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A novel definition of the conditional smooth Renyi entropy, which isdifferent from that of Renner and Wolf, is introduced. It is shown that ourdefinition of the conditional smooth Renyi entropy is appropriate to give lowerand upper bounds on the optimal guessing moment in a guessing problem where theguesser is allowed to stop guessing and declare an error. Further a generalformula for the optimal guessing exponent is given. In particular, asingle-letterized formula for mixture of i.i.d. sources is obtained. Anotherapplication in the problem of source coding with the common side-informationavailable at the encoder and decoder is also demonstrated.

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