We propose a private information retrieval (PIR) protocol for distributed
storage systems with noncolluding nodes where data is stored using an arbitrary
linear code. An expression for the PIR rate, i.e., the ratio of the amount of
retrieved data per unit of downloaded data, is derived, and a necessary and a
sufficient condition for codes to achieve the maximum distance separable (MDS)
PIR capacity are given. The necessary condition is based on the generalized
Hamming weights of the storage code, while the sufficient condition is based on
code automorphisms. We show that cyclic codes and Reed-Muller codes satisfy the
sufficient condition and are thus MDS-PIR capacity-achieving.Comment: To be presented at 2018 IEEE International Symposium on Information
Theory (ISIT). arXiv admin note: substantial text overlap with
arXiv:1712.0389