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