Resolution Limits for the Noisy Non-Adaptive 20 Questions Problem

• Published in: IEEE transactions on information theory Vol. 67; no. 4; pp. 2055 - 2073
• Main Authors: Zhou, Lin, Hero, Alfred O.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 20 questions; adaptive; Asymptotic methods; Asymptotic properties; Channel coding; Constraints; Entropy; finite blocklength analysis; Loss measurement; multidimensional target; Noise measurement; non-adaptive; Probability distribution; probably approximately correct learning; Queries; Questions; resolution; second-order asymptotics; sorted posterior matching; Transforms; Upper bound

We establish fundamental limits on estimation accuracy for the noisy 20 questions problem with measurement-dependent noise and introduce optimal non-adaptive procedures that achieve these limits. The minimal achievable resolution is defined as the absolute difference between the estimated and the tr...