  We study a multi-task private semantic communication problem, in which an
encoder has access to an information source arbitrarily correlated with some
latent private data. A user has $L$ tasks with priorities. The encoder designs
a message to be revealed which is called the semantic of the information
source. Due to the privacy constraints the semantic can not be disclosed
directly and the encoder adds noise to produce disclosed data. The goal is to
design the disclosed data that maximizes the weighted sum of the utilities
achieved by the user while satisfying a privacy constraint on the private data.
In this work, we first consider a single-task scenario and design the added
noise utilizing various methods including the extended versions of the
Functional Representation Lemma, Strong Functional Representation Lemma, and
separation technique. We then study the multi-task scenario and derive a simple
design of the source semantics. We show that in the multi-task scenario the
main problem can be divided into multiple parallel single-task problems.
