Random coding bound for E-capacity region of the broadcast channel with two confidential messages

The discrete memoryless broadcast channel with two independent confidential messages (BC-2CM) involves three sources, one encoder and two receivers. A common message is sent to both receivers and each private message is transmitted to the intended receiver, while keeping the other receiver as ignorant of it as possible. The level of ignorance is measured by the equivocation rate. We derived a random coding bound for E-capacity region of the BC-2CM. When error probability exponents are going to zero, this bound converges to the inner bound of the capacity region of the BC-2CM obtained by Xu, Cao and Chen.