# Secrecy Control of Wireless Networks with Finite Encoding Blocklength
## 4 Numerical Results and Discussions
Based on the setting of simulation, i.e., \(M=8\), \(B\approx 20\) and \(\eta\approx 0.5\), we can obtain the good operating point \(V\approx 20\). Next, we analyze the performance of MSCAFB algorithm and compare with MSCA algorithm in [23]. Figure 5 reflects the influence of secrecy codeword length on the network utility, as well as comparing with infinite secrecy codeword. The average arrival of confidential message is 2 bit/s and the parameter \(V\) is 80. The maximum allowable portion of confidential message \(\gamma_{n}\) is chosen from \(\{0.05,\ 0.1,\ 0.2\}\), and the secrecy codeword length varies from \(\{50,100,500,1000,2000,4000\}\) bits. From Figure 5, we find: (1) When the secrecy codeword length is 50 bits, the network utility is only 30% of the optimal value. (2) With the increasing of secrecy codeword length, the network utility is increased. When secrecy codeword length is up to 1000 bits, the network utility trends to be gentle, but closes to the value with infinite secrecy codeword. The reason for this is that, when the secrecy codeword length is small, subject to the constraint of \(\gamma_{n}\), the confidential message inserted to the codeword is decreased. Such that the network utility is low, and vice versa. (3) The network utility is increased with the value of \(\gamma_{n}\). The reason is that, with \(\gamma_{n}\) increasing, more confidential message can be inserted into a secrecy codeword. Particularly, when \(\gamma_{n}=0.2\) and secrecy codeword length is 1000 bits, the network utility is larger than that of infinite secrecy codeword. In order to depict the influence of \(\gamma_{n}\) on the network utility, we have Figure 6.  
Figure 4: Average queue backlog with varying confidential data arrival rate. In Figure 6, assuming the secrecy codeword length is \(\{100,1000,4000\}\) bits, we vary \(\gamma_{n}\) from 0.05 to 0.5. The results show that: (1) With \(\gamma_{n}\) increasing, we have the similar results with Figure 5. (2) With the increasing of secrecy codeword length, the threshold of \(\gamma_{n}\) at which network utility is larger than that of infinite secrecy codeword is decreased. The reason is that larger secrecy codeword length means more confidential message can be inserted into a secrecy codeword. Particularly, when the secrecy codeword length is small, even \(\gamma_{n}\) is large, the network utility can not exceed the optimal value. (3) Although both \(\gamma_{n}\) and secrecy codeword length are large, the network utility can exceed the optimal value, it can not exceed the network capacity without secrecy constraint. Each node needs the information of queue length from eavesdroppers to decide the control algorithm, considers a situation that queue length information is shared among all the nodes, but in some environment it is impossible to know this information precisely. Compared with getting perfect information about \(Z_{e}^{n,c}(t)\), it is more realistic to know the time-average packet arrival rate of eavesdroppers. Considering this, we propose an imperfect estimation of \(Z_{e}^{n,c}(t)\). The estimated queue length in legitimate node is:  
\[\hat{Z}_{e}^{n,c}(t+1)=[\hat{Z}_{e}^{n,c}(t)-\hat{R}^{c}(t)]^{+}+(R_{n}^{k,cs}+t) \tag{25}\]  
Figure 5: Long-term utility with varying secrecy codeword length. Figure 6: Long-term utility with varying secrecy outage constraint. where \(i\) is an over-estimated slack variable to queue stability. As to the control algorithm, we use \(\hat{Z}_{e}^{n,c}\) to substitute \(Z_{e}^{n,c}\) in resource allocation algorithm.