An Explicit, Coupled-Layer Construction of a High-Rate Regenerating Code with Low Sub-Packetization Level, Small Field Size and $d< (n-1)$

Birenjith Sasidharan; Myna Vajha; P. Vijay Kumar

An Explicit, Coupled-Layer Construction of a High-Rate Regenerating Code with Low Sub-Packetization Level, Small Field Size and $d< (n-1)$

Information Theory 2022-04-07 v3 math.IT

Authors: Birenjith Sasidharan , Myna Vajha , P. Vijay Kumar

Abstract

This paper presents an explicit construction for an $((n=2qt,k=2q(t-1),d=n-(q+1)), (\alpha = q(2q)^{t-1},\beta = \frac{\alpha}{q}))$ regenerating code (RGC) over a field $\mathbb{F}_Q$ having rate $\geq \frac{t-2}{t}$ . The RGC code can be constructed to have rate $k/n$ as close to $1$ as desired, sub-packetization level $\alpha \leq r^{\frac{n}{r}}$ for $r=(n-k)$ , field size $Q$ no larger than $n$ and where all code symbols can be repaired with the same minimum data download.

Keywords

regenerating code explicit construction high rate low sub-packetization coupled-layer small field size distributed storage

Cite

@article{arxiv.1701.07447,
  title  = {An Explicit, Coupled-Layer Construction of a High-Rate Regenerating Code with Low Sub-Packetization Level, Small Field Size and $d< (n-1)$},
  author = {Birenjith Sasidharan and Myna Vajha and P. Vijay Kumar},
  journal= {arXiv preprint arXiv:1701.07447},
  year   = {2022}
}

Comments

In the revised version, a correction is made in the rate calculation. The rate reduces and the code fails to be an MSR code. arXiv admin note: text overlap with arXiv:1607.07335

An Explicit, Coupled-Layer Construction of a High-Rate Regenerating Code with Low Sub-Packetization Level, Small Field Size and $d< (n-1)$

Abstract

Keywords

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