Abstract
A coding theorem is proved for a class of stationary channels with 'feedback in which the output Yn = f(Xn-m n, Zn-m n) is the function of the current and past m symbols from the channel input Xn and the stationary ergodic channel noise Zn. In particular, it is shown that the feedback capacity is equal to where I(Xn rarr Yn) = Sigmai=1 n I(Xi;Yi|Yi-1) denotes the Massey directed information from the channel input to the output, and the supremum is taken over all causally conditioned distributions p(xnparyn-1) = Pii=1 np(xi|xi-1,yi-1)- The main ideas of the proof are the Shannon strategy for coding with side information and a new elementary coding technique for the given channel model without feedback, which is in a sense dual to Gallager's lossy coding of stationary ergodic sources. A similar approach gives a simple alternative proof of coding theorems for finite state channels by Yang-Kavcic-Tatikonda, Chen-Berger, and Permuter-Weissman-Goldsmith.
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