Blind Fingerprinting

We study blind fingerprinting, where the host sequence into which fingerprints are embedded is partially or completely unknown to the decoder. This problem relates to a multiuser version of the Gel'fand-Pinsker problem. The number of colluders and the collusion channel are unknown, and the colluders and the fingerprint embedder are subject to distortion constraints. We propose a conditionally constant-composition random binning scheme and a universal decoding rule and derive the corresponding false-positive and false-negative error exponents. The encoder is a stacked binning scheme and makes use of an auxiliary random sequence. The decoder is a {\em maximum doubly-penalized mutual information decoder}, where the significance of each candidate coalition is assessed relative to a threshold that trades off false-positive and false-negative error exponents. The penalty is proportional to coalition size and is a function of the conditional type of host sequence. Positive exponents are obtained at all rates below a certain value, which is therefore a lower bound on public fingerprinting capacity. We conjecture that this value is the public fingerprinting capacity. A simpler threshold decoder is also given, which has similar universality properties but also lower achievable rates. An upper bound on public fingerprinting capacity is also derived.