The general wiretap channel with noiseless feedback is first investigated by Ahlswede and Cai, where lower and upper bounds on the secrecy capacity are provided in their work. The upper bound is met with equality only in some special cases. In this paper, we study a special case of the general wiretap channel with noiseless feedback (called non-degraded wiretap channel with noiseless feedback). Inner and outer bounds on the capacity-equivocation region of this special model are provided. The outer bound is achievable if the main channel is more capable than the wiretap channel. The inner bound is constructed especially for the case that the wiretap channel is more capable than the main channel. The results of this paper are further explained via binary and Gaussian examples. Compared with the capacity results for the non-degraded wiretap channel, we find that the security is enhanced by using the noiseless feedback.
The general wiretap channel with noiseless feedback is first investigated by Ahlswede and Cai, where lower and upper bounds on the secrecy capacity are provided in their work. The upper bound is met with equality only in some special cases. In this paper, we study a special case of the general wiretap channel with noiseless feedback (called non-degraded wiretap channel with noiseless feedback). Inner and outer bounds on the capacity-equivocation region of this special model are provided. The outer bound is achievable if the main channel is more capable than the wiretap channel. The inner bound is constructed especially for the case that the wiretap channel is more capable than the main channel. The results of this paper are further explained via binary and Gaussian examples. Compared with the capacity results for the non-degraded wiretap channel, we find that the security is enhanced by using the noiseless feedback.
The non-degraded wiretap channel with noiseless feedback is first investigated by R. Ahlswede and N. Cai, where lower and upper bounds on the secrecy capacity are provided in their work. However, the capacity-equivocation region has not been determined yet. In this paper, the capacity-equivocation region is determined for the non-degraded wiretap channel with noiseless feedback. Furthermore, the secrecy capacity of this model is formulated, which provides the best transmission rate with perfect secrecy.
The concept of the wiretap channel was first proposed by Wyner. He considered the case in which data is to be transmitted reliably over a discrete memoryless main channel to a legitimate receiver. The wiretapper views the output of the main channel through another discrete memoryless channel. It is assumed that the wiretapper knows the code being used and his only handicap is the additional noise in his signal. The problem is to maximize the transmission rate R to the legitimate receiver and the equivocation d of the wiretapper. In this dissertation, the additive white Gaussian noise wiretap channel is introduced and the set of all achievable (R,d) pairs is determined explicitly through the use of certain special properties of the Gaussian channel. Some useful characterizations of a special class of wiretap channels are also explored. A model of the wiretap channel with feedback is proposed. It turns out that with the introduction of feedback, even when the main channel is inferior to the wiretapper's channel, it is still possible to reliably communicate with the legitimate receiver in complete secrecy. The binary erasure wiretap channel with feedback is examined and inner and outer bounds on the achievable (R,d) region are given. Finally, a scheme for enlarging the capacity region of multiple-access channels using feedback is analyzed. It is shown that conditions under which an enlargement is possible are fairly weak, indicating that feedback can almost increase the capacity region. (Author)
The physical layer security in the up-link of the wireless communication systems is often modeled as the multiple access wiretap channel (MAC-WT), and recently it has received a lot attention. In this paper, the MAC-WT has been re-visited by considering the situation that the legitimate receiver feeds his received channel output back to the transmitters via two noiseless channels, respectively. This model is called the MAC-WT with noiseless feedback. We present a new hybrid inner bound on the secrecy capacity region of this feedback model, and it is constructed by using the feedback as a tool not only to allow the independent transmitters to co-operate with each other (decode each other's transmitted message from the feedback), but also to generate two secret keys respectively shared between the legitimate receiver and the two transmitters. We show that this hybrid inner bound is strictly larger than the already existing decode-and-forward (DF) inner bound. Moreover, we provide a sato-type outer bound on the secrecy capacity region of the MAC-WT with noiseless feedback. The results of this paper are further explained via a Gaussian example.
The dirty paper wiretap channel, also referred to as the Gaussian wiretap channel with noncausal state at the transmitter, is revisited. First, we determine the secrecy capacity of the dirty paper wiretap channel with noiseless feedback, where the feedback channel is from the legitimate receiver to the transmitter. Next, we obtain lower and upper bounds on the secrecy capacity of the action-dependent dirty paper wiretap channel with noiseless feedback, and show that these bounds meet for a special case. Unlike the fact that action on the state helps to enhance the capacity of the dirty paper channel with feedback, numerical results of this paper indicate that it may not help to enhance the secrecy capacity of the dirty paper wiretap channel with feedback.
The noiseless feedback is introduced in channels with information embedding on actions. Two channel models are considered. One is wiretap channel with information embedding on actions and noiseless feedback (WT-IEANF), the other is degraded broadcast channel with noncausal action-dependent states and noiseless feedback (DBC-NADSNF). For the WT-IEANF, we characterize both inner and outer bounds on the capacity-equivocation region. For the DBC-NADSNF, an inner bound on the capacity-equivocation region is obtained, and a proper coding scheme is constructed, in which the noiseless feedback plays the role of a shared secret key between the transmitter and legal receiver. We find that the feedback does help increase the secure information transmission rates of the two models, but, at the same time, it enables the illegal receiver to get another chance to eavesdrop the private message. Besides, when secrecy constraint condition is removed, it is found that feedback is not useful for enhancing the capacity of the channel with information embedding on actions.
In this paper, the general wiretap channel with channel state information (CSI) at the transmitter and noiseless feedback is investigated, where the feedback is from the legitimate receiver to the transmitter, and the CSI is available at the transmitter in a causal or noncausal manner. The capacity-equivocation regions are determined for this model in both causal and noncausal cases, and the results are further explained via Gaussian and binary examples. For the Gaussian model, we find that in some particular cases, the noiseless feedback performs better than Chia and El Gamal’s CSI sharing scheme, i.e., the secrecy capacity of this feedback scheme is larger than that of the CSI sharing scheme. For the degraded binary model, we find that the noiseless feedback performs no better than Chia and El Gamal’s CSI sharing scheme. However, if the cross-over probability of the wiretap channel is large enough, we show that the two schemes perform the same.