Node repair on connected graphs, Part II

TL;DR

This paper extends the study of node repair in graph-constrained distributed storage systems to general regenerating codes, deriving bounds and repair procedures that optimize bandwidth and processing costs.

Contribution

It generalizes previous work from MSR codes to all regenerating codes, providing new bounds and repair strategies involving intermediate processing on graphs.

Findings

Derived a lower bound on repair bandwidth for general regenerating codes.

Formulated repair procedures with intermediate processing for multiple code families.

Established a lower bound on data retrieval bandwidth and achieved it at the MBR point.

Abstract

We continue our study of regenerating codes in distributed storage systems where connections between the nodes are constrained by a graph. In this problem, the failed node downloads the information stored at a subset of vertices of the graph for the purpose of recovering the lost data. This information is moved across the network, and the cost of node repair is determined by the graphical distance from the helper nodes to the failed node. This problem was formulated in our recent work (IEEE IT Transactions, May 2022) where we showed that processing of the information at the intermediate nodes can yield savings in repair bandwidth over the direct forwarding of the data. While the previous paper was limited to the MSR case, here we extend our study to the case of general regenerating codes. We derive a lower bound on the repair bandwidth and formulate repair procedures with intermediate processing for several families of regenerating codes, with an emphasis on the recent constructions from multilinear algebra. We also consider the task of data retrieval for codes on graphs, deriving a lower bound on the communication bandwidth and showing that it can be attained at the MBR point of the storage-bandwidth tradeoff curve.