Channel neural decoding is very promising as it outperforms the traditional channel decoding algorithms. Unfortunately, it still faces the disadvantage of high computational complexity and storage complexity compared with the traditional decoding algorithms. In this paper, we propose that low rank decomposition techniques based on tensor train decomposition and tensor ring decomposition can be utilized in neural offset min-sum (NOMS) and neural scale min-sim (NSMS) decoding algorithms. The experiment results show that the proposed two algorithms achieve near state-of-the-art performance with low complexity.
Channel neural decoding is very promising as it outperforms the traditional channel decoding algorithms. Unfortunately, it still faces the disadvantage of high computational complexity and storage complexity compared with the traditional decoding algorithms. In this paper, we propose that low rank decomposition techniques based on tensor train decomposition and tensor ring decomposition can be utilized in neural offset min-sum (NOMS) and neural scale min-sim (NSMS) decoding algorithms. The experiment results show that the proposed two algorithms achieve near state-of-the-art performance with low complexity.
Compared with traditional low-density parity-check (LDPC) decoding algorithms, the current model-driven deep learning (DL)-based LDPC decoding algorithms face the disadvantage of high computational complexity. Based on the Neural Normalized Min-Sum (NNMS) algorithm, we propose a low-complexity model-driven DL-based LDPC decoding algorithm using Tensor-Train (TT) decomposition and syndrome loss function, called TT-NNMS+ algorithm. Our experiments show that the proposed TT-NNMS+ algorithm is more competitive than the NNMS algorithm in terms of bit error rate (BER) performance, memory requirement and computational complexity.
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.
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.
With the rapid development of deep learning and its applications in physical layer communication, deep learning-based channel coding has gradually become a research hotspot. In this paper, based on the neural offset min-sum (NOMS) low-density parity-check (LDPC) decoding network, we propose a neural adaptive offset min-sum (NAOMS) LDPC decoding network. By considering the current input values of the check nodes when learning the additive offset parameters and introducing an adaptive offset weight vector, we can better leverage deep learning techniques. Experimental results show that, with a slight increase in complexity, the proposed decoder achieves a 0.8dB improvement in bit error rate (BER) over the NOMS LDPC decoding network. Moreover, the NAOMS decoder requires fewer learning offset parameters compared to the NOMS decoder.
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.
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.