On the Parameters of Codes for Data Access

TL;DR

This paper investigates optimal parameters for coded distributed storage systems, focusing on the minimum number of servers and alphabet size needed to achieve specific service rate regions, using bounds and code constructions.

Contribution

It provides new bounds and constructions for system parameters ensuring desired service rate regions in coded storage systems.

Findings

Established bounds on server number and alphabet size for given service regions.

Developed code constructions based on coding theory, optimization, and projective geometry.

Enhanced understanding of parameter trade-offs in distributed storage performance.

Abstract

This paper studies two crucial problems in the context of coded distributed storage systems directly related to their performance: 1) for a fixed alphabet size, determine the minimum number of servers the system must have for its service rate region to contain a prescribed set of points; 2) for a given number of servers, determine the minimum alphabet size for which the service rate region of the system contains a prescribed set of points. The paper establishes rigorous upper and lower bounds, as well as code constructions based on techniques from coding theory, optimization, and projective geometry.