The Capacity Region of the Degraded Finite-State Broadcast Channel

Ron Dabora, Andrea J. Goldsmith
2010 IEEE Transactions on Information Theory  
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 consider
more » ... rios, we consider indecomposable as well as nonindecomposable channels. Index Terms-Broadcast channels, capacity, channels with memory, finite-state channels, indecomposable channels, network information theory, superposition codebook. B. Finite-State Channels The capacity of FSCs without feedback was originally studied by Shannon in 1957 [3]. In his work, Shannon analyzed the capacity of FSCs subject to the assumptions that the transmitter can calculate the state sequence (i.e., the current state is a function of the previous state and the current channel input), the initial state is known at the transmitter, any state is accessible 0018-9448/$26.00
doi:10.1109/tit.2010.2040974 fatcat:eymdqq52tnfr3bkepkcuwnqywq