Chapter 15: The Degraded Broadcast Channel

Learning Objectives

• Define the broadcast channel and the degraded broadcast channel, and explain why degradedness simplifies the capacity analysis
• Understand superposition coding as the fundamental achievability technique for the degraded BC, including the cloud-satellite geometric interpretation
• Derive the capacity region of the degraded broadcast channel and prove its achievability using superposition coding with joint typicality decoding
• Specialize the capacity region to the Gaussian broadcast channel and show that power splitting between users traces the boundary
• Compare superposition coding with orthogonal access schemes (TDMA/FDMA) and prove that superposition coding achieves a strictly larger rate region
• Understand the converse for the degraded BC via the entropy power inequality and Bergmans' argument
• Appreciate the duality relationships between the MAC and BC capacity regions