Lower Bound on the Redundancy of PIR Codes

Sankeerth Rao; Alexander Vardy

Lower Bound on the Redundancy of PIR Codes

Information Theory 2017-03-01 v2 math.IT

Authors: Sankeerth Rao , Alexander Vardy

Abstract

We prove that the redundancy of a $k$ -server PIR code of dimension $s$ is $\Omega(\sqrt{s})$ for all $k \ge 3$ . This coincides with a known upper bound of $O(\sqrt{s})$ on the redundancy of PIR codes. Moreover, for $k=3$ and $k = 4$ , we determine the lowest possible redundancy of $k$ -server PIR codes exactly. Similar results were proved independently by Mary Wootters using a different method.

Keywords

PIR codes redundancy lower bound upper bound k-server dimension exact redundancy

Cite

@article{arxiv.1605.01869,
  title  = {Lower Bound on the Redundancy of PIR Codes},
  author = {Sankeerth Rao and Alexander Vardy},
  journal= {arXiv preprint arXiv:1605.01869},
  year   = {2017}
}

Related papers

View all related →