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We introduce and study the discrete, finite-state broadcast channel (FSBC) with memory. For this class of channels we define physical degradedness and stochastic degradedness, and demonstrate these definitions with practical communication scenarios. We then show that a superposition codebook with memory achieves the capacity region of physically degraded FSBCs. This result is subsequently used to characterize the capacity region of stochastically degraded FSBCs. In both scenarios, we considerdoi:10.1109/tit.2010.2040974 fatcat:eymdqq52tnfr3bkepkcuwnqywq