Abstract
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.
Highlights
Wyner, in his outstanding paper on the degraded wiretap channel [1], first studied secure transmission over a physically degraded broadcast channel in the presence of an additional wiretapper.Wyner showed that the secrecy capacity of the degraded wiretap channel model was given byCsd = max( I ( X; Y ) − I ( X; Z )), P( x ) (1)where X, Y and Z are the channel input, channel output for the legitimate receiver and channel output for the wiretapper, respectively, and they satisfy the Markov chain X → Y → Z
Wyner’s work [1] to a more general case: the broadcast channel with confidential messages (BC-CM), where common and confidential messages were transmitted through a discrete memoryless general broadcast channel, and the common message was intended to be decoded by both the legitimate receiver and the wiretapper, while the confidential message was only allowed to be decoded by the legitimate receiver
Note that the secrecy capacities in (5) and (6) can be viewed as a combination of two parts: the first part is the difference between the main channel capacity (I (V; Y ) or I ( X; Y )) and the wiretap channel capacity (I (V; Z ) or I ( X; Z )), and the second part is the rate H (Y |V, Z ) (H (Y | X, Z )) of a secret key generated by the noiseless feedback and shared between the legitimate receiver and the transmitter
Summary
In his outstanding paper on the degraded wiretap channel [1], first studied secure transmission over a physically degraded broadcast channel in the presence of an additional wiretapper. Similar to the work of [2], using (4), Ahlswede and Cai provided an achievable secrecy rate Rs (lower bound on the secrecy capacity) of the general wiretap channel with noiseless feedback, and it is given by f −cai. Note that the secrecy capacities in (5) and (6) can be viewed as a combination of two parts: the first part is the difference between the main channel capacity (I (V; Y ) or I ( X; Y )) and the wiretap channel capacity (I (V; Z ) or I ( X; Z )), and the second part is the rate H (Y |V, Z ) (H (Y | X, Z )) of a secret key generated by the noiseless feedback and shared between the legitimate receiver and the transmitter.
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