The Capacity Region of the Degraded Finite-State Broadcast Channel

TL;DR

This paper characterizes the capacity regions of discrete, finite-state broadcast channels under physically and stochastically degraded conditions, considering both indecomposable and non-indecomposable cases, advancing understanding of their limits.

Contribution

It derives the capacity regions for both physically and stochastically degraded finite-state broadcast channels, including non-indecomposable cases, which was previously unresolved.

Findings

Capacity region for physically degraded finite-state broadcast channels derived.

Capacity region for stochastically degraded finite-state broadcast channels established.

Results apply to both indecomposable and non-indecomposable channel models.

Abstract

We consider the discrete, time-varying broadcast channel with memory under the assumption that the channel states belong to a set of finite cardinality. We first define the physically degraded finite-state broadcast channel for which we derive the capacity region. We then define the stochastically degraded finite-state broadcast channel and derive the capacity region for this scenario as well. In both scenarios we consider the non-indecomposable finite-state channel as well as the indecomposable one.