A Note on Parity Check Matrices of Private Information Retrieval Codes

A private information retrieval (PIR) is an information retrieval scheme that allows a user to retrieve messages from information databases while keeping secret which one the user wants to retrieve. Sun et al. formulated the download rate and showed that there is an upper limit to it (PIR capacity). Previous construction methods for a capacity-achieving linear PIR (CALPIR) are ad hoc. We show a suffiecient condition of a CALPIR using its extended parity check matrix.