2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156642We 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.5 pages. Accepted to the Information Theory Workshop 2008, Porto, PortugalInformation Theorytext