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Joint European Conference on Networks and Communications & 6G Summit (EuCNC/6G Summit)

A Neuromorphic Approach to LDPC Decoding with Spiking Belief Propagation

Lucas Pelz, Ahsan Javed Awan, Mustafa Özger

Published Jun 2, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1109/eucnc/6gsummit68295.2026.11577434

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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.
For short to moderate-length block codes, neural belief propagation (NBP) decoders are developed to ameliorate the performance of the belief propagation algorithm (BPA). The core concept underlying these decoders is to model belief propagation (BP) as a neural network, allowing adaptable decoding through trainable weights. The article proposes a novel Gated neural min-sum (GNMS) decoding technique with learnable parameters as a more hardware-efficient substitute for conventional NBP decoders. By using parameterised updates and gating techniques, our approach reformulates the min-sum (MS) algorithm, which is an approximation of BP, while preserving the flexibility of neural approaches and drastically lowering computing overhead. Additionally, we develop an autoencoder-assisted framework that supports flexible, learning-based optimisation for GNMS and Gated Neural Offset Min-Sum (GNOMS) decoders. The suggested decoders achieve error-correction performance at par with the most advanced NBP decoders by evaluating them on a variety of short to moderate-length block codes. Notably, when compared to traditional BP, the suggested approach lowers the bit error rate (BER) 10-fold for signal-to-noise ratio (SNR) greater than 3 dB. Furthermore, the efficacy of the proposed work is exhibited by comparing the computational complexity of the neural network-based decoders, highlighting the advantages in terms of practical implementation and hardware feasibility. The simulation results demonstrate that GNMS decoding with learnable parameters offers a convincing trade-off between complexity and performance, offering a potential path for future decoder design in contemporary communication systems.
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.
In this letter, we propose various low-complexity neural layered min-sum (NLMS) algorithms to improve the decoding performance of the fifth generation (5G) new radio (NR) low-density parity-check (LDPC) codes. Our proposals are based on the computationally-efficient normalized offset min-sum (NOMS) approach for the layered belief propagation (LBP). The main novelty of our proposals is a deep neural network (DNN) that implements the layered mode decoding and that additionally learns the normalization and the offset parameters of the NOMS scheme. The schemes that we propose use the DNN as well as adaptation and filtering for estimating the optimum values of these parameters. We show by simulation that our proposed decoders achieve a significant computational benefit compared to the standard (non-neural) LBP decoder without an appreciable performance penalty.
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.
A novel Neural Offset Min-Sum(NOMS) Belief Propagation(BP) decoding algorithm based on model-driven is proposed which applied to LDPC decoding. NOMS is improved multiplication in Neural Normalized Min-Sum(NNMS) into addition operation to reduce the complexity of calculation., a better Bit Error Rate (BER) performance is simultaneously achieved in the same condition. Secondly, considering that there are still many multiplication operations in NOMS, we propose a novel Shared Offset Min-Sum(SNOMS) to reduce the number of weights in the network by sharing parameters. Finally, codebook-based quantization is used to further reduce the memory consumption. Simulation experimental results show that the proposed method has a better BER performance, and the decoding accuracy of the decoder is 0.65dB higher than that of the NNMS after 5 iterations. In addition, SNOMS decoding method achieves almost the same decoding performance comparable to that of NOMS, but requires less complex calculation. Proposed quantization of code-book method reduces memory requirement significantly with slight performance loss.
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.