Asynchronous Guessing Subject to Distortion

The problem of guessing subject to distortion is considered, and the performance of randomized guessing strategies is investigated. A one-shot achievability bound on the guessing moment (i.e., moment of the number of required queries) is given. Applying this result to i.i.d. sources, it is shown that randomized strategies can asymptotically attain the optimal guessing moment. Further, a randomized guessing scheme which is feasible even when the block size is extremely large is proposed, and a single-letter characterization of the guessing moment achievable by the proposed scheme is obtained.