The role of feedback in channels with information embedding on actions

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.