The Capacity Region of the Degraded Finite-State Broadcast Channel

We consider the discrete, time-varying broadcast channel with memory, under the assumption that the channel states belong to a set of nite cardinality. We begin with the de nition of the general nite-state broadcast channel and discuss the possible de nitions of the probability of error for this model. Next, we de ne the physically degraded nite-state broadcast channel and show that a superposition codebook with memory achieves capacity for this scenario. We then de ne the stochastically degraded nite-state broadcast channel, and relate this model to a physical communication scenario. We use the capacity result for the physically degraded channel to characterize the capacity of the stochastically degraded one. In both scenarios we consider the general nite-state channel as well as the indecomposable one, in which the effect of the initial state on future states becomes negligible with time.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Ron Dabora, Andrea J. Goldsmith
• Keywords: CORR 2008, Education, General Nite-state Broadcast, Nite-state Broadcast Channel, Time-varying Broadcast