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

We study a relay channel with confidential messages (RCC), which involves a sender, a receiver and a relay. In the RCC, a common information must be transmitted to both a receiver and a relay and also a private information to the intended receiver, while keeping the relay as ignorant of it as possible. The level of ignorance of the relay rather than the private message is measured by the equivocation rate. We consider two error probability exponents (reliabilities) E₁, E₂ of exponentially decrease of error probability of the receiver decoder and the relay decoder, respectively. For E = (E₁, E₂), the E-capacity region is the set of all E-achievable rates of codes with given reliability E. We derive a random coding bound for E-capacity region of the RCC using block Markov strategies over a fixed number of blocks. We also show that, when E tends to zero, our obtained inner bound for E-capacity region converges to the inner bound for the capacity region of the RCC obtained by Y. Oohama and S. Watanabe.