In this paper, we investigate the fundamental limits of the chief executive officer (CEO) problem in which physical identifiers are treated as information sources. To make the information leakage of the identifiers to the eavesdropper via helper data negligible, private keys, uniformly and independently chosen, are bonded to measurements of the identifiers at the encoders to generate the helper data. The CEO problem is renowned for the difficulty in characterizing the tight rate-distortion region, which is still an open question for the general case. In this study, we characterize the tight rate-key-distortion regions of such a problem under two specific distortion measures, namely logarithmic loss (both discrete and Gaussian settings) and quadratic distortion measures. We also provide numerical calculations of the characterized regions, and the calculated results show that when a larger distortion is permitted, smaller storage and private-key rates are achievable. For special cases where the constraints of private-key rates and negligible leakage are not imposed, our characterizations naturally reduce to the rate-distortion regions provided by Courtade and Weissman (2014) for logarithmic loss distortion, and Prabhakaran et al. (2004), Chen et al. (2004), and Oohama (2005) for quadratic distortion measure.

翻译：本文研究了以物理标识符作为信息源的首席执行官（CEO）问题的基本极限。为使标识符通过辅助数据向窃听者的信息泄露可忽略不计，编码器将均匀独立选择的私钥与标识符的测量值相结合以生成辅助数据。CEO问题因其紧致率失真区域的刻画困难而闻名，对于一般情况而言这仍然是一个未解决的问题。本研究在两种特定失真度量下——即对数损失（离散与高斯设置）与二次失真度量——刻画了该问题的紧致率-密钥-失真区域。我们还对所刻画区域进行了数值计算，计算结果表明：当允许更大失真时，可达到更小的存储和私钥速率。对于未施加私钥速率与可忽略泄露约束的特殊情形，我们的刻画自然退化为：Courtape与Weissman（2014）给出的对数损失失真的率失真区域，以及Prabhakaran等人（2004）、Chen等人（2004）和Oohama（2005）给出的二次失真度量的率失真区域。