An achievable rate region for the broadcast channel

Let p( yl, y2 1 X) denote a discrete memoryless channel with a single source X and two independent receivers YI and Y2. W e exhibit an achievable region of rates (R11,R12,R22) 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 equipartit ion property involving many simultaneous “typicality” constraints. These results immediately general ize to yield an achievable rate region for the m-sender n-receiver channel in terms of s tandard mutual information quantities.