Nearly Optimal Constructions of PIR and Batch Codes

A general private information retrieval scheme for MDS coded databases with colluding servers

“…The general model considers a distributed storage system consisting of N servers. The system stores M files, denoted as W [1] , W [2] , . .…”

“…[i] j g n . Thus, the whole contents y n ∈ F M L q stored on the nth server are the concatenated projections of all the files {W [1] , W [2] , . .…”

“…Let G denote a random variable generated by the servers and also known to the user. G represents the randomness of the server's strategy to produce the feedbacks 1 . Both F and G are generated independently of the files and the identity of the desired file, i.e., H(F, G, i, W [1] , W [2] , .…”

“…These codes characterize how to design distributed storage systems that may emulate any classic k-server PIR scheme, with relatively a smaller storage overhead. Researches along this line include, for example, [1], [6], [17], [27], [31].…”

“…But for any other arbitrary storage code, it is uncertain whether similar results hold. Based on the intuition from existing explicit expressions shown in (1), in [15] Freij-Hollanti et al further conjecture that if T + K ≤ N , then the optimal PIR capacity is given by…”