Regenerating codes with minimal disk I/O cost achieving optimal tradeoff between storage and repair bandwidth

TL;DR

This paper introduces a new coding scheme for distributed storage that minimizes disk I/O cost and achieves the optimal tradeoff between storage and repair bandwidth, using gammoid theory for design.

Contribution

It presents a novel encoding scheme based on gammoid theory that achieves optimal tradeoff points with minimal disk I/O cost and supports unlimited repair iterations.

Findings

Achieves all points on the storage-bandwidth tradeoff curve.

Supports unlimited node repair iterations.

Ensures uncoded repair with minimal computational overhead.

Abstract

There are multiple performance metrics in the design of coding schemes for distributed storage systems. The first metric is called repair bandwidth, which measures the network resources required during the repair process. Another critical metric for repair efficiency is disk I/O cost, defined as the amount of data packets accessed at helper nodes to repair the failed node. In an encoding scheme with optimal I/O cost, the number of packets sent to the newcomer is exactly the same as the number of packets read from memory. This mode of repair is referred to as uncoded repair, as no coding operations are performed at the helper node. In addition to minimizing disk I/O cost, an uncoded repair mechanism has the advantage of incurring minimal computational overhead at the helper node. In this paper, we demonstrate that for single node failures, if all surviving nodes participate in the repair of the failed node, we can achieve all points on the fundamental tradeoff curve between storage and repair bandwidth. The design of the proposed encoding scheme is based on the theory of gammoids, a specialized class of graph-based matroids. We prove that this scheme can tolerate an unlimited number of node repair iterations over a field of fixed size.