New constructions of cooperative MSR codes: Reducing node size to $\exp(O(n))$

TL;DR

This paper introduces new explicit MDS code constructions for cooperative repair in distributed storage that significantly reduce node size from exponential in n^h to exponential in n, improving efficiency for all parameters.

Contribution

The authors present novel explicit MDS code constructions with optimal cooperative repair bandwidth and reduced node size scaling as exp(O(n)), advancing the state-of-the-art in distributed storage codes.

Findings

Node size scales as exp(O(n)) for all failed nodes.

Constructed codes achieve optimal cooperative repair bandwidth.

Node size is smaller than existing codes for the centralized model.

Abstract

We consider the problem of multiple-node repair in distributed storage systems under the cooperative model, where the repair bandwidth includes the amount of data exchanged between any two different storage nodes. Recently, explicit constructions of MDS codes with optimal cooperative repair bandwidth for all possible parameters were given by Ye and Barg (IEEE Transactions on Information Theory, 2019). The node size (or sub-packetization) in this construction scales as $\exp(\Theta(n^h))$, where $h$ is the number of failed nodes and $n$ is the code length. In this paper, we give new explicit constructions of optimal MDS codes for all possible parameters under the cooperative model, and the node size of our new constructions only scales as $\exp(O(n))$ for any number of failed nodes. Furthermore, it is known that any optimal MDS code under the cooperative model (including, in particular, our new code construction) also achieves optimal repair bandwidth under the centralized model, where the amount of data exchanged between failed nodes is not included in the repair bandwidth. We further show that the node size of our new construction is also much smaller than that of the best known MDS code constructions for the centralized model.