The Capacity Region for Classes of Sum-Broadcast Channels

2026-06-10

AI Summary

This study investigates the capacity region of the sum of multiple broadcast channels, encompassing degraded, less noisy, more capable, deterministic, and semi-deterministic cases. By demonstrating that the outer bound for auxiliary receivers coincides with Marton’s inner bound, the work extends El Gamal’s capacity result for the sum of two reversely degraded broadcast channels to a significantly broader class of channels. A key contribution is the introduction of the notion of a “dominant broadcast channel,” which provides a unified analytical framework for these settings. The paper fully characterizes the capacity region for the sum of such broadcast channels, thereby establishing a rigorous theoretical foundation for understanding the fundamental limits of information transmission in complex broadcast networks.

Abstract

We compute the capacity region of a sum of broadcast channels whose components are degraded, less-noisy, more-capable, deterministic, or semi-deterministic. We achieve this by showing that an auxiliary-receiver outer bound, previously introduced by some of the authors, matches Marton's inner bound. This result generalizes a previously known result for the sum of two reversely degraded broadcast channels due to El Gamal (1980). Moreover, we define a class of primary broadcast channels and show an analogous result for the sum of primary broadcast channels.

Problem

• broadcast channels
• capacity region
• sum channels
• degraded channels
• Marton's inner bound

Innovation

• broadcast channel
• capacity region
• Marton's inner bound
• auxiliary-receiver outer bound
• sum-channel