In this paper, we investigate the fundamental limits of the chief executive officer (CEO) problem in which physical and biometric identifiers are treated as information sources. In order to make the information leakage of the identifiers to the eavesdropper via helper data negligible, private keys, uniformly and independently chosen, are bonded into measurements of the identifiers at the encoders to generate the helper data. The CEO problem is renowned for the difficulty of 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 problem under two specific distortion measures, namely, logarithmic loss (both discrete and Gaussian settings) and quadratic distortion measures. Also, we 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. As 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：本文研究了以物理与生物识别标识符作为信息源的首席执行官（CEO）问题的基本极限。为使通过辅助数据泄露给窃听者的标识符信息可忽略不计，编码器将均匀且独立选择的私钥融入标识符测量值中以生成辅助数据。CEO问题因率失真区域的精确刻画具有高难度而著称，其一般情形至今仍是未解难题。我们针对两种特定失真度量（即离散与高斯设定下的对数损失及二次失真度量）刻画了该问题的紧致率-密钥-失真区域。通过数值计算所刻画的区域，结果表明：当允许更大失真时，可达成更低的存储率与私钥率。在无私钥率约束及可忽略泄漏约束的特例下，我们的刻画自然退化为Courtade与Weissman（2014）针对对数损失失真度量、以及Prabhakaran等（2004）、Chen等（2004）与Oohama（2005）针对二次失真度量所提供的率失真区域。