t-PIR Schemes with Flexible Parameters via Star Products of Berman Codes

We present a new class of private information retrieval (PIR) schemes that keep the identity of the file requested private in the presence of at most t colluding servers, based on the recent framework developed for such t-PIR schemes using star products of transitive codes. These t-PIR schemes employ the class of Berman codes as the storage-retrieval code pairs. Berman codes, which are binary linear codes of length n
^m
for any n ≥ 2 and m ≥ 1 being positive integers, were recently shown to achieve the capacity of the binary erasure channel. We provide a complete characterization of the star products of the Berman code pairs, enabling us to calculate the PIR rate of the star product-based schemes that employ these codes. The schemes we present have flexibility in the number of servers, the PIR rate, the storage rate, and the collusion parameter t, owing to numerous codes available in the class of Berman codes.Due to space restrictions, the full version of this paper containing proofs of claims, additional examples, and results, is made available in [1].