TL;DR
This paper investigates the performance of randomized guessing strategies under distortion constraints, providing bounds and schemes that achieve near-optimal guessing moments, especially for large block sizes.
Contribution
It introduces a one-shot achievability bound for guessing moments and proposes a feasible randomized scheme with a single-letter characterization for large blocks.
Findings
Randomized strategies can asymptotically attain optimal guessing moments.
A new feasible guessing scheme is proposed for large block sizes.
A single-letter characterization of the guessing moment is derived.
Abstract
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.
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