Non-Asymptotic and Asymptotic Fundamental Limits of Guessing Subject to Distortion
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This paper considers the problem of guessing random variables subject to distortion. We investigate both non-asymptotic and asymptotic fundamental limits of the minimum t-th moment of the number of guesses. These fundamental limits are characterized by the quantity related to the Rényi entropy. To derive the non-asymptotic bounds, we use our techniques developed in lossy compression. Moreover, using the results obtained in the non-asymptotic setting, we derive the asymptotic result and show that it coincides with the previous result by Arikan and Merhav.
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