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

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 $\ge \frac{t-2}{t}$. The RGC code can be constructed to have rate $k/n$ as close to $1$ as desired, sub-packetization level $\alpha \le r^{\frac{n}{r}}$ 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.

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