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Achieving Private Information Retrieval Capacity in Distributed Storage Using an Arbitrary Linear Code. (arXiv:1712.03898v2 [cs.IT] UPDATED)
来源于:arXiv
We propose three private information retrieval (PIR) protocols for
distributed storage systems (DSSs) where data is stored using an arbitrary
linear code. The first two protocols, named Protocol 1 and Protocol 2, achieve
privacy for the scenario with noncolluding nodes. Protocol 1 requires a file
size that is exponential in the number of files in the system, while the file
size required for Protocol 2 is independent of the number of files and is hence
simpler. We prove that, for certain linear codes, Protocol 1 achieves the PIR
capacity, i.e., its PIR rate (the ratio of the amount of retrieved stored data
per unit of downloaded data) is the maximum possible for any given (finite and
infinite) number of files, and Protocol 2 achieves the asymptotic PIR capacity
(with infinitely large number of files in the DSS). In particular, we provide a
sufficient and a necessary condition for a code to be PIR capacity-achieving
and prove that cyclic codes, Reed-Muller (RM) codes, and optimal informa 查看全文>>