## 2 Design of WSNs with Non-Binary LDPC Coding
### The Basic Principles of WSNs Coding with Non-Binary LDPC Codes  
In the sensor network, the physical layer is the key to determine the volume, cost and energy consumption of the nodes of the sensors network [20; 21; 22]. Because of the low capability of WSNs node processors and relatively small storage space, the design should have the following characteristics:  
1. Designing non-binary LDPC codes with relatively short code length. WSN energy supply and wireless communication bandwidth is very limited, the size of the node is small, the processing speed of the microcontroller in the node is relatively low, the ability to process data is low and most of the nodes are powered by the battery. Although academia is studying renewable energy and automatic charging mechanisms, too small a node is still a factor limiting its application. Therefore, this paper designs a non-binary LDPC code with a relatively short code length to suit the processor capabilities of the WSN node. Considering the comprehensive advantages of  
Figure 1: Node structure of wireless sensor. the short-code and low-complexity of the construction of the hybrid parity check matrix construction algorithm, this paper adopts the hybrid method to construct the check matrix. 2. Because of the check matrix H of non-binary LDPC code is very large, we use reasonable storage technology to store check matrix H and generate matrix G.  
The storage space of WSN nodes is relatively small but the check matrix dimension is large, so it is impossible to store the entire check matrix. The solution to this problem is to store only the position of non-zero elements in the base matrix constructed by the irPEG algorithm and its corresponding cyclic shift matrix in each row or column of the check matrix. 3. Selection of modulation methods suitable for WSNs. In order to improve the frequency band utilization of WSNs and reduce redundant information, continuous phase modulation (CPM) is used to form a non-binary LDPC-CPM system. CPM is an advanced phase modulation technology with continuous phase characteristics and excellent spectral characteristics. Compared with the phase-shift keying (PSK) modulation method, CPM has a higher frequency band utilization ratio. Moreover, CPM modulation system is a combination of channel coding and modulation. By controlling the state transition at the next moment by generating the phase state lattice sequence, the modulation of the information symbol has a coding effect directly, so that no more redundant symbols are needed. 4. On the basis of satisfying certain performance, we use the algorithm of encoding and decoding with loss computation and at the same time, the number of bits of data quantization is less. Because WSN node energy supply and communication bandwidth are limited and the processing speed of the microcontroller in the node is relatively low. Therefore, a non-binary LDPC code encoding and decoding scheme with good error correction performance and low algorithm complexity should be selected. According to the previous analysis, the choice of iterative encoding algorithm and Log-FFT-BP decoding algorithm [23; 24] is relatively suitable for the requirements of WSN nodes. 5. The number of iterations is as few as possible. The number of decoding iterations is an important factor influencing the decoding performance of a non-binary LDPC code. When the number of iterations is too small, error correction performance will be reduced but too high number of iterations will increase the amount of decoding operations. Therefore, the non-binary LDPC codes applied to the WSN should be chosen in combination with the actual situation to select the appropriate number of decoding iterations. 3. Non-Binary Iterative Encoding Algorithm  
The Gaussian elimination coding algorithm is the most basic coding algorithm in LDPC codes. Like the binary LDPC code, the non-binary LDPC code is also applicable to the Gaussian elimination coding algorithm.