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On the Capacity of Indecomposable Finite-State Channels With Feedback

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2 Author(s)
Ron Dabora ; Department of Electrical and Computer Engineering, Ben-Gurion University, Israel ; Andrea J. Goldsmith

We study the capacity of indecomposable finite-state channels (IFSCs) with feedback. It is first shown that the capacity-achieving input distribution for IFSCs with feedback is independent of the initial channel state, even though the capacity depends on the worst-case channel state. In addition, it is shown that for a large class of IFSCs for which the channel state is a deterministic function of a finite number of the most recent channel inputs and outputs, the feedback capacity depends only on the best-case channel state. This result is obtained by a novel transmission strategy whereby feedback is used to synchronize the beginning of the codeword transmission to be at the best-case channel state.

Published in:

IEEE Transactions on Information Theory  (Volume:59 ,  Issue: 1 )