Msr codes with flexible repair and smaller data chunks improve storage efficiency
New Minimum Storage Regenerating Codes With Small Sub-packetization Levels for All Admissible Repair Degrees
Information Theory
Summary
Distributed storage systems save data across many machines and need ways to rebuild lost data efficiently. The authors propose a new kind of code that reduces the size of data pieces stored, making data repair more flexible and less computationally heavy. Their approach relaxes certain strict mathematical requirements while still ensuring data can be reliably recovered. This helps make storage systems faster and more efficient when fixing failures.
What this means in practice
- •For data center engineers: Implement storage that repairs failed nodes with fewer data splits and flexible repair options, improving recovery speed and reducing load.
- •For cloud platform developers: Design cloud storage solutions that encode data with sparser parity checks to enhance encoding and decoding efficiency while supporting varying repair demands.
Authors
Jie Li, Xiaohu Tang, Linqi Song
Abstract
In this paper, {we propose a new family of $(n, k)$ Minimum Storage Regenerating (MSR) codes} for distributed storage systems. By structuring the parity-check matrix as a block Vandermonde matrix composed of diagonal matrices and generalized permutation matrices, the proposed code achieves a sub-packetization level of $N = (d-k+1)^{\lceil\frac{n}{2}\rceil}$ and supports any repair degree $k+1\le d<n$. A key innovation of the new construction lies in relaxing the strict commutativity condition previously required for the building blocks in the parity-check matrices of Ye-Barg codes. We introduce a novel proof technique to establish the MDS property without relying on full commutativity, thereby generalizing the applicability of block Vandermonde matrices and enriching the family of Ye-Barg codes. Additionally, the sparsity of the parity-check matrix enhances encoding and decoding efficiency by reducing computational complexity. This work provides new insights into the construction of MSR codes.