Node repair on connected graphs

TL;DR

This paper investigates erasure correction in graph-based regenerating codes, proposing bounds and modifications to MSR codes to reduce communication costs during node repair, especially in random graph scenarios.

Contribution

It introduces information-theoretic bounds and demonstrates how MSR codes can be adapted for intermediate processing to minimize communication during node repair.

Findings

Derived bounds on communication in graph-based repairs

Modified MSR codes enable lower communication costs

Conditions identified for efficient repair in random graphs

Abstract

We study the problem of erasure correction (node repair) for regenerating codes defined on graphs wherein the cost of transmitting the information to the failed node depends on the graphical distance from this node to the helper vertices of the graph. The information passed to the failed node from the helpers traverses several vertices of the graph, and savings in communication complexity can be attained if the intermediate vertices process the information rather than simply relaying it toward the failed node. We derive simple information-theoretic bounds on the amount of information communicated between the nodes in the course of the repair. Next we show that Minimum Storage Regenerating (MSR) codes can be modified to perform the intermediate processing, thereby attaining the lower bound on the information exchange on the graph. We also consider node repair when the underlying graph is random, deriving conditions on the parameters that support recovery of the failed node with communication complexity smaller than required by the simple relaying.