Rack-Aware Regenerating Codes with Multiple Erasure Tolerance

TL;DR

This paper introduces a relaxed rack-aware regenerating code model that tolerates multiple node failures, reducing intra- and cross-rack repair bandwidth, with explicit code constructions and systematic encoding for practical use.

Contribution

It proposes a new relaxed repair model for rack-aware codes that can handle multiple failures and provides explicit code constructions with systematic encoding.

Findings

Derived a tradeoff between storage and repair bandwidth under the relaxed model.

Characterized parameters at the extreme points for minimum storage and minimum bandwidth.

Constructed explicit codes with low sub-packetization and practical systematic encoding.

Abstract

In a modern distributed storage system, storage nodes are organized in racks, and the cross-rack communication dominates the system bandwidth. In We study the rack-aware storage system where all storage nodes are organized in racks and within each rack the nodes can communicate freely without taxing the system bandwidth. Rack-aware regenerating codes (RRCs) were proposed for minimizing the repair bandwidth for single erasures. In the initial setting of RRCs, the repair of a single node requires the participation of all the remaining nodes in the rack containing the failed node as well as a large number of helper racks containing no failures. Consequently, the repair may be infeasible in front of multiple node failures. In this work, a relaxed repair model that can tolerate multiple node failures by simultaneously reducing the intra-rack connections and cross-rack connections is proposed. A tradeoff between the storage and repair bandwidth under the relaxed repair model is derived, and parameters of the two extreme points on the tradeoff curve are characterized for the minimum storage and minimum bandwidth respectively. Moreover, two codes corresponding to the extreme points are explicitly constructed over the fields of size comparable to the code length and with the lowest sub-packetization. Finally, for the convenience of practical use, systematic encoding processes for the two codes are also established.