Existence and construction of complete traceability multimedia fingerprinting codes resistant to averaging attack and adversarial noise

It was shown very recently in [1] that there are no multimedia digital fingerprinting codes capable of fully recovering a coalition of malicious users under the general linear attack and adversarial noise. We show that such codes exist if the class of attacks is narrowed to the averaging attack. The arising mathematical problem is close to the problem of constructing signature codes for a noisy binary adder channel.