The CEO Problem With Secrecy Constraints

Abstract

We study a lossy source coding problem with secrecy constraints in which a remote information source should be transmitted to a single destination via multiple agents in the presence of a passive eavesdropper. The agents observe noisy versions of the source and independently encode and transmit their observations to the destination via noiseless rate-limited links. The destination should estimate the remote source based on the information received from the agents within a certain mean distortion threshold. The eavesdropper, with access to side information correlated to the source, is able to listen in on one of the links from the agents to the destination in order to obtain as much information as possible about the source. This problem can be viewed as the so-called CEO problem with additional secrecy constraints. We establish inner and outer bounds on the ratedistortion-equivocation region of this problem. We also obtain the region in special cases where the bounds are tight. Furthermore, we study the quadratic Gaussian case and provide the optimal rate-distortion-equivocation region when the eavesdropper has no side information and an achievable region for a more general setup with side information at the eavesdropper.

Estimation in Wireless Sensor Networks With Security Constraints

“…In [71], the Chief Executive Officer (CEO) problem is investigated in which a center controller (or CEO) attempts to minimize the estimate distortion from the noisy observations of a random source it receives. The authors related the equivocation rate 2 to the normalized distortion at the eavesdropper in the CEO problem with additional secrecy constraints, where they showed that the estimation error at the eavesdropper is an upper bound of the equivocation rate.…”

“…[30]. Motivated by this idea, plus a close relation between MMSE and the mutual information of the channel input and output [32,71], we consider a notion of secrecy in estimation from a non-information theoretic viewpoint by requiring the distortion at the eavesdropper to be greater than a threshold D e . In this way, some level of confidentiality can be achieved at the FC.…”

“…From an information theoretic perspective, the authors in [30,51,60] studied the secrecy capacity in the case of full channel state information (CSI) or partial CSI, and investigated MIMO channels in [10,50,62]. Multiterminal source coding or CEO problems with secrecy constraints were also considered in [5,17,71,96]. In particular, in [96], the authors investigated secure lossy source coding in the presence of an eavesdropper who is 1 Perfect secrecy was first introduced in 1949 by Shannon.…”

“…SNR is equal to half the MMSE, as long as the input signals are observed through an additive Gaussian noise channel. In [71], the authors related the equivocation rate to the normalized distortion at the eavesdropper in the CEO problem with additional secrecy constraints, where they showed that the estimation error at the eavesdropper is an upper bound of the equivocation rate.…”

Distortion Outage Minimization in Distributed Estimation With Estimation Secrecy Outage Constraints

“…From an information theoretic perspective, the authors in [19], [20], [21] studied the secrecy capacity in the case of full CSI or partial CSI, and investigated MIMO channels in [22], [23], [24]. Multiterminal source coding or CEO problems with secrecy constraints were also considered in [25], [26], [27], [28]. In particular, in [28], the authors investigated secure lossy source coding in the presence of an eavesdropper who is able to observe the coded information bits and has access to correlated side information.…”