New Capacity-Achieving Encoding Schemes for Degraded Binary Broadcast Channels

We study two-receiver degraded binary broadcast channels (DBBCs), focusing on the capacity region and the encoding schemes that achieve its boundary. First, we derive the conditions for a general binary broadcast channel to be degraded, and show that only a very limited subset of the possible degraded configurations have been investigated in the previous literature. Then, we show how to design a capacity-achieving encoding scheme for a general DBBC, and give a detailed specific example. The designed scheme turns out to be very general and to include, as special cases, the encoding schemes that achieve the capacity boundary of the DBBCs previously studied in the literature.