Two-Level Private Information Retrieval

In the conventional robust $T$ -colluding private information retrieval (PIR) system, user needs to retrieve one of possible messages while keeping identity requested message from any colluding servers. Motivated by heterogeneous privacy requirements for different messages, we consider notation="LaTeX">$(N, T_{1}~:~K_{1}, T_{2}~:~K_{2})$ two-level PIR system with a total notation="LaTeX">$K_{2}$ in where notation="LaTeX">$T_{1}\geq T_{2}$ and notation="LaTeX">$K_{1}\leq K_{2}$ . Any notation="LaTeX">$K_{1}$ be retrieved privately against notation="LaTeX">$T_{1}$ servers, full set notation="LaTeX">$T_{2}$ We obtain lower bound capacity proposing two novel coding schemes, namely non-uniform successive cancelation scheme block scheme. A upper is also derived. The gap between bounds analyzed, shown vanish when notation="LaTeX">$T_{1}=T_{2}$ Lastly, show that general not tight providing stronger special setting.