Multi-file Private Information Retrieval from MDS Coded Databases with Colluding Servers

Private information retrieval (PIR) gets renewed attentions in recent years due to its information-theoretic reformulation and its application in distributed storage system (DSS). We study a variant of the information-theoretic and DSS-oriented PIR problem which considers retrieving several files simultaneously, known as the multi-file PIR. In this paper, we give an upper bound of the multi-file PIR capacity (the maximal number of bits privately retrieved per one bit of downloaded bit) for the degenerating cases. We then present two general multi-file PIR schemes according to different ratios of the number of desired files to the total number of files. In particular, if the ratio is at least half, then the rate of our scheme meets the upper bound of the capacity for the degenerating cases and is thus optimal.

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