## 1 Introduction  
In wireless communication systems, such as sensor networks, mobile networks and satellite communications, sensitive data is transferred through multiple hops. The nodes in the network usually need to take various type of actions to acquire the state of the network before transferring the packets. The state acquisition in the network often requires the exchange of control information, which uses physical resources within the system. For example, routers measure the network congestion levels via the transmission of probing packets; wireless transceivers evaluate the channel quality through training or feedback; and radio terminals switch among different operating modes, such as transmit, receive or idle. Based on these motivating observations, [PERSON] introduced channels with action-dependent states where the encoder in a point-to-point channel could take actions to affect the channel state information [1]. The capacity of such a channel where the channel inputs depended noncausally (and causally) on the channel states was determined. After [PERSON]'s publication, [2] investigated the channel model where both the channel encoder and decoder could probe the channel states and obtained the cost constrained \"probing capacity\". Different from this, [1; 2; 3] studied the degraded broadcast channel with causal action-dependent states where the transmitter sent two kinds of messages to two different receivers. The capacity region was derived. For the noncausal case, only inner and outer bounds on the capacity region were obtained [4]. Other extensions of the channel with action-dependent states can be seen in [5; 6; 7; 8; 9; 10]. Recently, [11; 12] explored information embedding on actions in the channel with noncausal action-dependent states; see Figure 1. In this new setup, an additional decoder was introduced to observe a function of the actions taken by the encoder. It tried to get part of the transmitted message. Actually, the idea of \"information embedding\" on actions in such a channel is related to the classical topic of information hiding (e.g., [13; 14; 15; 16; 17]) and could be explained by the following example. In communication networks, probing the congestion state requires sending training packets to the nearest router. Meanwhile, the router (the \"recipient\" of the actions) may need to obtain partial information, such as the header of the packet, to find the address of the intended receiver. Since the actions play the role of providing necessary information about the message for the router, it is natural to ask how much information could be embedded in the actions without affecting the system performance. [11] got the capacity-cost region and showed that the communication requirements of the action-cribbing decoder were generally in conflict with the goal of improving the efficiency of the communication link. However, the above action-dependent channel models [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12] considered no secrecy constraint, which was extremely important in communications. For instance, the broadcast nature of wireless networks gives rise to the hidden danger of information leakage to malicious receiver when broadcasting the sensitive data and acquiring the state information. Recent works [18; 19] studied the secure communication problems in channels with action-dependent states. [18] added a wiretapper to the model in [1] and got the inner and outer bounds on the capacity-equivocation region. The capacity-equivocation region is the set of all the achievable rate pairs \((R,R_{e})\), where \(R\) and \(R_{e}\) are the rates of the confidential message and wiretapper's equivocation about the message. [19] studied the effects of feedback on the secrecy capacity, which is the maximum rate of data transmission at which the message can be communicated in perfect secrecy, of the wiretap channel with action-dependent states.