Single-Server Pliable Private Information Retrieval with Identifiable Side Information

In Pliable Private Information Retrieval (PPIR) with a single server, messages are partitioned into T 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 [cs.IT]], 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. Identity of each message can be represented as a class-subclass index pair, where subclass index represents the membership of a message within a class. If the user does not know the subclass indices of its side information from a class, that class is termed as unidentifiable. Conversely, if the user knows the subclass indices of its side information from a class, that class is termed as identifiable. A scheme for the PPIR-SI is given by Obead et al. for the case when all classes are unidentifiable, i.e., the user is unaware of the subclass indices of all its side information, 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). There are η number of identifiable classes, where 1 ≤η≤r. We give a scheme for PPIR-ISI, and we prove that having some 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.