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.

翻译：我们研究了一个多任务私有语义通信问题，其中编码器可访问与某些潜在私有数据任意相关的信息源。用户有$L$个优先级不同的任务。编码器设计一个待揭示的消息，称为信息源的语义。由于隐私约束，语义不能直接披露，编码器通过添加噪声生成披露数据。目标是在满足私有数据隐私约束的同时，最大化用户所实现效用的加权和。在本工作中，我们首先考虑单任务场景，利用包括函数表示引理、强函数表示引理的扩展版本以及分离技术在内的多种方法设计添加的噪声。随后研究多任务场景，并推导出源语义的简单设计方案。我们证明，在多任务场景中，主要问题可分解为多个并行的单任务问题。