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 a new privacy leakage metric; (3) the function computed is allowed to be a distorted version of the target function, which allows the storage rate to be reduced 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, including invertible and partially invertible functions, and degraded measurement channels, simplified lossless and lossy rate regions are characterized, and one achievable region is evaluated as an example scenario.
Highlights
We consider function computation scenarios in a network with multiple nodes involved
In a classic function computation scenario, the nodes exchange messages through authenticated, noiseless, and public communication links, which results in undesired information leakage about the computed function [3,4,5]
We consider function computation scenarios where the function computed is allowed to be a distorted version of the target function, which is relevant for various recent function computation applications
Summary
We consider function computation scenarios in a network with multiple nodes involved. An extension of the results in [18] are given in [20], where two privacy constraints are considered on a remote source whose different noisy measurements are observed by multiple nodes in the same network. The extension in [20] is different from the previous secure and private function computation models due to the assumption that there exists a remote source that is the main reason for the correlation between the random sequences observed by the nodes in the same network. It is shown in [20] that with such a remote source model, two different privacy leakage rate values should be limited, unlike a single constraint considered in [18]. We consider function computation scenarios where the function computed is allowed to be a distorted version of the target function, which is relevant for various recent function computation applications
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