.75 dB and performs within 1 dB from maximum-likelihood decoding at a block error rate of 10−410^{-4}10−4.
We introduce a two-stage decimation process to improve the performance of neural belief propagation (NBP), recently introduced by Nachmani et al., for short low-density parity-check (LDPC) codes. In the first stage, we build a list by iterating between a conventional NBP decoder and guessing the least reliable bit. The second stage iterates between a conventional NBP decoder and learned decimation, where we use a neural network to decide the decimation value for each bit. For a (128,64) LDPC code, the proposed NBP with decimation outperforms NBP decoding by 0.75dB and performs within 1dB from maximum-likelihood decoding at a block error rate of 10−4.