A High-Rate MSR Code With Polynomial Sub-Packetization Level

2015/01/27 by Birenjith Sasidharan, Sasidharan, Birenjith, Gaurav Kumar Agarwal +3 · 1 citation
Computer Science · #Advanced Data Storage Technologies #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1501.06662

openalex publication_date 2015/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We present a high-rate (n,k,d=n-1)-MSR code with a sub-packetization level that is polynomial in the dimension k of the code. While polynomial sub-packetization level was achieved earlier for vector MDS codes that repair systematic nodes optimally, no such MSR code construction is known. In the low-rate regime (i. e., rates less than one-half), MSR code constructions with a linear sub-packetization level are available. But in the high-rate regime (i. e., rates greater than one-half), the known MSR code constructions required a sub-packetization level that is exponential in k. In the present paper, we construct an MSR code for d=n-1 with a fixed rate R=(t-1)/(t), t ≥ 2, achieveing a sub-packetization level α= O(k^t). The code allows help-by-transfer repair, i. e., no computations are needed at the helper nodes during repair of a failed node.

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