Local Reconstruction Codes: A Class of MDS-PIR Capacity-Achieving Codes

TL;DR

This paper proves that a class of distance-optimal local reconstruction codes (LRCs), including Pyramid codes, achieve the maximum private information retrieval capacity in distributed storage systems with noncolluding nodes.

Contribution

It establishes that certain LRCs are capacity-achieving for private information retrieval, expanding understanding of their efficiency in distributed storage.

Findings

LRCs achieve PIR capacity in noncolluding settings

Includes Pyramid codes as a special case

Distance-optimal LRCs are capacity-achieving

Abstract

We prove that a class of distance-optimal local reconstruction codes (LRCs), an important family of repair-efficient codes for distributed storage systems, achieve the maximum distance separable private information retrieval capacity for the case of noncolluding nodes. This particular class of codes includes Pyramid codes and other LRCs proposed in the literature.