Extended Functional Representation Lemma: A Tool for Privacy, Semantic Representation, Caching, and Compression Design

This paper provides an overview of a problem in information-theoretic privacy mechanism design, addressing two scenarios in which private data is either observable or hidden. In each scenario, different privacy measures are used, including bounded mutual information and per-letter privacy constraints. Considering the first scenario, an agent observes useful data that is correlated with private data, and wants to disclose the useful information to a user. Due to the privacy concerns, direct disclosure is prohibited. Hence, a privacy mechanism is designed to generate disclosed data which maximizes the revealed information about the useful data while satisfying a privacy constraint. In the second scenario, the agent has additionally access to the private data. We discuss how the Functional Representation Lemma, the Strong Functional Representation Lemma, and their extended versions are useful for designing low-complexity privacy mechanisms that achieve optimal privacy-utility trade-offs under certain constraints. Finally, we provide various information-theoretic problems including semantic communications, caching and delivery, and compression designs, where the approach can be applied.