  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, where
$K_1$ messages need to be retrieved privately against $T_1$ colluding servers,
and all the messages need to be retrieved privately against $T_2$ colluding
servers where $T_2\leq T_1$. 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.
