Exact Cooperative Regenerating Codes with Minimum-Repair-Bandwidth for Distributed Storage

TL;DR

This paper presents a new explicit construction of exact cooperative regenerating codes at the MBCR point, applicable to all parameters, with efficient data reconstruction and specific subspace properties.

Contribution

It introduces a universal explicit scalar code construction for all parameters at the MBCR point, expanding beyond previous limited cases.

Findings

Code applies to all n, k, d, r parameters.

Data reconstruction via bivariate polynomial interpolation.

Linear exact MBCR codes cannot achieve repair-by-transfer.

Abstract

We give an explicit construction of exact cooperative regenerating codes at the MBCR (minimum bandwidth cooperative regeneration) point. Before the paper, the only known explicit MBCR code is given with parameters $n=d+r$ and $d=k$, while our construction applies to all possible values of $n,k,d,r$. The code has a brief expression in the polynomial form and the data reconstruction is accomplished by bivariate polynomial interpolation. It is a scalar code and operates over a finite field of size $q\geq n$. Besides, we establish several subspace properties for linear exact MBCR codes. Based on these properties we prove that linear exact MBCR codes cannot achieve repair-by-transfer.