Quasi-cyclic Flexible Regenerating Codes

TL;DR

This paper introduces a new family of quasi-cyclic regenerating codes that optimize data repair bandwidth and storage in distributed systems, offering simple, low-complexity solutions for node failure recovery.

Contribution

It presents the construction and proof of existence for quasi-cyclic flexible regenerating codes, including codes with optimal bandwidth and storage properties.

Findings

Achieves optimal MBR parameters for storage and repair bandwidth.

Supports exact repair-by-transfer and pseudo repair-by-transfer.

Codes are simple with low complexity operations.

Abstract

In a distributed storage environment, where the data is placed in nodes connected through a network, it is likely that one of these nodes fails. It is known that the use of erasure coding improves the fault tolerance and minimizes the redundancy added in distributed storage environments. The use of regenerating codes not only make the most of the erasure coding improvements, but also minimizes the amount of data needed to regenerate a failed node. In this paper, a new family of regenerating codes based on quasi-cyclic codes is presented. Quasi-cyclic flexible minimum storage regenerating (QCFMSR) codes are constructed and their existence is proved. Quasi-cyclic flexible regenerating codes with minimum bandwidth constructed from a base QCFMSR code are also provided. These codes not only achieve optimal MBR parameters in terms of stored data and repair bandwidth, but also for an specific choice of the parameters involved, they can be decreased under the optimal MBR point. Quasi-cyclic flexible regenerating codes are very interesting because of their simplicity and low complexity. They allow exact repair-by-transfer in the minimum bandwidth case and an exact pseudo repair-by-transfer in the MSR case, where operations are needed only when a new node enters into the system replacing a lost one.