PIR with Low Storage Overhead: Coding instead of Replication

Understand

Private information retrieval (PIR) protocols allow a user to retrieve a data item from a database without revealing any information about the identity of the item being retrieved.

• Specifically, in information-theoretic $k$-server PIR, the database is replicated among $k$ non-communicating servers, and each server learns nothing about the item retrieved by the user.
• The cost of PIR protocols is usually measured in terms of their communication complexity, which is the total number of bits exchanged between the user and the servers, and storage overhead, which is the ratio between the total number of bits stored on all the servers and the number of bits in the database.
• Since single-server information-theoretic PIR is impossible, the storage overhead of all existing PIR protocols is at least $2$.