We establish the randomized distributed function computation (RDFC) framework, in which a sender transmits just enough information for a receiver to generate a randomized function of the input data. Describing RDFC as a form of semantic communication, which can be essentially seen as a generalized remote-source-coding problem, we show that security and privacy constraints naturally fit this model, as they generally require a randomization step. Using strong coordination metrics, we ensure (local differential) privacy for every input sequence and prove that such guarantees can be met even when no common randomness is shared between the transmitter and receiver.
This work provides lower bounds on Wyner's common information (WCI), which is the communication cost when common randomness is absent, and proposes numerical techniques to evaluate the other corner point of the RDFC rate region for continuous-alphabet random variables with unlimited shared randomness. Experiments illustrate that a sufficient amount of common randomness can reduce the semantic communication rate by up to two orders of magnitude compared to the WCI point, while RDFC without any shared randomness still outperforms lossless transmission by a large margin. A finite blocklength analysis further confirms that the privacy parameter gap between the asymptotic and non-asymptotic RDFC methods closes exponentially fast with input length. Our results position RDFC as an energy-efficient semantic communication strategy for privacy-aware distributed computation systems.
University of California, Los Angeles（加州大学洛杉矶分校）；University of California, San Diego（加州大学圣地亚哥分校）
这项工作探讨了一个新的问题：有多少随机性需要实现本地差分隐私（LDP）？一个激励场景是使用\emph{same}（随机化）输出向多个分析师提供{ \em多个隐私级别}，用于分布或用于重量级人物估计。我们将此设置称为\emph{successive refinement of privacy}，因为它提供了对具有不同隐私级别的原始数据的分层访问。例如，相同的随机化输出可以使一个分析师能够重建输入，而另一个分析师只能估计服从LDP要求的分布。这将经典的Shannon（窃听）安全设置扩展到本地差分隐私。我们提供（顺序）紧特性的隐私效用随机性权衡分布估计，包括随机性约束下的标准LDP设置在几种情况下。我们还提供了一个非平凡的多层次隐私的隐私机制。此外，我们表明，随着时间的推移，我们不能重用随机密钥，同时保护每个用户的隐私。
