Batch and PIR Codes and Their Connections to Locally Repairable Codes

TL;DR

This survey explores batch and PIR codes as generalizations of locally repairable codes, discussing bounds, constructions, and interrelations to enhance fault-tolerant distributed data storage systems.

Contribution

It provides a comprehensive overview of bounds, constructions, and connections among batch, PIR, and locally repairable codes, highlighting their theoretical relationships.

Findings

Bounds on code parameters are established.

Basic constructions for these codes are presented.

Connections between different code families are analyzed.

Abstract

In this survey, two related families of codes are discussed: batch codes and codes for private information retrieval. These two families can be viewed as natural generalizations of locally repairable codes, which were extensively studied in the context of coding for fault tolerance in distributed data storage systems. Bounds on the parameters of the codes, as well as basic constructions, are presented. Connections between different code families are discussed.