  In this paper we study the problem of private information retrieval where a
user seeks to retrieve one of the $F$ files from a cluster of $N$ non-colluding
servers without revealing the identity of the requested file. In our setting
the servers are storage constrained in that they can only store a fraction
$\mu=t/N$ of each file. Furthermore, we assume that the files are stored in an
uncoded fashion. The rate of a PIR protocol is defined as the ratio of the file
size and the total number of bits downloaded. The maximum achievable rate is
referred to as capacity. It was previously shown that there are capacity
achieving PIR protocols when the file size is $N^F$ and complete files were
stored on all the servers. These results were further extended for the case
when servers store only a fraction of each file. However, the subpacketization
$v$ of the files required is exponential in the number of servers $N$. We
propose a novel uncoded PIR protocol based on combinatorial designs that are
also capacity achieving when the file size is $v \times t^F$. Our protocol has
linear subpacketization in the number of servers in contrast to previous work
in storage constrained uncoded PIR schemes. In the proposed PIR protocol, the
given system is projected to multiple instances of reduced systems with
replicated servers having full storage capacity. The subfiles stored in these
various instances are separately retrieved and lifted to solve the PIR problem
for the original system.
