The Capacity of Private Information Retrieval Under Arbitrary Collusion Patterns

Xinyu Yao; Nan Liu; Wei Kang

The Capacity of Private Information Retrieval Under Arbitrary Collusion Patterns

Information Theory 2020-01-14 v1 math.IT

Authors: Xinyu Yao , Nan Liu , Wei Kang

Abstract

We study the private information retrieval (PIR) problem under arbitrary collusion pattern for replicated databases. We find its capacity, which is the same as the capacity of the original PIR problem with the number of databases $N$ replaced by a number $S^*$ . The number $S^*$ is the optimal solution to a linear programming problem that is a function of the collusion pattern. Hence, the collusion pattern affects the capacity of the PIR problem only through the number $S^*$ .

Keywords

private information retrieval

Cite

@article{arxiv.2001.03843,
  title  = {The Capacity of Private Information Retrieval Under Arbitrary Collusion Patterns},
  author = {Xinyu Yao and Nan Liu and Wei Kang},
  journal= {arXiv preprint arXiv:2001.03843},
  year   = {2020}
}

Comments

This is a full version of the paper submitted to ISIT 2020

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