Quasi-cyclic Flexible Regenerating Codes

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.

💡 Research Summary

The paper addresses the problem of node failure in distributed storage systems by introducing a new family of regenerating codes built on quasi‑cyclic (QC) structures, termed Quasi‑Cyclic Flexible Minimum Storage Regenerating (QCFMSR) codes. Traditional regenerating codes focus on either the Minimum Storage Regenerating (MSR) point, which minimizes per‑node storage, or the Minimum Bandwidth Regenerating (MBR) point, which minimizes the amount of data transferred during repair. Existing constructions typically achieve optimality at one of these two extreme points but lack flexibility to operate efficiently across the whole trade‑off curve. QCFMSR codes fill this gap by offering a flexible parameterization that can be tuned to approach or even surpass the theoretical MBR bound while preserving the MSR storage efficiency.

Core Construction
The authors define a system with n storage nodes, each storing α symbols. A file of size k·α symbols is encoded using a generator matrix G of size (n·α) × (k·α). G has a quasi‑cyclic form G =