Year: 2019
Type: preprint
Abstract: A functional $k$-PIR code of dimension $s$ consists of $n$ servers storing linear combinations of $s$ linearly independent information symbols. Any linear combination of the $s$ information symbols can be recovered by $k$ disjoint subsets of servers. The goal is to find the smallest number of servers for given $k$ and $s$. We provide lower bounds on the number of servers and constructions which yield upper bounds on this number. For $k \leq 4$, exact bounds on the number of servers are proved. Furthermore, we provide some asymptotic bounds. The problem coincides with the well known private information retrieval problem based on a coded database to reduce the storage overhead, when each linear combination contains exactly one information symbol. If any multiset of size $k$ of linear combinations from the linearly independent information symbols can be recovered by $k$ disjoint subset of servers, then the servers form a functional $k$-batch code. A~functional $k$-batch code is a functional $k$-PIR code, where all the $k$ linear combinations in the multiset are equal. We provide some bounds on the number of servers for functional $k$-batch codes. In particular we present a random construction and a construction based on simplex codes, WOM codes, and RIO codes.
Source: arXiv (Cornell University)
Authors: Zhang, Yiwei, yaakobi, Eitan, Etzion, Tuvi
Institution: Technion – Israel Institute of Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G2518451108, G7085403337
OpenAlex ID: W2908154691