Article
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Function Computation Under Privacy, Secrecy, Distortion, and Communication Constraints
Version 1
: Received: 7 December 2021 / Approved: 8 December 2021 / Online: 8 December 2021 (14:33:36 CET)
A peer-reviewed article of this Preprint also exists.
Günlü, O. Function Computation under Privacy, Secrecy, Distortion, and Communication Constraints †. Entropy 2022, 24, 110. Günlü, O. Function Computation under Privacy, Secrecy, Distortion, and Communication Constraints †. Entropy 2022, 24, 110.
Abstract
The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function computation problem include 1) privacy leakage to an eavesdropper is measured with respect to the remote source rather than the transmitting terminals’ observed sequences; 2) the information leakage to a fusion center with respect to the remote source is considered as a new privacy leakage metric; 3) the function computed is allowed to be a distorted version of the target function, which allows to reduce the storage rate as compared to a reliable function computation scenario in addition to reducing secrecy and privacy leakages; 4) two transmitting node observations are used to compute a function. Inner and outer bounds on the rate regions are derived for lossless and lossy single-function computation with two transmitting nodes, which recover previous results in the literature. For special cases that include invertible and partially-invertible functions, and degraded measurement channels, exact lossless and lossy rate regions are characterized, and one exact region is evaluated for an example scenario.
Keywords
Information theoretic privacy; secure function computation; remote source; distributed computation.
Subject
Engineering, Electrical and Electronic Engineering
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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