Two-Level Private Information Retrieval

TL;DR

This paper introduces a two-level private information retrieval system with heterogeneous privacy requirements, providing new coding schemes, capacity bounds, and analyzing the gap between bounds.

Contribution

It proposes two novel coding schemes for the two-level PIR system and derives capacity bounds, addressing heterogeneous privacy needs.

Findings

Lower bound on capacity via two coding schemes

Upper bound on capacity established

Gap between bounds vanishes when T1 equals T2

Abstract

In the conventional robust $T$-colluding private information retrieval (PIR) system, the user needs to retrieve one of the possible messages while keeping the identity of the requested message private from any $T$ colluding servers. Motivated by the possible heterogeneous privacy requirements for different messages, we consider the $(N, T_1:K_1, T_2:K_2)$ two-level PIR system with a total of $K_2$ messages in the system, where $T_1\geq T_2$ and $K_1\leq K_2$. Any one of the $K_1$ messages needs to be retrieved privately against $T_1$ colluding servers, and any one of the full set of $K_2$ messages needs to be retrieved privately against $T_2$ colluding servers. We obtain a lower bound to the capacity by proposing two novel coding schemes, namely the non-uniform successive cancellation scheme and the non-uniform block cancellation scheme. A capacity upper bound is also derived. The gap between the upper bound and the lower bounds is analyzed, and shown to vanish when $T_1=T_2$. Lastly, we show that the upper bound is in general not tight by providing a stronger bound for a special setting.