TY - JOUR
T1 - Probabilistic Existence Results for Parent-Identifying Schemes
AU - Gu, Yujie
AU - Cheng, Minquan
AU - Kabatiansky, Grigory
AU - Miao, Ying
N1 - Funding Information:
Manuscript received June 5, 2018; revised April 2, 2019; accepted June 24, 2019. Date of publication July 5, 2019; date of current version September 13, 2019. This work was supported in part by RFBR under Project 18-07-01427, in part by 2016GXNSFFA380011, 2018GXNSFAA138152, Guangxi Collaborative Innovation Center of Multi-source Information Integration and Intelligent Processing, in part by the Guangxi “Bagui Scholar” Teams for Innovation and Research Project, and in part by JSPS Grant-in-Aid for Scientific Research (B) under Grant 18H01133.
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2019/10
Y1 - 2019/10
N2 - 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\ge 3. Furthermore, we analyze the structure of 2-IPPS and prove some bounds for certain cases.
AB - 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\ge 3. Furthermore, we analyze the structure of 2-IPPS and prove some bounds for certain cases.
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U2 - 10.1109/TIT.2019.2927020
DO - 10.1109/TIT.2019.2927020
M3 - Article
AN - SCOPUS:85077384870
SN - 0018-9448
VL - 65
SP - 6160
EP - 6170
JO - IRE Professional Group on Information Theory
JF - IRE Professional Group on Information Theory
IS - 10
M1 - 8756061
ER -