On the Conditional Smooth Renyi Entropy and its Applications in Guessing and Source Coding

Abstract: A novel definition of the conditional smooth Renyi entropy, which is different from that of Renner and Wolf, is introduced. It is shown that our definition of the conditional smooth Renyi entropy is appropriate to give lower and upper bounds on the optimal guessing moment in a guessing problem where the guesser is allowed to stop guessing and declare an error. Further a general formula for the optimal guessing exponent is given. In particular, a single-letterized formula for mixture of i.i.d. sources is obtained. Another application in the problem of source coding with the common side-information available at the encoder and decoder is also demonstrated.