An MDS-PIR Capacity-Achieving Protocol for Distributed Storage Using Non-MDS Linear Codes

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

Asymmetry Helps: Improved Private Information Retrieval Protocols for Distributed Storage

We consider private information retrieval (PIR) for distributed storage systems (DSSs) with noncolluding nodes where data is stored using a non maximum distance separable (MDS) linear code. It was recently shown that if data is stored using a particular class of non-MDS linear codes, the MDS-PIR capacity, i.e., the maximum possible PIR rate for MDS-coded DSSs, can be achieved. For this class of codes, we prove that the PIR capacity is indeed equal to the MDS-PIR capacity, giving the first family of non-MDS codes for which the PIR capacity is known. For other codes, we provide asymmetric PIR protocols that achieve a strictly larger PIR rate compared to existing symmetric PIR protocols.Comment: To be presented at 2018 IEEE Information Theory Workshop (ITW'18). See arXiv:1808.09018 for its extended versio