A Detection Theoretic Approach to Digital Fingerprinting with Focused Receivers Under Uniform Linear Averaging Gaussian Attacks

We consider the digital fingerprinting problem where colluders apply uniform linear averaging followed by AWGN. For each user, the receiver computes the correlation between the attacked signal and that user's fingerprint, and performs thresholding (focused detection). We model the fingerprinting problem as a multi-user communications problem and develop a detection theoretic framework. Assuming independent colluders, we derive generic exact bit error probability expressions, together with tight bounds, for arbitrary fingerprinting systems. Then, we specialize our results to orthogonal, simplex and Gaussian codes; under MSE distortion constraints on the embedder and the colluders, we compute the optimal detection rule, the resulting minimum bit error probability, the collusion resistance for the aforementioned codes, and compare their performances.