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New Locally Decodable Codes and Private Information Retrieval Schemes. Sergey Yekhanin. LDCs and PIRs.

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New locally decodable codes and private information retrieval schemes

New Locally Decodable Codes and Private Information Retrieval Schemes

Sergey Yekhanin


Ldcs and pirs

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.


Ldcs progress

LDCs: progress


Pirs progress

PIRs: progress


Proof overview

Proof overview

Goal: 3 query LDCs of length Exp(n1/3)

  • Regular Intersecting Families (RIFs)

  • RIFs yield LDCs

  • Basic linear-algebraic construction of RIFs

  • Combinatorial and algebraic niceness of sets

  • Main construction of RIFs


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