双亲识别方案的概率存在性结果
Probabilistic Existence Results for Parent-Identifying Schemes
摘要：
父母识别方案为一些信息系统（如数字指纹和组测试）提供了一种从结果中识别原因的方法。在本文中，我们考虑组合结构的父母识别计划。首先，我们建立了双亲识别方案和禁止配置之间的等价关系。基于这种关系，我们推导出两个相关的组合结构，即$t$ -父母识别集系统（$t$ -IPPS）和$t$ -多媒体父母识别码（$t$ -MIPPC），这分别用于广播加密和多媒体指纹的概率存在下界。$t$的最大尺寸的概率下界在许多情况下具有渐近最优数量级，并且$t$-MIPPC的概率下界在$t=2$时提供渐近最优码率，并且在$t\geq 3$时提供最佳已知渐近码率。此外，我们分析了$2$ -IPPS的结构，并证明了某些情况下的一些界限。
英文摘要：
Parent-identifying schemes provide a way to identify causes from effects for some information systems such as digital fingerprinting and group testing. In this paper, we consider combinatorial structures for parent-identifying schemes. First, we establish an equivalent relationship between parent-identifying schemes and forbidden configurations. Based on this relationship, we derive probabilistic existence lower bounds for two related combinatorial structures, that is, $t$-parent-identifying set systems ($t$-IPPS) and $t$-multimedia parent-identifying codes ($t$-MIPPC), which are used in broadcast encryption and multimedia fingerprinting respectively. The probabilistic lower bound for the maximum size of a $t$-IPPS has the asymptotically optimal order of magnitude in many cases, and that for $t$-MIPPC provides the asymptotically optimal code rate when $t=2$ and the best known asymptotic code rate when $t\geq 3$. Furthermore, we analyze the structure of $2$-IPPS and prove some bounds for certain cases.
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