Function Computation Under Privacy, Secrecy, Distortion, and Communication Constraints

TL;DR

This paper extends the classical function computation problem by incorporating privacy, secrecy, distortion, and communication constraints, providing bounds on rate regions for multi-party scenarios with noisy measurements.

Contribution

It introduces new privacy leakage metrics related to remote sources and develops bounds for lossy and lossless computation with multiple transmitting nodes.

Findings

Derived inner and outer bounds on rate regions for various scenarios.

Established simplified bounds for special cases like invertible functions.

Evaluated a specific example scenario to illustrate the bounds.

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, including invertible and partially invertible functions, and degraded measurement channels, simplified lossless and lossy rate region bounds are established, and one region is evaluated as an example scenario.