An achievable rate region for discrete memoryless broadcast channels with confidential messages

In this paper, we consider non-degraded discrete memoryless broadcast channels where two private messages as well as a common message are transmitted at rate R₁, R₂ and R_o respectively. The common message is for both receivers to decode; the private message is only for its intended receiver of which the other receiver shall be kept as ignorant as possible. Measuring ignorance by equivocation, we propose an achievable rate region (R₁, R₂, R_o, R_e1, R_e2) for this channel where R_e1 and R_e2 are the equivocation rates for the two receivers respectively. This result generalizes Csiszar and Kornerpsilas capacity region for broadcast channels with single private message, Liu et alpsilas result for broadcast channels with perfect secrecy, Gelpsilafand and Pinskerpsilas achievable rate region for broadcast channels with common message, and Martonpsilas achievable rate region for general broadcast channels.