Abstract
We study the problem of semantic private information retrieval (Sem-PIR) with T colluding servers (Sem-TPIR), i.e., servers that collectively share user queries. In Sem-TPIR, the message sizes are different, and message retrieval probabilities by any user are not uniform. This is a generalization of the classical PIR problem where the message sizes are equal and message retrieval probabilities are identical. The earlier work on Sem-PIR considered the case of no collusions, i.e., the collusion parameter of T=1. In this paper, we consider the general problem for arbitrary T < N. We find an upper bound on the retrieval rate and design a scheme that achieves this rate, i.e., we derive the exact capacity of Sem-TPIR.