Related papers: Erasure codes with symbol locality and group decod…
In distributed storage systems, erasure codes with locality $r$ is preferred because a coordinate can be recovered by accessing at most $r$ other coordinates which in turn greatly reduces the disk I/O complexity for small $r$. However, the…
A Maximum Distance Separable code over an alphabet $F$ is defined via an encoding function $C:F^k \rightarrow F^n$ that allows to retrieve a message $m \in F^k$ from the codeword $C(m)$ even after erasing any $n-k$ of its symbols. The…
We consider the locality of encoding and decoding operations in distributed storage systems (DSS), and propose a new class of codes, called locally encodable and decodable codes (LEDC), that provides a higher degree of operational locality…
Guess & Check (GC) codes are systematic binary codes that can correct multiple deletions, with high probability. GC codes have logarithmic redundancy in the length of the message $k$, and the encoding and decoding algorithms of these codes…
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 $t$…
Data centres that use consumer-grade disks drives and distributed peer-to-peer systems are unreliable environments to archive data without enough redundancy. Most redundancy schemes are not completely effective for providing high…
In a {\em locally recoverable} or {\em repairable} code, any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distributed…
Batch codes are a family of codes that represent a distributed storage system (DSS) of $n$ nodes so that any batch of $t$ data symbols can be retrieved by reading at most one symbol from each node. Fractional repetition codes are a family…
Distributed storage systems employ codes to provide resilience to failure of multiple storage disks. Specifically, an $(n, k)$ MDS code stores $k$ symbols in $n$ disks such that the overall system is tolerant to a failure of up to $n-k$…
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…
Data storage applications require erasure-correcting codes with prescribed sets of dependencies between data symbols and redundant symbols. The most common arrangement is to have $k$ data symbols and $h$ redundant symbols (that each depends…
The MDS property (aka the $k$-out-of-$n$ property) requires that if a file is split into several symbols and subsequently encoded into $n$ coded symbols, each being stored in one storage node of a distributed storage system (DSS), then an…
We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder. We first establish the characterization of various locality properties in terms…
We consider the problem of constructing codes that can correct $\delta$ deletions occurring in an arbitrary binary string of length $n$ bits. Varshamov-Tenengolts (VT) codes can correct all possible single deletions $(\delta=1)$ with an…
In this paper, we study the problem of storing an archive of versioned data in a reliable and efficient manner in distributed storage systems. We propose a new storage technique called differential erasure coding (DEC) where the differences…
We consider the design of regenerating codes for distributed storage systems that enjoy the property of local, exact and uncoded repair, i.e., (a) upon failure, a node can be regenerated by simply downloading packets from the surviving…
In this work we present a class of locally recoverable codes, i.e. codes where an erasure at a position $P$ of a codeword may be recovered from the knowledge of the entries in the positions of a recovery set $R_P$. The codes in the class…
We consider the problem of constructing an erasure code for storage over a network when the data sources are distributed. Specifically, we assume that there are n storage nodes with limited memory and k<n sources generating the data. We…
Erasure codes play an important role in storage systems to prevent data loss. In this work, we study a class of erasure codes called Multi-Erasure Locally Recoverable Codes (ME-LRCs) for storage arrays. Compared to previous related works,…
Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more generally, $ \partial - 1 $ erasures per local group), and…