Collusion-resistant fingerprinting of parallel content channels

The fingerprinting game is analysed when the coalition size $k$ is known to the tracer, but the colluders can distribute themselves across $L$ TV channels. The collusion channel is introduced and the extra degrees of freedom for the coalition are made manifest in our formulation. We introduce a payoff functional that is analogous to the single TV channel case, and is conjectured to be closely related to the fingerprinting capacity. For the binary alphabet case under the marking assumption, and the restriction of access to one TV channel per person per segment, we derive the asymptotic behavior of the payoff functional. We find that the value of the maximin game for our payoff is asymptotically equal to $L^2/k^2 2 \ln 2$, with optimal strategy for the tracer being the arcsine distribution, and for the coalition being the interleaving attack across all TV channels, as well as assigning an equal number of colluders across the $L$ TV channels.