# Research on Data Link Channel Decoding Optimization Scheme for Drone Power Inspection Scenarios
## 2 Materials and Methods
### Prior Work
#### 2.3.1 Normalized Minimum Sum Algorithm (NMS) and Model-Driven Methods  
The main idea of the NMS algorithm is to adjust the calculation result by multiplying it with a correction factor during the step of updating the verification node information in the MS algorithm. The LDPC parity-check matrix H can be visually represented using a Tanner graph, where variable nodes (VNs) represent the bits in the codeword, and check nodes (CNs) represent the parity-check equations. In the LDPC parity-check matrix, H(i, j) = 1 indicates that the ith variable node (VN) is connected to the jth check node (CN) in the Tanner graph, while H(i, j) = 0 indicates no connection [40]. The LDPC decoding framework, as shown in Figure 4, is a bidirectional graph composed of check nodes, variable nodes, and the edges connecting them. The implementation of the NMS decoding process is represented on the Tanner diagram as iteratively updating and passing messages between VNs and CNs. The Tanner graph is used to describe the structure of the codeword and the parity-check equations. If there is a connection between a VN and a CN in the Tanner graph, it indicates that the corresponding bit participates in the parity-check calculation. In the iterative update process of message passing, VNs update their log-likelihood ratio (LLR) based on the received messages and then send the messages to the connected CNs. CNs calculate the parity equations based on the received messages and send back the updated  
Figure 4: NMS LDPC decoding framework. Figure 3: LDPC iterative decoding flowchart. messages to the connected VNs. By iteratively passing messages, errors can be corrected, and the accuracy of decoding can be improved. Considering that the NMS algorithm reduces complexity at the cost of performance degradation, there is a need to enhance its performance while maintaining a relatively unchanged computational complexity in order to better apply it to the long-code decoding application of large amounts of drone data. Due to the successful combination of deep learning (DL) with many physical layer communication algorithms [41], the NMS algorithm is combined with DL techniques. DL can be divided into two methods: the data-driven methods and the model-driven methods. On the one hand, the data-driven methods require a large amount of training data to improve performance at the cost of significant latency and significant resource consumption. On the other hand, the model-driven methods combine communication knowledge with deep learning, based on prior knowledge of specific models and decoding algorithms, making neural networks interpretable to a certain extent, reducing the need for a large amount of training data, computational overhead, and training time [42]. Therefore, the NMS algorithm is expanded into a deep feed-forward neural network based on the Tanner graph structure, and the neural-network-normalized minimum sum (NNMS) decoding network based on the NMS decoding algorithm and model-driven deep learning network is obtained. The NNMS decoding algorithm can meet the high reliability requirements of drone communication. In the air-to-air data transmission link model, binary code and binary phase shift keying (BPSK) modulation are used, and message bits are transmitted through the Rice small-scale fading channel [43]. The approximate decoding process of the NNMS LDPC decoder in this transmission model is as follows: after the decoder receives the signal affected by channel noise, the received channel LLR is calculated using the received symbol y for initialization, that is,  
\[L_{v}=\log\biggl{(}\frac{P(Y_{v}=y_{v}\mid X_{v}=-1)}{P(Y_{v}=y_{v}\mid X_{v}= +1)}\biggr{)}=\frac{2y_{v}}{\delta^{2}} \tag{1}\]  
Then, it is fed into the deep forward-propagation neural network of the LDPC decoder where the updates of the CN-to-VN messages and VN-to-CN messages in the MS algorithms are implemented by the CN layer and VN layer of the hidden layer of the neural network, respectively. Finally, the transmitted information bits are estimated.