A fundamental fact about polynomial interpolation is that k evaluations of a degree-(k-1)
polynomial f are sufficient to determine f. This is also necessary in a strong sense: given k-1 …

Reed-Solomon codes have found many applications in practical storage systems, but were
until recently considered unsuitable for distributed storage applications due to the widely …

The repair problem for an (n, k) error-correcting code calls for recovery of an unavailable
coordinate of the codeword by downloading as little information as possible from a subset of …

Despite their exceptional error-correcting properties, Reed-Solomon (RS) codes have been
overlooked in distributed storage applications due to the common belief that they have poor …

The repair problem in distributed storage addresses recovery of the data encoded using an
erasure code, for instance, a Reed-Solomon (RS) code. We consider the problem of …

Several works have developed vector-linear maximum-distance separable (MDS) storage
codes that minimize the total communication cost required to repair a single coded symbol …

In a distributed storage system, code symbols are dispersed across space in nodes or
storage units as opposed to time. In settings such as that of a large data center, an important …

In distributed storage, a file is stored in a set of nodes and protected by erasure-correcting
codes. Regenerating code is a type of code with two properties: first, it can reconstruct the …

Regenerating codes allow distributed storage systems to recover from the loss of a storage
node while transmitting the minimum possible amount of data across the network. We …

Large distributed storage systems use erasure codes to reliably store data. Compared to
replication, erasure codes are capable of reducing storage overhead. However, repairing …