Locally Encodable and Decodable Codes for Distributed Storage Systems

TL;DR

This paper introduces a new class of codes called locally encodable and decodable codes (LEDC) that improve operational locality in distributed storage systems, providing optimal codes with high efficiency and practical constructions.

Contribution

The paper defines LEDC, derives an upper bound on global distance, and constructs optimal LEDC families for large and linear field sizes, advancing distributed storage coding techniques.

Findings

Derived an upper bound on global distance for LEDC

Proved existence of optimal LEDC for large fields

Constructed two families of optimal LEDC for linear field sizes

Abstract

We consider the locality of encoding and decoding operations in distributed storage systems (DSS), and propose a new class of codes, called locally encodable and decodable codes (LEDC), that provides a higher degree of operational locality compared to currently known codes. For a given locality structure, we derive an upper bound on the global distance and demonstrate the existence of an optimal LEDC for sufficiently large field size. In addition, we also construct two families of optimal LEDC for fields with size linear in code length.