PIR codes from combinatorial structures

TL;DR

This paper introduces new combinatorial constructions for $k$-server PIR codes, improving bounds on their parameters and reducing storage overhead in private information retrieval protocols.

Contribution

It proposes novel PIR code constructions based on combinatorial structures and introduces the concept of $k$-partial packing, enhancing existing bounds.

Findings

Improved bounds on PIR code parameters.

New constructions using combinatorial structures.

Reduced storage overhead in PIR protocols.

Abstract

A $k$-server Private Information Retrieval (PIR) code is a binary linear $[m,s]$-code admitting a generator matrix such that for every integer $i$ with $1\le i\le s$ there exist $k$ disjoint subsets of columns (called recovery sets) that add up to the vector of weight one, with the single $1$ in position $i$. As shown in \cite{Fazeli1}, a $k$-server PIR code is useful to reduce the storage overhead of a traditional $k$-server PIR protocol. Finding $k$-server PIR codes with a small blocklength for a given dimension has recently become an important research challenge. In this work, we propose new constructions of PIR codes from combinatorial structures, introducing the notion of $k$-partial packing. Several bounds over the existing literature are improved.