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

TL;DR

This paper reformulates the fingerprinting capacity game under the marking assumption as a saddle-point problem, enabling numerical solutions and bounds for arbitrary coalition sizes, with insights into asymptotic behavior.

Contribution

It introduces a saddle-point formulation of the fingerprinting capacity game, facilitating numerical computation and analysis under the Boneh-Shaw marking assumption.

Findings

Capacity can be computed via saddle-point equations for any coalition size.

Tight upper and lower bounds on the fingerprinting capacity are provided.

Asymptotic analysis reveals behavior for large coalition sizes.

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.