On the Capacity Region of the K-User Discrete Memoryless Broadcast Channel with Two Degraded Messages

The K-user discrete memoryless (DM) broadcast channel (BC) with two degraded messages, with one common message to he decoded by all receivers and a private message by a subset of receivers, is studied. The receivers that must decode both messages are referred to as private receivers and the remaining ones that need only decode the common message as common receivers. We obtain two main results. The first one establishes the capacity region of two classes of DM BCs characterized by the associated sets of pair-wise relationships between and among the common and private receivers, each described by the well-known more capable and less noisy conditions. For both these classes, the capacity region is achieved by superposition coding and joint decoding so that the main contribution herein lies in the proofs of the converses. When specialized to the two previously well-studied cases of a single private receiver and a single common receiver, the two aforementioned classes are respectively as large as or larger than those for which capacity was previously obtained. The second main result is a new inner bound in closed form that involves rate splitting, superposition coding, and indirect decoding and we state its capacity optimality for a new class of four-receiver DM BCs.