TY - JOUR
T1 - Codes with the identifiable parent property for multimedia fingerprinting
AU - Cheng, Minquan
AU - Fu, Hung-Lin
AU - Jiang, Jing
AU - Lo, Yuan Hsun
AU - Miao, Ying
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - Let C be a q-ary code of length n and size M, and C(i)={c(i)|c=(c(1),c(2),…,c(n))T∈C} be the set of ith coordinates of C. The descendant code of a sub-code C′⊆C is defined to be C′(1)×C′(2)×⋯×C′(n). In this paper, we introduce a multimedia analogue of codes with the identifiable parent property (IPP), called multimedia IPP codes or t-MIPPC(n, M, q), so that given the descendant code of any sub-code C′ of a multimedia t-IPP code C, one can always identify, as IPP codes do in the generic digital scenario, at least one codeword in C′. We first derive a general upper bound on the size M of a multimedia t-IPP code, and then investigate multimedia 3-IPP codes in more detail. We characterize a multimedia 3-IPP code of length 2 in terms of a bipartite graph and a generalized packing, respectively. By means of these combinatorial characterizations, we further derive a tight upper bound on the size of a multimedia 3-IPP code of length 2, and construct several infinite families of (asymptotically) optimal multimedia 3-IPP codes of length 2.
AB - Let C be a q-ary code of length n and size M, and C(i)={c(i)|c=(c(1),c(2),…,c(n))T∈C} be the set of ith coordinates of C. The descendant code of a sub-code C′⊆C is defined to be C′(1)×C′(2)×⋯×C′(n). In this paper, we introduce a multimedia analogue of codes with the identifiable parent property (IPP), called multimedia IPP codes or t-MIPPC(n, M, q), so that given the descendant code of any sub-code C′ of a multimedia t-IPP code C, one can always identify, as IPP codes do in the generic digital scenario, at least one codeword in C′. We first derive a general upper bound on the size M of a multimedia t-IPP code, and then investigate multimedia 3-IPP codes in more detail. We characterize a multimedia 3-IPP code of length 2 in terms of a bipartite graph and a generalized packing, respectively. By means of these combinatorial characterizations, we further derive a tight upper bound on the size of a multimedia 3-IPP code of length 2, and construct several infinite families of (asymptotically) optimal multimedia 3-IPP codes of length 2.
KW - Bipartite graph
KW - Generalized packing
KW - Generalized quadrangle
KW - IPP code
KW - Separable code
UR - http://www.scopus.com/inward/record.url?scp=84963997656&partnerID=8YFLogxK
U2 - 10.1007/s10623-016-0203-x
DO - 10.1007/s10623-016-0203-x
M3 - Article
AN - SCOPUS:84963997656
SN - 0925-1022
VL - 83
SP - 71
EP - 82
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 1
ER -