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.

翻译：本文建立了随机化分布式函数计算（RDFC）框架，在该框架中，发送方仅传输足够的信息，使接收方能够生成输入数据的随机化函数。将RDFC描述为一种语义通信形式——其本质上可视为广义的远程信源编码问题——我们证明了安全性与隐私约束自然契合该模型，因为它们通常需要随机化步骤。利用强协调度量，我们确保每个输入序列满足（局部差分）隐私，并证明即使发射机与接收机之间未共享任何公共随机性，此类保障仍可实现。本工作给出了韦纳公共信息（WCI）的下界（即无公共随机性时的通信成本），并提出了数值技术以评估连续字母随机变量在无限共享随机性条件下RDFC速率区域的另一角点。实验表明，与WCI点相比，充足的公共随机性可将语义通信速率降低多达两个数量级；而完全无共享随机性的RDFC仍大幅优于无损传输。有限码长分析进一步证实，渐近与非渐近RDFC方法间的隐私参数差距随输入长度呈指数级快速收敛。我们的研究结果确立了RDFC作为面向隐私感知分布式计算系统的能效优化语义通信策略。