Codes with the identifiable parent property for multimedia fingerprinting

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)) ∈ 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 subcode 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.