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The entropy of a randomly stopped sequence

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1 Author(s)

A Wald-like equation is proved for the entropy of a randomly stopped sequence of independent identically distributed discrete random variables X1, X2. . ., with a nonanticipating stopping time N. The authors first define a general stopping time and the associated stopped sequence, and then present the two main theorems for the entropy of a stopped sequence. The formal proofs of the lemmas necessary for the proof of the theorems are given. The randomness in the stopped sequence XN is the expected number of calls for X times the entropy per call plus the residual randomness in the stopping time conditioned on the unstopped sequence X

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Information Theory, IEEE Transactions on  (Volume:37 ,  Issue: 6 )