Feedback Coding Schemes for the Broadcast Channel with Mutual Secrecy Requirement

Recently, the physical layer security (PLS) of the communication systems has been shown to be enhanced by using legal receiver's feedback. The present secret key based feedback scheme mainly focuses on producing key from the feedback and using this key to protect part of the transmitted message. However, this feedback scheme has been proved only optimal for several degraded cases. The broadcast channel with mutual secrecy requirement (BC-MSR) is important as it constitutes the essence of physical layer security (PLS) in the down-link of the wireless communication systems. In this paper, we investigate the feedback effects on the BC-MSR, and propose two inner bounds and one outer bound on the secrecy capacity region of the BC-MSR with noiseless feedback. One inner bound is constructed according to the already existing secret key based feedback coding scheme for the wiretap channel, and the other is constructed by a hybrid coding scheme using feedback to generate not only keys protecting the transmitted messages but also cooperative messages helping the receivers to improve their decoding performance. The performance of the proposed feedback schemes and the gap between the inner and outer bounds are further explained via two examples.