Asymptotics of Fingerprinting and Group Testing: Capacity-Achieving Log-Likelihood Decoders
This addresses the need for provably optimal decoders in information theory and security applications, though it appears incremental as it builds on existing models and decoders.
The paper tackles the problem of designing capacity-achieving decoders for fingerprinting and group testing in large-coalition asymptotics, showing that log-likelihood decoders achieve capacity for various models, including universal decoders for arbitrary attacks in fingerprinting and more efficient decoders than prior work in group testing.
We study the large-coalition asymptotics of fingerprinting and group testing, and derive explicit decoders that provably achieve capacity for many of the considered models. We do this both for simple decoders (fast but suboptimal) and for joint decoders (slow but optimal), and both for informed and uninformed settings. For fingerprinting, we show that if the pirate strategy is known, the Neyman-Pearson-based log-likelihood decoders provably achieve capacity, regardless of the strategy. The decoder built against the interleaving attack is further shown to be a universal decoder, able to deal with arbitrary attacks and achieving the uninformed capacity. This universal decoder is shown to be closely related to the Lagrange-optimized decoder of Oosterwijk et al. and the empirical mutual information decoder of Moulin. Joint decoders are also proposed, and we conjecture that these also achieve the corresponding joint capacities. For group testing, the simple decoder for the classical model is shown to be more efficient than the one of Chan et al. and it provably achieves the simple group testing capacity. For generalizations of this model such as noisy group testing, the resulting simple decoders also achieve the corresponding simple capacities.