## 5 Experimental Section
### Experiments about the Error Correction in WSN Based on L1 Optimization and Social Networks Method  
We will give the experiment results about the error correction in a WSN environment based on L1 optimization and social networks method with OMNET++. The WSN is an underwater acoustic sensor network whose network structure is shown in Figure 14. The green rhombus is the sink node. The red circle is the common sensor node. The sink node in the green circle and the sensor node in the red circle are the examples with special emphasis. Underwater acoustic sensor networks are a typical application of WSN. Underwater acoustic sensor networks have the following properties: (i) limited bandwidth capacity and high propagation delays which is due to the low speed of sound; (ii) the underwater acoustic channel is severely impaired; (iii) high bit error rates and temporary losses of connectivity; (iv) underwater sensors are prone to failures; (v) batteries are energy constrained and cannot be recharged [37]. Thus, the underwater acoustic sensor network is in severe need of transmission methodology like our scheme which can increase the information rate and correct dense error. The underwater acoustic sensor network is a typical scenario of WSN which will be a good test for our scheme.  
The experiment environment is as follows. There are 100 sensor nodes and 1 base station. Sensor nodes are randomly distributed on the approximately 1000 square meter roof. The communication distance for a sensor node is 100 m. The finite field is \(GF(2^{8})\) which is a common field for network coding. The nodes will send ACKs along the corresponding incoming edges to all the \(h\) hops upstream nodes. \(h\) is set as 2. We employed two metrics to evaluate the performance of wireless sensor networks. SDR is the number of successful delivered packets over the total packets sent by the source node, the normalized energy consumption is equal to total energy consumption divided by SDR. Three schemes are compared from the perspective of SDR and normalized consumed energy. The three schemes are traditional network coding, network coding which is based on only L1 optimization, and network coding which is based on L1 optimization and social characteristic. In L1 optimization, the fraction of original messages by secret channel is set as \(\vartheta=0.1\).  
Figure 15 shows network coding which is based on L1 optimization and social characteristic has the most powerful error correction ability. The reason is that L1 optimization and the method which is based on social network are very effective.  
\begin{table}
\begin{tabular}{c c} \hline
**Algorithm** & **Time (s)** \\ \hline LDPC & 0.7527 \\ Our & 0.6285 \\ \hline \end{tabular}
\end{table}
Table 2: Comparison of times.  
Figure 13: The time of different kernel L1 optimization.  
Figure 16 shows the comparison between the consumed energies with three schemes. When the bit error rate is low, traditional network coding has the lowest consumed energy while network coding which is based on L1 optimization and social characteristic has the most consumed energy, because the operation for the L1 optimization and social network method will consume energy. However, as the bit error rate increases, the benefits of L1 optimization and social network method are being realized, and network coding which is based on L1 optimization and social characteristic has the least consumed energy.  
Figure 14: The architecture of underwater acoustic sensor networks. The sink node in the green circle and the sensor node in the red circle are the examples with special emphasis.  
Figure 15: The successful delivered packets based on the bit error rate in WSN.