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Without feedback, the back-off from capacity due to non-asymptotic block-length can be quite substantial for block-lengths and error probabilities of interest in many practical applications. In this paper, novel achievability bounds are used to demonstrate that in the non-asymptotic regime, the maximal achievable rate improves dramatically thanks to variable-length coding with feedback. For example, for the binary symmetric channel with capacity 1/2 the block-length required to achieve 90% of the capacity is smaller than 200, compared to at least 3100 for the best fixed-block-length, non-feedback code. Virtually all the advantages of noiseless feedback are shown to be achievable with decision-feedback only. It is demonstrated that the non-asymptotic behavior of the fundamental limit depends crucially on the particular model chosen for the "End-of-packet" control signal.
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