标记假设下指纹容量博弈的鞍点解
Saddle-point Solution of the Fingerprinting Capacity Game Under the Marking Assumption
摘要：
研究了一个合谋渠道未知的指纹博弈。编码器将指纹嵌入到主机序列中，并为解码器提供追溯盗版副本到共谋者的能力。指纹容量是以互信息为支付函数的一系列极大极小博弈的极限值。然而，这些游戏一般不承认鞍点解决方案，是非常难以解决的数字。在这里，在所谓的Boneh-Shaw标记假设下，我们将容量重新表示为单个两人零和博弈的值，并表明它是通过鞍点解实现的。如果最大联盟的大小是$k$和指纹字母表是二进制的，我们推导出方程，可以数值求解任意$k$的容量游戏。我们还提供了严格的上限和下限的能力。最后，我们讨论了大型$k$的指纹游戏的渐近行为和实际实现问题。
英文摘要：
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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