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：在本文中,我们调查了首席执行官(CEO)问题的基本局限性,即将物理识别特征作为信息来源处理。为了使通过帮助者数据向窃听器泄漏信息的信息,可忽略不计,统一和独立地选择的私人钥匙与编码器对识别特征的测量相连接,以便生成帮助者数据。首席执行官问题之所以突出,是因为很难说明紧凑的比例扭曲区域的特点,对于一般案件来说,这仍然是一个未决问题。在本研究报告中,我们根据两种具体的扭曲措施,即对数损失(离散和高斯安环境)和四面形扭曲措施,将这一问题的收费-关键扭曲区域定性为紧凑的区域。我们还对特征区域进行数字计算,计算结果显示,如果允许更大程度的扭曲,则可以实现较小的存储率和私人钥匙率。对于私人钥匙利率的限制和微不足道的渗漏等特殊情况,我们的特征自然将这一区域降为Courde和Weissman提供的比率扭曲区域,用于对数值的扭曲性损失(离散和高斯安氏设置) 和正氏度扭曲措施(Cenharma) (2005年)。