# Codes with the identifiable parent property for multimedia fingerprinting

Research paper by Minquan Cheng, Hung-Lin Fu, Jing Jiang, Yuan-Hsun Lo, Ying Miao

Indexed on: 07 Apr '16Published on: 07 Apr '16Published in: Designs, Codes and Cryptography

#### Abstract

Let $${\mathcal {C}}$$ be a q-ary code of length n and size M, and $${\mathcal {C}}(i) = \{\mathbf{c}(i) \ | \ \mathbf{c}=(\mathbf{c}(1), \mathbf{c}(2), \ldots , \mathbf{c}(n))^{T} \in {\mathcal {C}}\}$$ be the set of ith coordinates of $${\mathcal {C}}$$. The descendant code of a sub-code $${\mathcal {C}}^{'} \subseteq {\mathcal {C}}$$ is defined to be $${\mathcal {C}}^{'}(1) \times {\mathcal {C}}^{'}(2) \times \cdots \times {\mathcal {C}}^{'}(n)$$. 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 $${\mathcal {C}}^{'}$$ of a multimedia t-IPP code $${\mathcal {C}}$$, one can always identify, as IPP codes do in the generic digital scenario, at least one codeword in $${\mathcal {C}}^{'}$$. 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.