Beyond the MDS Bound in Distributed Cloud Storage

TL;DR

This paper introduces Hermitian code-based regenerating codes for distributed storage that outperform Reed-Solomon based codes in hostile networks by achieving theoretical bounds, detecting errors, and reducing computational complexity.

Contribution

It proposes novel Hermitian code-based regenerating codes that achieve theoretical bounds and improve error detection and computational efficiency over existing Reed-Solomon based codes.

Findings

Hermitian codes achieve theoretical MSR and MBR bounds.

Enhanced error detection and correction in hostile networks.

Lower computational complexity compared to RS-based codes.

Abstract

Distributed storage plays a crucial role in the current cloud computing framework. After the theoretical bound for distributed storage was derived by the pioneer work of the regenerating code, Reed-Solomon code based regenerating codes were developed. The RS code based minimum storage regeneration code (RS-MSR) and the minimum bandwidth regeneration code (RS-MBR) can achieve theoretical bounds on the MSR point and the MBR point respectively in code regeneration. They can also maintain the MDS property in code reconstruction. However, in the hostile network where the storage nodes can be compromised and the packets can be tampered with, the storage capacity of the network can be significantly affected. In this paper, we propose a Hermitian code based minimum storage regenerating (H-MSR) code and a minimum bandwidth regenerating (H-MBR) code. We first prove that our proposed Hermitian code based regenerating codes can achieve the theoretical bounds for MSR point and MBR point respectively. We then propose data regeneration and reconstruction algorithms for the H-MSR code and the H-MBR code in both error-free network and hostile network. Theoretical evaluation shows that our proposed schemes can detect the erroneous decodings and correct more errors in hostile network than the RS-MSR code and the RS-MBR code with the same code rate. Our analysis also demonstrates that the proposed H-MSR and H-MBR codes have lower computational complexity than the RS-MSR/RS-MBR codes in both code regeneration and code reconstruction.