Semantic Private Information Retrieval

Abstract

We investigate the problem of semantic private information retrieval (semantic PIR). In semantic PIR, a user retrieves a message out of K independent messages stored in N replicated and non-colluding databases without revealing the identity of the desired message to any individual database. The messages come with different semantics, i.e., the messages are allowed to have non-uniform a priori probabilities denoted by (p i > 0, i ∈ [K]), which are a proxy for their respective popularity of retrieval, and arbitrary message sizes). This is a generalization of the classical private information retrieval (PIR) problem, where messages are assumed to have equal a priori probabilities and equal message sizes. We derive the semantic PIR capacity for general K, N . The results show that the semantic PIR capacity depends on the number of databases N , the number of messages K, the a priori probability distribution of messages p i , and the message sizes L i . We present two achievable semantic PIR schemes: The first one is a deterministic scheme which is based on message asymmetry. This scheme employs non-uniform subpacketization. The second scheme is probabilistic and is based on choosing one query set out of multiple options at random to retrieve the required message without the need for exponential subpacketization. We derive necessary and sufficient conditions for the semantic PIR capacity to exceed the classical PIR capacity with equal priors and sizes. Our results show that the semantic PIR capacity can be larger than the classical PIR capacity when longer messages have higher popularities. However, when messages are equal-length, the non-uniform priors cannot be exploited to improve the retrieval rate over the classical PIR capacity.

Private Retrieval, Computing and Learning: Recent Progress and Future Challenges

“…Yet another practical constraint is that the messages stored at the databases do not have to be of equal length, and their apriori probabilities of retrieval (popularities) do not have to be the same. These give rise to message semantics that need to be taken into account during a PIR code design [66]. An interesting observation in [66] is that if longer messages have higher popularities then the semantic PIR capacity may be larger than classical PIR capacity.…”

“…These give rise to message semantics that need to be taken into account during a PIR code design [66]. An interesting observation in [66] is that if longer messages have higher popularities then the semantic PIR capacity may be larger than classical PIR capacity.…”

Two-Level Private Information Retrieval

“…Message size: The K messages are assumed to have equal length and allowed to approach infinity in the canonical model. The generalization to arbitrary different lengths was considered in [10] and the iterative construction from [1] was applied to truncated subsets of messages with the same length [10]. The minimum message sizes for capacity-achieving codes were considered in [5,7] where server symmetry and side information were utilized in the code constructions.…”