Storage Capacity of Repairable Networks

TL;DR

This paper models distributed storage networks with limited connectivity, estimates their storage capacity, and extends the model to handle multiple failures, linking it to index coding and providing bounds on code distance.

Contribution

It introduces a new model for locally recoverable storage networks considering network connectivity constraints and analyzes their capacity and code properties.

Findings

Estimated storage capacity for undirected and directed networks.

Proposed constructive schemes for local recovery.

Derived bounds on code distance related to network structure.

Abstract

In this paper, we introduce a model of a distributed storage system that is locally recoverable from any single server failure. Unlike the usual local recovery model of codes for distributed storage, this model accounts for the fact that each server or storage node in a network is connectible to only some, and not all other, nodes. This may happen for reasons such as physical separation, inhomogeneity in storage platforms etc. We estimate the storage capacity of both undirected and directed networks under this model and propose some constructive schemes. From a coding theory point of view, we show that this model is approximately dual of the well-studied index coding problem. Further in this paper, we extend the above model to handle multiple server failures. Among other results, we provide an upper bound on the minimum pairwise distance of a set of words that can be stored in a graph with the local repair guarantee. The well-known impossibility bounds on the distance of locally recoverable codes follow from our result.