New private information retrieval codes for imperfect privacy

In this paper, we introduce new codes for the private information retrieval (PIR). The conventional Tian-Sun-Chen (TSC) scheme achieves PIR capacity under the perfect privacy condition with the minimum message length. Based on the TSC scheme, weakly PIR (WPIR) studies have been developed to benefit download costs by relaxing privacy. We show that the proposed scheme has lower download cost than the TSC scheme in the weak privacy setting. While our scheme is not capacity-achieving under perfect privacy, it has smaller message sizes compared with the TSC scheme.