Breaking the MDS-PIR Capacity Barrier via Joint Storage Coding

TL;DR

This paper introduces new joint encoding schemes for private information retrieval from MDS-coded databases, surpassing the traditional capacity limits of separate message encoding.

Contribution

It presents two classes of novel joint encoding code constructions and PIR protocols that outperform existing separate MDS-coded systems, with a generalization technique expanding their applicability.

Findings

Joint encoding schemes outperform separate MDS coding in PIR capacity.

Two classes of novel code constructions enable capacity breaking.

A simple expansion technique broadens the range of capacity-breaking cases.

Abstract

The capacity of private information retrieval (PIR) from databases coded using maximum distance separable (MDS) codes has been previously characterized by Banawan and Ulukus, where it was assumed that the messages are encoded and stored separably into the databases. This assumption was also usually taken in other related works in the literature, and this capacity is usually referred to as the MDS-PIR capacity colloquially. In this work, we considered the question if and when this capacity barrier can be broken through joint encoding and storing of the messages. Our main results are two classes of novel code constructions which allow joint encoding as well as the corresponding PIR protocols, which indeed outperform the separate MDS-coded systems. Moreover, we show that a simple but novel expansion technique allows us to generalize these two classes of codes, resulting in a wider range of the cases where this capacity barrier can be broken.