Resolution Limits for the Noisy Non-Adaptive 20 Questions Problem

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 absolute difference between estimated true locations of a target over unit cube, given finite number queries constrained by excess-resolution probability. Inspired relationship channel coding problem, we derive non-asymptotic bounds to estimate location. Furthermore, applying Berry--Esseen theorem our bounds, obtain second-order asymptotic approximation query subject probability constraint. specialize results versions several models including binary symmetric, erasure Z- channels. As complement, achievability bound adaptive querying use this benefit querying.