We consider a distributed function computation problem in which parties observing noisy versions of a remote source facilitate the computation of a function of their observations at a fusion center through public communication. The distributed function computation is subject to constraints, including not only reliability and storage but also privacy and secrecy. Specifically, 1) the remote source should remain private from an eavesdropper and the fusion center, measured in terms of the information leaked about the remote source; 2) the function computed should remain secret from the eavesdropper, measured in terms of the information leaked about the arguments of the function, to ensure secrecy regardless of the exact function used. We derive the exact rate regions for lossless and lossy single-function computation and illustrate the lossy single-function computation rate region for an information bottleneck example, in which the optimal auxiliary random variables are characterized for binary-input symmetric-output channels. We extend the approach to lossless and lossy asynchronous multiple-function computations with joint secrecy and privacy constraints, in which case inner and outer bounds for the rate regions differing only in the Markov chain conditions imposed are characterized.
翻译:我们考虑到一个分布函数计算问题,即观察远程源的噪音版本的各方通过公共通信在聚变中心计算其观测功能时会通过公共通信进行计算。分布函数计算受到制约,不仅包括可靠性和存储,也包括隐私和保密性。具体地说,1)远程源应保持来自窃听器和聚变中心的隐私,以关于远程源的信息泄漏量来衡量;2)计算函数应保持由窃听器的保密性,以关于该功能参数的信息泄漏来衡量,以确保其观测功能的保密性,不论所使用的确切功能如何。我们为无损和损失的单功能计算得出准确的速率区域,并举例说明信息瓶颈的单一功能计算率损失率区域,其中最佳辅助随机变量的特征是二元输入对称输出渠道。我们推广了无损和损失的多功能计算方法,并采用联合保密和隐私限制的方法,在这种情况下,只对在Markov链条条件下不同的比例区域规定了内外界限。