This paper presents an explicit construction of multimedia codes with complete traceability resistant to the averaging attack and δ-noise. The obtained code is a combination of a class of signature codes together with a generalization of superimposed codes, for which existence lower bounds, using the Lovász Local Lemma, are obtained. The constructions are a consequence of the Moser-Tardos variable framework.

The usefulness of Identifiable Parent Property (IPP) schemes in diverse scenarios has led to several distinct but related concepts. This work focuses on three of these concepts: “classical” IPP codes, Multimedia IPP codes, and IPP set systems. Although several existence bounds for all of the above schemes are known, constructions are scarce. In this paper, we present explicit constructions of all mentioned IPP notions, in the form of combinatorial objects. Our discussion follows a systematic procedure. First, we use the Lovász Local Lemma (LLL) to obtain existence bounds for the object to be constructed. The bounds derived essentially match the previously best-known ones. Additionally, our proof strategy enables for further development. It allows us to use the Moser-Tardos algorithmic version of the LLL in order to construct, with polynomial complexity, the actual objects. Moreover, we extend the results of Giotis et al. to precisely establish the computational complexity of the proposed algorithms.