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.Comment: 5 pages, to appear in 2009 IEEE International Symposium on
Information Theory (ISIT 2009), Seoul, Korea, June 200