An achievable rate region for the broadcast channel

Let denote a discrete memoryless channel with a single source and two independent receivers and . We exhibit an achievable region of rates at which independent information can be sent, respectively, to receiver 1, to both receivers 1 and 2, and to receiver 2. The achievability of the region is shown by using a version of the asymptotic equipartition property involving many simultaneous "typicality" constraints. These results immediately generalize to yield an achievable rate region for the -sender -receiver channel in terms of standard mutual information quantities.