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We study the problem of simultaneous search for multiple targets over amultidimensional unit cube and derive fundamental resolution limits ofnon-adaptive querying procedures using the 20 questions estimation framework.The performance criterion that we consider is the achievable resolution, whichis defined as the maximal $L_\infty$ norm between the location vector and itsestimated version where the maximization is over all target location vectors.The fundamental resolution limit is defined as the minimal achievableresolution of any non-adaptive query procedure, where each query has binaryyes/no answers. We drive non-asymptotic and second-order asymptotic bounds onthe minimal achievable resolution, using tools from finite blocklengthinformation theory. Specifically, in the achievability part, we relate the 20questions problem to data transmission over a multiple access channel, use theinformation spectrum method by Han and borrow results from finite blocklengthanalysis for random access channel coding. In the converse part, we relate the20 questions problem to data transmission over a point-to-point channel andadapt finite blocklength converse results for channel coding. Our resultsextend the purely first-order asymptotic analyses of Kaspi \emph{et al.} (ISIT2015) for the one-dimensional case: we consider channels beyond the binarysymmetric channel and derive non-asymptotic and second-order asymptotic boundson the performance of optimal non-adaptive query procedures.

Resolution Limits of Non-Adaptive 20 Questions Search for Multiple Targets