Capacity-Equivocation Region Bounds for Degraded Broadcast Channel with Action-Dependent States

From the perspective of secure communication, we study transmitting confidential messages in broadcast channel with action-dependent states. Transmitter aims to convey a common message to both receiver 1 and 2, and a confidential message only to receiver 1. It can take actions to affect the generation of channel states which are causally known to the encoder. The inner and outer bounds on the capacity-equivocation region of such a channel are characterized. The corresponding bounds on the secrecy capacity are also obtained. To achieve the rate-equivocation triples, we construct coding schemes using superposition coding and Wyner's random binning. For the special case where no common message is sent, the inner and outer bounds coincide with each other. A binary example is given to illustrate the results.