This paper investigates the problem of leaky-private Private Information Retrieval with Side Information (L-PIR-SI), which relaxes the requirement of perfect privacy to achieve improved communication efficiency in the presence of side information. While the capacities of PIR-SI under both $W$-privacy and $(W,S)$-privacy have been partially explored, the impact of controlled information leakage in these settings remains unaddressed. We propose a unified probabilistic framework to construct L-PIR-SI schemes where the privacy leakage is quantified by a parameter $\varepsilon$, consistent with differential privacy standards. We characterize the achievable download costs and show that our results generalize several landmark results in the PIR literature: they recover the capacity of PIR-SI when $\varepsilon \to 0$, and reduce to the known bounds for leaky-PIR when side information is absent. This work provides the first look at the trade-offs between leakage, side information, and retrieval efficiency.

翻译：本文研究了带侧信息的泄露式私有信息检索问题，该问题通过放宽完美隐私要求，以在存在侧信息的情况下提升通信效率。尽管在$W$-隐私和$(W,S)$-隐私两种设定下的PIR-SI容量已得到部分探索，但受控信息泄露在这些场景中的影响尚未得到解决。我们提出了一个统一的概率框架来构建L-PIR-SI方案，其中隐私泄露通过参数$\varepsilon$进行量化，该参数与差分隐私标准保持一致。我们刻画了可达的下载成本，并证明我们的结果推广了PIR文献中的若干里程碑结论：当$\varepsilon \to 0$时，结果退化为PIR-SI的容量；当侧信息不存在时，则简化为泄露式PIR的已知界。这项工作首次揭示了泄露程度、侧信息与检索效率之间的权衡关系。