# Secrecy Control of Wireless Networks with Finite Encoding Blocklength
## 1 Introduction  
A wireless multi-hops network is a decentralized network which is contained by a set of nodes. The message is transmitted over the wireless channel with multi-hops mode. Since the wireless channel is a broadcast channel, it is easy to eavesdrop on the data transmission. Therefore, when designing a network, in addition to considering the quality of service (QoS) constraint, the data transmission security should also be involved. In 1975, [PERSON] [1] studied a wire-tapped noisy channel and encoded the data to confuse the eavesdropper. After ground-breaking work in [1], many works have tackled the secrecy transmission of wireless networks. [PERSON] et al. [2] considered a cellular network where the base station needed to transmit data to multiuser confidentially, they designed a dynamic control algorithm to maximize the network utility by employing infinite secrecy encoding block. Since secrecy outage was inevitable, [PERSON] et al. [3] investigated the secrecy outage and and secrecy rate in a multiuser wireless systems. Jointly considering the reliability, security and stability, they designed an optimal online control algorithm by exploiting stochastic network optimization method. Later, in [4], the authors also considered a multi-user wireless scenario with imperfectly known channels. They aimed to maximize the worst case of secrecy throughput and developed a low complexity and rapid convergence algorithm for the optimal power allocation. In [5], [PERSON] et al. investigated a cross-layer security in wireless network and proposed a dynamic control algorithm to maximize the network utility. After that, in [6], aiming to minimize the secrecy outage probability, the authors extended the dynamic control algorithm to a cognitive radio network and developed a bandwidth and resource allocation algorithm. Recently, on the basis of the works mentioned above, the secrecy control problem in wireless networks has been extensively studied, such as the OFDMA-based wireless network and cognitive wireless network. In [7, 8], the authors formulated an analytical framework for secure resourceallocation in a downlink OFDMA-based broadband network. Jointly considering the power and subcarrier allocation, they proposed an optimal algorithm to maximize the average aggregate rate of all users for a base station. In [9], the authors extended the cellular network to cognitive network and proposed a scheduling policy to maximize the secrecy rate of second users. In [10; 11], they designed a scheduling policy in cognitive radio networks to analyze the ergodic capacity on the impact of fading channel and distributed eavesdroppers. In [12], [PERSON] et al. considered the cognitive wiretap channel and proposed multiple antennas to secure the transmission at the physical layer. They revealed the impact of the primary network on the secondary network in the presence of a multi-antenna wiretap channel. Although these security control algorithms improved the network performance, most of them focused on the cellular networks. In contrast, for the multi-hop wireless networks, there were few works involved. In [13; 14], the authors considered a multi-hop wireless network and proposed an optimal control to maximize the network throughput. However, they did not consider the data transmission security. In [15; 16], the authors investigate the confidential message secure transmission in a large scale wireless networks. By using infinite secure encoding blocklength, they derived the secrecy throughput with ideal control policies. After that, [PERSON] et al. [17] extended the infinite secure encoding blocklength to the finite case and revealed the relation of secrecy outage probability to the length of codewords. As for the mobile ad hoc networks, [PERSON] et al. [18] jointly exploited cooperative jamming and secrecy guard zone scheme and derived the exact secrecy throughput based on the physical layer security technology. To enhance security, [PERSON] et al.