In this letter, we propose a low-complexity hypernetwork for channel neural decoding with learning weights in tensor ring (TR) format, called TRHyper. The internal parameters and the number of layers of the TRHyper based channel neural decoding algorithm can be updated without retraining. We design the size of each TRHyper layer according to the size of the factor tensor in tensor ring format. During the training phase, we reuse the storage space for the learning weights of the main decoding network, so the proposed TRHyper no longer require additional storage space for its learning weights. Numerical results show that for low-density parity check (LDPC) codes, the performance of the TRHyper based channel neural decoder is similar to that of the original decoder, while for Bose-Chaudhuri-Hocquenghem (BCH) codes, the performance slightly exceeds the original decoder.
In this letter, we propose a low-complexity hypernetwork for channel neural decoding with learning weights in tensor ring (TR) format, called TRHyper. The internal parameters and the number of layers of the TRHyper based channel neural decoding algorithm can be updated without retraining. We design the size of each TRHyper layer according to the size of the factor tensor in tensor ring format. During the training phase, we reuse the storage space for the learning weights of the main decoding network, so the proposed TRHyper no longer require additional storage space for its learning weights. Numerical results show that for low-density parity check (LDPC) codes, the performance of the TRHyper based channel neural decoder is similar to that of the original decoder, while for Bose-Chaudhuri-Hocquenghem (BCH) codes, the performance slightly exceeds the original decoder.
Channel decoding algorithms based on model-driven deep learning, also known as channel neural decoding algorithms, have received a lot of attention in recent years. However, the internal parameters and number of layers of the current channel neural decoding algorithm cannot be changed after training. Once changed, retraining of the channel neural decoding network is required. Hypernetwork is a neural network that can generate internal parameters for the main neural network to reduce the training cost of the main neural network and improve the flexibility of the main neural network. In this study, a novel hypernetwork based channel neural decoder is proposed for neural belief propagation algorithms (NBP), including the neural normalized min-sum (NNMS) and neural offset min-sum (NOMS) algorithm. According to the type of information interaction between the hypernetwork and the main decoding network, hypernetwork-based channel neural decoders can be divided into two types: static and dynamic. The internal parameters of the static hypernetwork-based channel neural decoder can be updated as needed without retraining of the main network. In addition to this benefit, the number of layers of the dynamic hypernetwork-based channel neural decoder can also be adjusted. Experimental results show that, compared with the existing NNMS decoding algorithms, the proposed hypernetwork-based NNMS decoding algorithms can achieve better performance on both low-density parity-check (LDPC) and Bose–Chaudhuri–Hocquenghem (BCH) codes.
Neural belief propagation (NBP) decoding can improve the performance of belief propagation (BP) decoding for high-density parity check (HDPC) codes, at the expense of higher memory storage requirement and computational complexity due to the addition of trainable weight coefficients. To reduce the high storage requirement of NBP, the cyclically equivariant neural BP (CENBP) algorithm makes full use of the cyclically invariant property of the cyclic code, optimizes and reuses the weight coefficients of the NBP algorithm, at the expense of further increasing the computational complexity of NBP. In this paper, we propose low-complexity, in terms of both memory storage requirement and computational complexity, NBP and CENBP decoding algorithms based on Tensor Ring (TR) decomposition. First, in order to reduce the memory storage and computational complexity of the NBP algorithm, we propose a TR-based compression algorithm to compress the messages and mathematical calculations in the NBP decoding algorithm, called TR-NBP algorithm. Second, to address the high computational complexity of the CENBP algorithm, we propose to apply TR decomposition-based compression to the odd layers of the CENBP decoding algorithm, called TR-CENBP, to reduce the computational complexity, and further reduce the required memory storage requirement of the CENBP algorithm. Furthermore, we use TR decomposition-based compression to simplify the mathematical computations associated with thetanhfunction in the NBP algorithm to further reduce the complexity of the hardware implementation. Experimental results show that direct compression of BP algorithm using TR decomposition results in significant performance degradation and our proposed low complexity TR-NBP algorithm and TR-CENBP algorithm can greatly reduce both the memory storage requirement and computation complexity, without significant performance degradation for typical BCH and LDPC codes.
In this paper, we propose low complexity joint-way compression algorithms with Tensor-Ring (TR) decomposition and weight sharing to further lower the storage and computational complexity requirements for low density parity check (LDPC) neural decoding. Compared with Tensor-Train (TT) decomposition, TR decomposition is more flexible for the selection of ranks, and is also conducive to the use of rank optimization algorithms. In particular, we use TR decomposition to decompose not only the weight parameter matrix of Neural Normalized Min-Sum (NNMS)+ algorithm [16], but also the message matrix transmitted between variable nodes and check nodes. Furthermore, we combine the TR decomposition and temporal and spatial weight sharing algorithm, called joint-way compression, to further lower the complexity of LDPC neural decoding algorithm. We show that the joint-way compression algorithm can achieve better compression efficiency than a single compression algorithm, while maintaining a comparable bit error rate (BER) performance. From the numerical experiments, we found that all the compression algorithms with appropriate selection of ranks give almost no performance BER degradation and that the TRwm-ssNNMS+ algorithm, which combines the spatial sharing and TR decomposition of both weight and message matrix, has the best compression performance. Comparing with our TT-NNMS+ algorithm proposed in [16], the number of parameters is reduced by about 70 times and the number of multiplications is reduced by about 6 times.
With the rapid development of deep learning research and physical layer communication applications, deep learning-based channel coding has gradually become a research hotspot. In this paper, we propose a LDPC decoding network based on neural belief propagation (NBP) decoding. By introducing weights sharing mechanism, the weights vary across different iterations. The number of parameters is reduced, which significantly lowers memory requirements. In addition, we optimize the loss function to better train the model, achieving a lower bit error rate (BER) performance. Experimental results show that the proposed decoder yields significant performance improvements with respect to NBP, and significantly reducing the number of learnable weights.
In this work, we propose a fully differentiable graph neural network (GNN)-based architecture for channel decoding and showcase a competitive decoding performance for various coding schemes, such as low-density parity-check (LDPC) and BCH codes. The idea is to let a neural network (NN) learn a generalized message passing algorithm over a given graph that represents the forward error correction (FEC) code structure by replacing node and edge message updates with trainable functions. Contrary to many other deep learning-based decoding approaches, the proposed solution enjoys scalability to arbitrary block lengths and the training is not limited by the curse of dimensionality. We benchmark our proposed decoder against state-of-the-art in conventional channel decoding as well as against recent deep learning-based results. For the (63,45) BCH code, our solution outperforms weighted belief propagation (BP) decoding by approximately 0.4 dB with significantly less decoding iterations and even for 5G NR LDPC codes, we observe a competitive performance when compared to conventional BP decoding. For the BCH codes, the resulting GNN decoder can be fully parametrized with only 9640 weights.
With the application of graph neural network (GNN) in the communication physical layer, GNN-based channel decoding algorithms have become a research hotspot. Compared with traditional decoding algorithms, GNN-based channel decoding algorithms have a better performance. GNN has good stability and can handle large-scale problems; GNN has good inheritance and can generalize to different network settings. Compared with deep learning-based channel decoding algorithms, GNN-based channel decoding algorithms avoid a large number of multiplications between learning weights and messages. However, the aggregation edges and nodes for GNN require many parameters, which requires a large amount of memory storage resources. In this work, we propose GNN-based channel decoding algorithms with shared parameters, called shared graph neural network (SGNN). For BCH codes and LDPC codes, the SGNN decoding algorithm only needs a quarter or half of the parameters, while achieving a slightly degraded bit error ratio (BER) performance.