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    Codes with the Identifiable Parent Property for Multimedia Fingerprinting

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    Let C{\cal C} be a qq-ary code of length nn and size MM, and C(i)={c(i) ∣ c=(c(1),c(2),…,c(n))T∈C}{\cal C}(i) = \{{\bf c}(i) \ | \ {\bf c}=({\bf c}(1), {\bf c}(2), \ldots, {\bf c}(n))^{T} \in {\cal C}\} be the set of iith coordinates of C{\cal C}. The descendant code of a sub-code C′⊆C{\cal C}^{'} \subseteq {\cal C} is defined to be C′(1)×C′(2)×⋯×C′(n){\cal C}^{'}(1) \times {\cal C}^{'}(2) \times \cdots \times {\cal C}^{'}(n). In this paper, we introduce a multimedia analogue of codes with the identifiable parent property (IPP), called multimedia IPP codes or tt-MIPPC(n,M,q)(n, M, q), so that given the descendant code of any sub-code C′{\cal C}^{'} of a multimedia tt-IPP code C{\cal C}, one can always identify, as IPP codes do in the generic digital scenario, at least one codeword in C′{\cal C}^{'}. We first derive a general upper bound on the size MM of a multimedia tt-IPP code, and then investigate multimedia 33-IPP codes in more detail. We characterize a multimedia 33-IPP code of length 22 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 33-IPP code of length 22, and construct several infinite families of (asymptotically) optimal multimedia 33-IPP codes of length 22.Comment: 7 pages, submitted to IEEE transction on information theor
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