Variable-Length Coding With Noiseless Feedback and Finite Messages

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This paper considers the problem of zero-rate (fixed number of messages) variable-length coding over a memoryless noisy channel with noiseless feedback. This problem is considered from a control theoretic point of view and is modeled as a special case of active sequential hypothesis testing. Techniques from dynamic programming are applied to characterize the optimal solution to this problem leading to an improvement over previous known results as well as a concise alternative proof for Burnashev's converse bound.