Information Structures for Feedback Capacity of Channels With Memory and Transmission Cost: Stochastic Optimal Control and Variational Equalities

The Finite Transmission Feedback Information (FTFI) capacity is characterized for any class of channel conditional distributions {\mathbf{P}}_{B_{i}|B^{i-1}, A_{i}} and {\mathbf{P}}_{B_{i}|B_{i-M}^{i-1}, A_{i}} , where M is the memory of the channel, B^{i} \stackrel {\triangle }{=}\{B^{-1},B_{...

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