On the Leaky Private Information Retrieval with Side Information

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.