The capacity region of classes of product broadcast channels
This work solves a theoretical problem in information theory by determining capacity regions for specific classes of broadcast channels, but it is incremental as it builds on existing bounds and focuses on specialized cases.
The paper establishes a new outer bound for the capacity region of product broadcast channels, matching Marton's inner bound for classes like reversely semi-deterministic and reversely more-capable channels, and shows via an example that the previous best outer bound is strictly suboptimal for general broadcast channels.
We establish a new outer bound for the capacity region of product broadcast channels. This outer bound matches Marton's inner bound for a variety of classes of product broadcast channels whose capacity regions were previously unknown. These classes include product of reversely semi-deterministic and product of reversely more-capable channels. A significant consequence of this new outer bound is that it establishes, via an example, that the previously best known outer-bound is strictly suboptimal for the general broadcast channel. Our example is comprised of a product broadcast channel with two semi-deterministic components in reverse orientation.