  Private information retrieval has been reformulated in an
information-theoretic perspective in recent years. The two most important
parameters considered for a PIR scheme in a distributed storage system are the
storage overhead and PIR rate. The complexity of the computations done by the
servers for the various tasks of the distributed storage system is an important
parameter in such systems which didn't get enough attention in PIR schemes. As
a consequence, we take into consideration a third parameter, the access
complexity of a PIR scheme, which characterizes the total amount of data to be
accessed by the servers for responding to the queries throughout a PIR scheme.
We use a general covering codes approach as the main tool for improving the
access complexity. With a given amount of storage overhead, the ultimate
objective is to characterize the tradeoff between the rate and access
complexity of a PIR scheme. This covering codes approach raises a new
interesting coding problem of generalized coverings similarly to the well-known
generalized Hamming weights.
