Capacity-Achieving Private Information Retrieval Codes with Optimal Message Size and Upload Cost
This work addresses the problem of efficient and private data retrieval for users in distributed storage systems, representing a significant advance rather than an incremental improvement.
The authors tackled the private information retrieval (PIR) problem by proposing a new capacity-achieving code that achieves the minimum message size (one less than the number of servers) and minimum upload cost (roughly linear in the number of messages) among a general class of codes, including all linear ones.
We propose a new capacity-achieving code for the private information retrieval (PIR) problem, and show that it has the minimum message size (being one less than the number of servers) and the minimum upload cost (being roughly linear in the number of messages) among a general class of capacity-achieving codes, and in particular, among all capacity-achieving linear codes. Different from existing code constructions, the proposed code is asymmetric, and this asymmetry appears to be the key factor leading to the optimal message size and the optimal upload cost. The converse results on the message size and the upload cost are obtained by a strategic analysis of the information theoretic proof of the PIR capacity, from which a set of critical properties of any capacity-achieving code in the code class of interest is extracted. The symmetry structure of the PIR problem is then analyzed, which allows us to construct symmetric codes from asymmetric ones, yielding a meaningful bridge between the proposed code and existing ones in the literature.