Improved Private Information Retrieval for Coded Storage From Code Decomposition

We consider private information retrieval (PIR) for distributed storage systems with noncolluding nodes where data is stored using a non maximum distance separable (MDS) linear code. Recently, it was shown that when data is stored using certain non-MDS codes, the MDS-PIR capacity can be achieved, and is indeed the capacity of the system. In this paper, for storage codes not belonging to this class, we present a heuristic algorithm for their decomposition into punctured subcodes and a PIR protocol based on these punctured subcodes. The code decomposition is guided by the generalized Hamming weights of the storage code. We show that the proposed PIR protocol can achieve a larger PIR rate than that of all existing PIR protocols

Private Information Retrieval Schemes Using Cyclic Codes

A Private Information Retrieval (PIR) scheme allows users to retrieve data from a database without disclosing to the server information about the identity of the data retrieved. A coded storage in a distributed storage system with colluding servers is considered in this work, namely the approach in [$t$-private information retrieval schemes using transitive codes, IEEE Trans. Inform. Theory, vol. 65, no. 4, pp. 2107-2118, 2019] which considers a storage and retrieval code with a transitive group and provides binary PIR schemes with the highest possible rate. Reed-Muller codes were considered in [$t$-private information retrieval schemes using transitive codes, IEEE Trans. Inform. Theory, vol. 65, no. 4, pp. 2107-2118, 2019]. In this work, we consider cyclic codes and we show that binary PIR schemes using cyclic codes provide a larger constellation of PIR parameters and they may outperform the ones coming from Reed-Muller codes in some cases

Private Information Retrieval: Combinatorics of the Star-Product Scheme

In coded private information retrieval (PIR), a user wants to download a file from a distributed storage system without revealing the identity of the file. We consider the setting where certain subsets of servers collude to deduce the identity of the requested file. These subsets form an abstract simplicial complex called the collusion pattern. In this thesis, we study the combinatorics of the general star-product scheme for PIR under the assumption that the distributed storage system is encoded using a repetition code

Breaking the MDS-PIR Capacity Barrier via Joint Storage Coding

Paper explores the possibility of the capacity of private information retrieval (PIR) from databases coded using maximum distance separable (MDS) codes to be broken through joint encoding and storage of messages