A Generalization of the Blackburn-Etzion Construction for Private Information Retrieval Array Codes

摘要

Private Information Retrieval (PIR) array codes were introduced by Fazeli et al. (2015) to reduce the storage overhead in designing PIR protocols. Blackburn and Etzion (2017) introduced the (virtual server) rate to quantify the storage overhead of the codes, and when s > 2 (here, $rac{1}{s}$ is the proportion of the database storing in one server), they gave a general construction of PIR array codes with the highest rate known so far. In this paper, we generalize their construction and reduce the number of servers, while maintaining the rate. In order to give PIR array codes with significantly fewer servers, we also construct classes of codes with a smaller rate $rac{s}{{2s - 1}}$.