Broadcast channels with confidential messages

Given two discrete memoryless channels (DMC's) with a common input, it is desired to transmit private messages to receiver 1 rate R₁ and common messages to both receivers at rate R₎, while keeping receiver 2 as ignorant of the private messages as possible. Measuring ignorance by equivocation, a single-letter characterization is given of the achievable triples (R₁, R₄, R₎) where R₄ is the equivocation rate. Based on this channel coding result, the related source-channel matching problem is also settled. These results generalize those of Wyner on the wiretap channel and of Körner-Marton on the broadcast Channel.