This paper investigates the secure data transmission in the broadcast channel with noiseless feedback by using the information-theoretic method. We consider transmitting a private message and a common message to two receivers, of which the common message is to be decoded by both receivers while the private message is only for the intended receiver. The channel to the intended receiver is assumed to be independent of that to the other receiver. Feedback from the output of the intended receiver is used as a shared secret key to enhance the secrecy in the transmission. The capacity-equivocation region and the secrecy capacity of this new model are obtained. We find the secrecy capacity is enhanced by using feedback, even in the case that the other receiver is in a better position than the intended receiver. In addition, our results generalize the secrecy capacity of the degraded wiretap channel with secure feedback, and the capacity region of the degraded broadcast channel.
This paper investigates the secure data transmission in the broadcast channel with noiseless feedback by using the information-theoretic method. We consider transmitting a private message and a common message to two receivers, of which the common message is to be decoded by both receivers while the private message is only for the intended receiver. The channel to the intended receiver is assumed to be independent of that to the other receiver. Feedback from the output of the intended receiver is used as a shared secret key to enhance the secrecy in the transmission. The capacity-equivocation region and the secrecy capacity of this new model are obtained. We find the secrecy capacity is enhanced by using feedback, even in the case that the other receiver is in a better position than the intended receiver. In addition, our results generalize the secrecy capacity of the degraded wiretap channel with secure feedback, and the capacity region of the degraded broadcast channel.
This paper studies the degraded broadcast channel with rate-limited feedback. The transmitter aims to convey a common message to receiver 1 and 2 in addition to a confidential message intended only for receiver 1. The feedback symbol, independent of the channel outputs, is introduced to serve as a secret key between the transmitter and receiver 1. The capacity-equivocation region of this channel model is obtained. A simpler and more intuitive derivation instead of the recursive argument is used to get the single-letter characterization of the upper bound. Furthermore, a novel coding scheme is presented to achieve the upper bound. This paper also derives the secrecy capacity of this channel which subsumes the secrecy capacity of the degraded wiretap channel with rate-limited feedback.
In this paper, we investigate the model of degraded broadcast channel with noncausal side information, confidential messages and noiseless feedback. This work is from Steinberg's work on the degraded broadcast channel with noncausal side information, and Csiszár and Körner's work on broadcast channel with confidential messages. In this new model, the transmitter sends a confidential message to the non-degraded receiver, and meanwhile sends a common message to both the degraded and non-degraded receivers. Moreover, the channel for the non-degraded receiver is controlled by channel state information (side information), and it is available to the transmitter in a noncausal manner (termed here noncausal side information). In addition, we assume that there is a noiseless feedback from the output of the channel for the non-degraded receiver to the transmitter, and it helps them share a secret key, which enlarges the degraded receiver's uncertainty about the confidential message. Measuring the uncertainty by equivocation (conditional entropy), the capacity-equivocation region composed of all achievable rates-equivocation triples is determined for this new model. Furthermore, the secrecy capacity is formulated, which provides the best transmission rate with perfect secrecy.
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.
The broadcast channel with mutual secrecy requirement at the receivers (BC-MSR-R) is a basic model characterizing the physical layer security (PLS) in the down-link of the wireless communication systems, where one transmitter sends two independent messages to two receivers via a broadcast channel, and each receiver can successfully decode his/her intended message and wishes to overhear the other one's message. This paper studies how to enhance the already existing secrecy rate region of the BC-MSR-R via receivers' feedback. Specifically, we propose two feedback strategies for the BC-MSR-R, where one uses the feedback to generate pure secret keys protecting the transmitted messages, and the other uses the feedback to generate not only keys but also cooperative messages helping the receivers to improve their decoding performance. Different inner bounds on the secrecy capacity region of the BC-MSR-R with noiseless feedback are constructed according to different feedback strategies, and these bounds are further illustrated by a Dueck-type example.
In this paper, we investigate the problem of secure broadcasting over block-fading channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having imperfect channel state information (CSI) via a finite rate feedback on the throughput of a broadcast channel where the transmission is intended for multiple legitimate receivers in the presence of an eavesdropper. First, we partially characterize the ergodic secrecy capacity of the system when the source broadcasts the same information to all the receivers, i.e., common message transmission. Then, we look at the independent messages case, where the transmitter broadcasts multiple independent messages to the legitimate receivers. For this case, we present lower and upper bounds on the ergodic secrecy sum-capacity. In both scenarios, we show that the proposed lower and upper bounds coincide asymptotically as the capacity of the feedback links becomes large, hence, fully characterizing the secrecy capacity in this case.
The model for a broadcast channel with confidential messages (BC-CM) plays an important role in the physical layer security of modern communication systems. In recent years, it has been shown that a noiseless feedback channel from the legitimate receiver to the transmitter increases the secrecy capacity region of the BC-CM. However, at present, the feedback coding scheme for the BC-CM only focuses on producing secret keys via noiseless feedback, and other usages of the feedback need to be further explored. In this paper, we propose a new feedback coding scheme for the BC-CM. The noiseless feedback in this new scheme is not only used to produce secret keys for the legitimate receiver and the transmitter but is also used to generate update information that allows both receivers (the legitimate receiver and the wiretapper) to improve their channel outputs. From a binary example, we show that this full utilization of noiseless feedback helps to increase the secrecy level of the previous feedback scheme for the BC-CM.