两级指纹编码
Two-Level Fingerprinting Codes
摘要：
我们介绍了两级指纹和可追溯性代码的概念。在这种设置中，通过将用户分类到各个组中，以分层方式组织用户;例如，通过将分布区域划分为若干地理区域，并将来自同一区域的用户收集到一个组中。两级指纹和可追溯性代码具有以下特性：与传统（一级）代码一样，当给定由用户联盟产生的非法副本时，如果联盟大小小于某个阈值$t$，则解码器识别出其中一个有罪用户。此外，即使当联盟是较大大小的$s$ $(> t)$时，解码器仍然通过跟踪包含有罪用户的组之一来提供部分信息。我们建立了代码具有两级可追溯性的充分条件。此外，我们还提供了两级指纹码的结构和特征的相应的一组可实现的速率。
英文摘要：
We introduce the notion of two-level fingerprinting and traceability codes. In this setting, the users are organized in a hierarchical manner by classifying them into various groups; for instance, by dividing the distribution area into several geographic regions, and collecting users from the same region into one group. Two-level fingerprinting and traceability codes have the following property: As in traditional (one-level) codes, when given an illegal copy produced by a coalition of users, the decoder identifies one of the guilty users if the coalition size is less than a certain threshold $t$. Moreover, even when the coalition is of a larger size $s$ $(> t)$, the decoder still provides partial information by tracing one of the groups containing a guilty user. We establish sufficient conditions for a code to possess the two-level traceability property. In addition, we also provide constructions for two-level fingerprinting codes and characterize the corresponding set of achievable rates.
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