Related papers: Exact Regeneration Codes for Distributed Storage R…
This paper considers capacity-achieving coding for the clustered form of distributed storage that reflects practical storage networks. To reflect the clustered structure with limited cross-cluster communication bandwidths, nodes in the same…
For an $(n,k,\ell)$ MDS array code over $\mathbb{F}_q$, how small can the repair bandwidth and repair I/O be under linear exact repair? We study this question in the regime where the field size $q$, the redundancy $r=n-k$, and the…
Cooperative regenerating codes are designed for repairing multiple node failures in distributed storage systems. In contrast to the original repair model of regenerating codes, which are for the repair of single node failure, data exchange…
We present the construction of a family of erasure correcting codes for distributed storage that achieve low repair bandwidth and complexity at the expense of a lower fault tolerance. The construction is based on two classes of codes, where…
Digital contents in large scale distributed storage systems may have different reliability and access delay requirements, and for this reason, erasure codes with different strengths need to be utilized to achieve the best storage…
Maximum distance separable (MDS) codes facilitate the achievement of elevated levels of fault tolerance in storage systems while incurring minimal redundancy overhead. Reed-Solomon (RS) codes are typical MDS codes with the sub-packetization…
This thesis makes several significant contributions to the theory of both Regenerating (RG) and Locally Recoverable (LR) codes. The two principal contributions are characterizing the optimal rate of an LR code designed to recover from $t$…
Typically, locally repairable codes (LRCs) and regenerating codes have been studied independently of each other, and it has not been clear how the parameters of one relate to those of the other. In this paper, a novel connection between…
The information-theoretic secure exact-repair regenerating codes for distributed storage systems (DSSs) with parameters $(n,k=d,d,\ell)$ are studied in this paper. We consider distributed storage systems with $n$ nodes, in which the…
An $(n,k,\ell)$-vector MDS code is a $\mathbb{F}$-linear subspace of $(\mathbb{F}^\ell)^n$ (for some field $\mathbb{F}$) of dimension $k\ell$, such that any $k$ (vector) symbols of the codeword suffice to determine the remaining $r=n-k$…
Fractional repetition (FR) codes are a family of repair-efficient storage codes that provide exact and uncoded node repair at the minimum bandwidth regenerating point. The advantageous repair properties are achieved by a tailor-made…
We revisit zigzag array codes, a family of MDS codes known for achieving optimal access and optimal rebuilding ratio in single-node repair. In this work, we endow zigzag codes with two new properties: small field size and low skip cost.…
Erasure codes are being increasingly used in distributed-storage systems in place of data-replication, since they provide the same level of reliability with much lower storage overhead. We consider the problem of constructing explicit…
In distributed storage systems that use coding, the issue of minimizing the communication required to rebuild a storage node after a failure arises. We consider the problem of repairing an erased node in a distributed storage system that…
We consider a communication problem in which an update of the source message needs to be conveyed to one or more distant receivers that are interested in maintaining specific linear functions of the source message. The setting is one in…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
An $(n,k,l)$ MDS array code of length $n,$ dimension $k=n-r$ and sub-packetization $l$ is formed of $l\times n$ matrices over a finite field $F,$ with every column of the matrix stored on a separate node in a distributed storage system and…
Minimum storage regenerating codes have minimum storage of data in each node and therefore are maximal distance separable (MDS for short) codes. Thus, the number of nodes is upper bounded by $2^{\fb}$, where $\fb$ is the bits of data stored…
An $(n,k)$ maximum distance separable (MDS) code has optimal repair access if the minimum number of symbols accessed from $d$ surviving nodes is achieved, where $k+1\le d\le n-1$. Existing results show that the sub-packetization $\alpha$ of…
When a node in a distributed storage system fails, it needs to be promptly repaired to maintain system integrity. While typical erasure codes can provide a significant storage advantage over replication, they suffer from poor repair…