We study a two-stage identification problem with pre-processing to enable efficient data retrieval and reconstruction. In the enrollment phase, users’ data are stored into the database in two layers. In the identification phase an observer obtains an observation, which originates from an unknown user in the enrolled database through a memoryless channel. The observation is sent for processing in two stages. In the first stage, the observation is pre-processed, and the result is then used in combination with the stored first layer information in the database to output a list of compatible users to the second stage. Then the second step uses the information of users contained in the list from both layers and the original observation sequence to return the exact user identity and a corresponding reconstruction sequence. The rate-distortion regions are characterized for both discrete and Gaussian scenarios. Specifically, for a fixed list size and distortion level, the compression-identification trade-off in the Gaussian scenario results in three different operating cases characterized by three auxiliary functions. While the choice of the auxiliary random variable for the first layer information is essentially unchanged when the identification rate is varied, the second one is selected based on the dominant function within those three. Due to the presence of a mixture of discrete and continuous random variables, the proof for the Gaussian case is highly non-trivial, which makes a careful measure theoretic analysis necessary. In addition, we study a connection of the previous setting to a two observer identification and a related problem with a lower bound for the list size, where the latter is motivated from privacy concerns.

中文翻译：

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带有预处理的分层识别

我们研究了一个带有预处理的两阶段识别问题，以实现高效的数据检索和重建。在注册阶段，用户的数据分两层存储到数据库中。在识别阶段，观察者通过无记忆通道获得来自注册数据库中的未知用户的观察。观察分两个阶段发送进行处理。在第一阶段，对观察进行预处理，然后将结果与数据库中存储的第一层信息结合使用，向第二阶段输出兼容用户列表。然后第二步使用来自两个层的列表中包含的用户信息和原始观察序列来返回准确的用户身份和相应的重建序列。速率失真区域的特征在于离散和高斯场景。具体来说，对于固定的列表大小和失真级别，高斯场景中的压缩识别权衡导致三种不同的操作情况，其特征是三个辅助函数。当识别率变化时，第一层信息的辅助随机变量的选择基本不变，而第二层信息的选择基于这三者中的主导函数。由于离散和连续随机变量的混合存在，高斯情况的证明非常重要，这使得仔细的测量理论分析成为必要。此外，