Bounds for Binary Multimedia Codes with the Identifiable Parent Property

Multimedia codes with the identifiable parent property (MIPPCs) were proposed to resist collusion attacks for multimedia fingerprinting. However, the largest possible code rate of binary MIPPCs is far from being understood yet. In this paper, we aim to establish lower and upper bounds for the largest code rate of binary MIPPCs. To that end, we introduce a new concept of locally thin and fat families (LTFFs) and establish relationships between LTFFs and binary MIPPCs. Accordingly, new lower and upper bounds for binary MIPPCs and LTFFs are derived by means of the probabilistic method and combinatorial techniques. In particular, the order of magnitude for the largest rate of binary MIPPCs is determined. It is shown that the code rate of binary MIPPCs outperforms other existing binary fingerprinting codes (e.g. binary separable codes) as well.