New Locally Decodable Codes and Private Information Retrieval Schemes. Sergey Yekhanin. LDCs and PIRs.
Definition: A code C encoding n bits to N bits is called q LDC if every bit of the message can be recovered (w.h.p.) by a randomized decoder reading only q bits of the encoding even after some constant fraction of the encoding has been corrupted.
Definition: A q server PIR protocol is a protocol between a user and q non-communicating servers holding an n bit database D, that allows the user to retrieve any bit Di, while leaking no information about i to any server.
Goal: 3 query LDCs of length Exp(n1/3)