Probabilistic Existence Results for Parent-Identifying Schemes
Yujie Gu, Minquan Cheng, Grigory A. Kabatiansky, Ying Miao · IEEE Transactions on Information Theory · 2019
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 the combinatorial structures for parent-identifying schemes. First, we establish an equivalent relationship between the parent-identifying schemes and forbidden configurations. Based on this relationship, we derive the 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 ≥ 3. Furthermore, we analyze the structure of 2-IPPS and prove some bounds for certain cases.