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.
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