  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.
