Random coding theorems for the general discrete memoryless broadcast channel

Three different communication situations are considered for the general nondegraded discrete memoryless broadcast channel with two components. In the most general situation, common and separate information is sent to both receivers. In another situation, only separate information is sent, and in a third, one Common and one separate message is sent. For each communication situation a random coding inner bound on the capacity region is derived. An example is presented which Shows that in the most general situation the inner bound strictly dominates the family of rates obtained by time-sharing. The capacity region for the general situation is characterized by a limiting expression. The relationship with the degraded broadcast channel and the connection with other multiway channels, such as the channel with two senders and two receivers, is shown.