Single-Server Pliable Private Information Retrieval with Identifiable Side Information

In Pliable Private Information Retrieval (PPIR) with a single server, messages are partitioned into $\Gamma$ non-overlapping classes. The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. In S. A. Obead, H. Y. Lin and E. Rosnes, Single-Server Pliable Private Information Retrieval With Side Information, arXiv:2305.06857, authors consider the problem of PPIR with Side Information (PPIR-SI), where the user now has side information. The user wants to retrieve any new message (not included in the side information) from its desired class without revealing the identity of the desired class and its side information. A scheme for the PPIR-SI is given by Obead et al. for the case when the users side information is unidentified, and this case is referred to as PPIR with Unidentifiable SI (PPIR-USI). In this paper, we study the problem of PPIR for the single server case when the side information is partially identifiable, and we term this case as PPIR with Identifiable Side Information (PPIR-ISI). The user is well aware of the identity of the side information belonging to $\eta$ number of classes, where $1\leq \eta \leq \Gamma$. In this problem, The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. We give a scheme for PPIR-ISI, and we prove that having identifiable side information is advantageous by comparing the rate of the proposed scheme to the rate of the PPIR-USI scheme given by Obead et al. for some cases. Further, we extend the problem of PPIR-ISI for multi-user case, where users can collaborately generate the query sets, and we give a scheme for this problem.