Robust broadcasting of common and confidential messages over compound channels: Strong secrecy and decoding performance

The broadcast channel with confidential messages (BCC) consists of one transmitter and two receivers, where the transmitter sends a common message to both receivers and, at the same time, a confidential message to one receiver which has to be kept secret from the other one. In this paper, this communication scenario is studied for compound channels, where it is only known to the transmitter and receivers that the actual channel realization is fixed and from a prespecified set of channels. The information theoretic criterion of strong secrecy is analyzed in detail and its impact on the decoding performance of the non-legitimate receiver is characterized. In particular, it is shown that regardless of the computational capabilities and the applied decoding strategy of the non-legitimate receiver, his decoding error always tends to one. This gives a valuable signal processing implication of the strong secrecy criterion and identifies desirable properties of an optimal code design. Further, an achievable strong secrecy rate region is derived and a multiletter outer bound is given. Both together yield a multiletter expression of the strong secrecy capacity region of the compound BCC.