Related papers: Explicit constructions of high-rate MDS array code…
We construct an explicit family of locally repairable and locally regenerating codes whose existence was proven in a recent work by Kamath et al. about codes with local regeneration but no explicit construction was given. This explicit…
A linear code with parameters $[n, k, n-k+1]$ is called a maximum distance separable (MDS for short) code. A linear code with parameters $[n, k, n-k]$ is said to be almost maximum distance separable (AMDS for short). A linear code is said…
We consider the problem of constructing linear Maximum Distance Separable (MDS) error-correcting codes with generator matrices that are sparsest and balanced. In this context, sparsest means that every row has the least possible number of…
Minimum storage regenerating (MSR) codes are MDS codes which allow for recovery of any single erased symbol with optimal repair bandwidth, based on the smallest possible fraction of the contents downloaded from each of the other symbols.…
Several works have developed vector-linear maximum-distance separable (MDS) storage codes that min- imize the total communication cost required to repair a single coded symbol after an erasure, referred to as repair bandwidth (BW). Vector…
Partial MDS (PMDS) codes are erasure codes combining local (row) correction with global additional correction of entries, while Sector-Disk (SD) codes are erasure codes that address the mixed failure mode of current RAID systems. It has…
We study linear exact repair for $(n,k,\ell)$ MDS array codes over $\mathbb{F}_q$, with redundancy $r=n-k$, in the regime where $q$, $r$, and $\ell$ are fixed and the code length $n$ varies. A recent projective counting argument gives a…
In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The…
A linear code with parameters of the form $[n, k, n-k+1]$ is referred to as an MDS (maximum distance separable) code. A linear code with parameters of the form $[n, k, n-k]$ is said to be almost MDS (i.e., almost maximum distance separable)…
Optimal locally repairable codes with information locality are considered. Optimal codes are constructed, whose length is also order-optimal with respect to a new bound on the code length derived in this paper. The length of the constructed…
An [n, k] linear code C that is subject to locality constraints imposed by a parity check matrix H0 is said to be a maximally recoverable (MR) code if it can recover from any erasure pattern that some k-dimensional subcode of the null space…
We derive a lower bound on the amount of information accessed to repair failed nodes within a single rack from any number of helper racks in the rack-aware storage model that allows collective information processing in the nodes that share…
As a special class of array codes, $(n,k,m)$ piggybacking codes are MDS codes (i.e., any $k$ out of $n$ nodes can retrieve all data symbols) that can achieve low repair bandwidth for single-node failure with low sub-packetization $m$. In…
In distributed storage, erasure codes -- like Reed-Solomon Codes -- are often employed to provide reliability. In this setting, it is desirable to be able to repair one or more failed nodes while minimizing the repair bandwidth. In this…
In a distributed storage system, recovering from multiple failures is a critical and frequent task that is crucial for maintaining the system's reliability and fault-tolerance. In this work, we focus on the problem of repairing multiple…
A maximum distance separable (MDS) array code is composed of $m\times (k+r)$ arrays such that any $k$ out of $k+r$ columns suffice to retrieve all the information symbols. Expanded-Blaum-Roth (EBR) codes and Expanded-Independent-Parity…
The reliability of erasure-coded distributed storage systems, as measured by the mean time to data loss (MTTDL), depends on the repair bandwidth of the code. Repair-efficient codes provide reliability values several orders of magnitude…
Symbol-pair codes are proposed to combat pair-errors in symbol-pair read channels. The minimum symbol-pair distance is of significance in determining the error-correcting capability of a symbol-pair code. Maximum distance separable (MDS)…
We present a new 'piggybacking' framework for designing distributed storage codes that are efficient in data-read and download required during node-repair. We illustrate the power of this framework by constructing classes of explicit codes…
For scalar maximum distance separable (MDS) codes, the conventional repair schemes that achieve the cut-set bound with equality for the single-node repair have been proven to require a super-exponential sub-packetization level.As is well…