On Private Information Retrieval Array Codes
Yiwei Zhang, Xin Wang, Hengjia Wei, Gennian Ge · IEEE Transactions on Information Theory · 2019
Given a database, the private information retrieval (PIR) protocol allows a user to make queries to several servers and retrieve a certain item of the database via the feedbacks without revealing the identity of the specific item to any single server. Classic k-server PIR protocols work on replicated databases, i.e., each of the k servers stores a whole copy of the database. Recently, new PIR models were proposed with coding techniques arising from the distributed storage system. In these new models, each server only stores a fraction 1/s of the whole database, where s > 1 is the given rational number. The PIR array codes are recently proposed by Fazeli, Vardy, and Yaakobi to characterize the new models. The central problem in designing a PIR array code with m servers and the k-PIR property (which indicates that these m servers may emulate a classic k-server PIR protocol) is to maximize k/m, known as the virtual server rate. Our main contribution to this problem is twofold. First, for the case 12, a new upper bound on the rate of a PIR array code is presented. Besides, we also have some discussions on an asymptotically optimal construction by Blackburn and Etzion.