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Locally repairable codes, or locally recoverable codes (LRC for short) are designed for application in distributed and cloud storage systems. Similar to classical block codes, there is an important bound called the Singleton-type bound for…
In this paper, we provide explicit constructions for a class of exact-repair regenerating codes that possess a layered structure. These regenerating codes correspond to interior points on the storage-repair-bandwidth tradeoff, and compare…
Erasure coding has been recognized as a powerful method to mitigate delays due to slow or straggling nodes in distributed systems. This work shows that erasure coding of data objects can flexibly handle skews in the request rates. Coding…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…
Recently, the research on local repair codes is mainly confined to repair the failed nodes within each repair group. But if the extreme cases occur that the entire repair group has failed, the local code stored in the failed group need to…
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…
Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite…
This paper presents a new explicit construction for locally repairable codes (LRCs) for distributed storage systems which possess all-symbols locality and maximal possible minimum distance, or equivalently, can tolerate the maximal number…
Locally repairable codes (LRCs) are ingeniously designed distributed storage codes with a (usually small) fixed set of helper nodes participating in repair. Since most existing LRCs assume exact repair and allow full exchange of the stored…
In this paper, a new repair scheme for a modified construction of MDS codes is studied. The obtained repair scheme has optimal bandwidth for multiple failed nodes under the cooperative repair model. In addition, the repair scheme has…
In distributed storage systems that employ erasure coding, the issue of minimizing the total {\it repair bandwidth} required to exactly regenerate a storage node after a failure arises. This repair bandwidth depends on the structure of the…
There are multiple performance metrics in the design of coding schemes for distributed storage systems. The first metric is called repair bandwidth, which measures the network resources required during the repair process. Another critical…
We propose two coding schemes for distributed matrix multiplication in the presence of stragglers. These coding schemes are adaptations of LT codes and Raptor codes to distributed matrix multiplication and are termed \emph{factored LT (FLT)…
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 $t$…
An $(n,k,d)$ cooperative regenerating code provides the optimal-bandwidth repair for any $t~(t\!>\!1)$ node failures in a cooperative way. In particular, an MSCR (minimum storage cooperative regenerating) code retains the same storage…
The issue of repairing Reed-Solomon codes currently employed in industry has been sporadically discussed in the literature. In this work we carry out a systematic study of these codes and investigate important aspects of repairing them…
In recent years, locally repairable codes (LRCs) have attracted considerable attention owing to their pivotal role in distributed storage systems. Since binary linear locally repairable codes can significantly reduce the complexity of both…
Maximum distance separable (MDS) codes have the optimal trade-off between storage efficiency and fault tolerance, which are widely used in distributed storage systems. As typical non-MDS codes, simple regenerating codes (SRCs) can achieve…
The repair bandwidth of a code is the minimum amount of data required to repair one or several failed nodes (erasures). For MDS codes, the repair bandwidth is bounded below by the so-called cut-set bound, and codes that meet this bound with…
In this survey, two related families of codes are discussed: batch codes and codes for private information retrieval. These two families can be viewed as natural generalizations of locally repairable codes, which were extensively studied in…