Saddle-point Solution of the Fingerprinting Capacity Game Under the Marking Assumption

Yen-Wei Huang; Pierre Moulin

doi:10.1109/isit.2009.5205882

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arXiv · 0905.1375

Saddle-point Solution of the Fingerprinting Capacity Game Under the Marking Assumption

Yen-Wei Huang·Pierre Moulin

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Abstract

We study a fingerprinting game in which the collusion channel is unknown. The encoder embeds fingerprints into a host sequence and provides the decoder with the capability to trace back pirated copies to the colluders. Fingerprinting capacity has recently been derived as the limit value of a sequence of maxmin games with mutual information as the payoff function. However, these games generally do not admit saddle-point solutions and are very hard to solve numerically. Here under the so-called Boneh-Shaw marking assumption, we reformulate the capacity as the value of a single two-person zero-sum game, and show that it is achieved by a saddle-point solution. If the maximal coalition size is $k$ and the fingerprint alphabet is binary, we derive equations that can numerically solve the capacity game for arbitrary $k$. We also provide tight upper and lower bounds on the capacity. Finally, we discuss the asymptotic behavior of the fingerprinting game for large $k$ and practical implementation issues.

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Yen-Wei Huang, Pierre Moulin. 2009-05-09. Saddle-point Solution of the Fingerprinting Capacity Game Under the Marking Assumption. https://doi.org/10.1109/isit.2009.5205882

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