Capacities and Capacity-Achieving Decoders for Various Fingerprinting Games
This work addresses fingerprinting and group testing problems, providing incremental improvements in decoder design and capacity bounds for specific applications.
The paper tackles the problem of fingerprinting capacities and decoders in various informed settings, deriving new capacity results and constructing log-likelihood decoders that asymptotically match these capacities, with a universal decoder achieving the simple capacity for unknown attacks and eliminating bias distribution cut-offs.
Combining an information-theoretic approach to fingerprinting with a more constructive, statistical approach, we derive new results on the fingerprinting capacities for various informed settings, as well as new log-likelihood decoders with provable code lengths that asymptotically match these capacities. The simple decoder built against the interleaving attack is further shown to achieve the simple capacity for unknown attacks, and is argued to be an improved version of the recently proposed decoder of Oosterwijk et al. With this new universal decoder, cut-offs on the bias distribution function can finally be dismissed. Besides the application of these results to fingerprinting, a direct consequence of our results to group testing is that (i) a simple decoder asymptotically requires a factor 1.44 more tests to find defectives than a joint decoder, and (ii) the simple decoder presented in this paper provably achieves this bound.