We study the problem of simultaneous search for multiple targets over a multidimensional unit cube and derive fundamental resolution limits of non-adaptive querying procedures using the 20 questions estimation framework. The performance criterion that we consider is the achievable resolution, which is defined as the maximal $L_\infty$ norm between the location vector and its estimated version where the maximization is over all target location vectors. The fundamental resolution limit is defined as the minimal achievable resolution of any non-adaptive query procedure, where each query has binary yes/no answers. We drive non-asymptotic and second-order asymptotic bounds on the minimal achievable resolution, using tools from finite blocklength information theory. Specifically, in the achievability part, we relate the 20 questions problem to data transmission over a multiple access channel, use the information spectrum method by Han and borrow results from finite blocklength analysis for random access channel coding. In the converse part, we relate the 20 questions problem to data transmission over a point-to-point channel and adapt finite blocklength converse results for channel coding. Our results extend the purely first-order asymptotic analyses of Kaspi \emph{et al.} (ISIT 2015) for the one-dimensional case: we consider channels beyond the binary symmetric channel and derive non-asymptotic and second-order asymptotic bounds on the performance of optimal non-adaptive query procedures.

翻译：我们用20个问题估计框架研究在多维单元立方体上同时搜索多个目标的问题,并得出非适应性查询程序的基本解析限度。我们所考虑的绩效标准是可实现的解析度,即定位矢量与其所有目标矢量的估算版本之间的最大值$L ⁇ infty$标准,即最大度最大化是所有目标矢量的设定值。基本解析限的定义是任何非适应性查询程序的最小可实现解析度,即每个查询都有二进制的是/否答案。我们利用有限块长信息理论的工具,在最小可实现的解析线上驱动非非非非非非非非非非非非非非非自动的解析界限。具体而言,在可实现性部分,我们将20个问题与所有非适应性查询程序的最低可实现解度解析度解析度。我们的结果将2015年的纯端端端端端端端端的直径直径直径直径/直径直径直径直径直径分析。我们把2015年的端端端端端端端端端端端端端端端端端端端端端端端端端端端端端的解/正ISIS。我们的结果将2015年端端端端端端端端端端端端端端端端端端端端端端的直的直方根直方根直方根直分析。