Improved Private Information Retrieval for Coded Storage From Code Decomposition

Paper in proceeding, 2019

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.