  This paper introduces a generalization of the Private Information Retrieval
with Side Information (PIR-SI) problem called Popularity-Aware PIR-SI
(PA-PIR-SI). The PA-PIR-SI problem includes one or more remote servers storing
copies of a dataset of $K$ messages, and a user who knows $M$ out of $K$
messages -- the identities of which are unknown to the server -- as a prior
side information, and wishes to retrieve one of the remaining $K-M$ messages.
The goal of the user is to minimize the amount of information they must
download from the server while revealing no information about the identity of
the desired message. In contrast to PIR-SI, in PA-PIR-SI, the dataset messages
are not assumed to be equally popular. That is, given the $M$ side information
messages, each of the remaining $K-M$ messages is not necessarily equally
likely to be the message desired by the user. In this work, we focus on the
single-server setting of PA-PIR-SI, and establish lower and upper bounds on the
capacity of this setting -- defined as the maximum possible achievable download
rate. Our upper bound holds for any message popularity profile, and is the same
as the capacity of single-server PIR-SI. We prove the lower bound by presenting
a PA-PIR-SI scheme which takes a novel probabilistic approach -- carefully
designed based on the popularity profile -- to integrate two existing PIR-SI
schemes. The rate of our scheme is strictly higher than that of the only
existing PIR-SI scheme applicable to the PA-PIR-SI setting.
