Related papers: Access-optimal Linear MDS Convertible Codes for Al…
Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure correcting codes that combine locality with strong erasure correction capabilities. We construct PMDS and SD codes with local regeneration where each local code is a…
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…
In coding for distributed storage systems, efficient data reconstruction and repair through accessing a predefined number of arbitrarily chosen storage nodes is guaranteed by regenerating codes. Traditionally, code parameters, specially the…
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…
Distributed storage systems often introduce redundancy to increase reliability. When coding is used, the repair problem arises: if a node storing encoded information fails, in order to maintain the same level of reliability we need to…
We consider the use of distributed storage (DS) to reduce the communication cost of content delivery in wireless networks. Content is stored (cached) in a number of mobile devices using an erasure correcting code. Users retrieve content…
We propose a coded computing strategy and examine communication costs of coded computing algorithms to make distributed Fast Fourier Transform (FFT) resilient to errors during the computation. We apply maximum distance separable (MDS) codes…
An erasure channel with a fixed alphabet size $q$, where $q \gg 1$, is studied. It is proved that over any erasure channel (with or without memory), Maximum Distance Separable (MDS) codes achieve the minimum probability of error (assuming…
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 $t$…
It is well known that an (n,k) code can be used to store 'k' units of information in 'n' unit-capacity disks of a distributed data storage system. If the code used is maximum distance separable (MDS), then the system can tolerate any (n-k)…
The exponential growth of data necessitates distributed storage models, such as peer-to-peer systems and data federations. While distributed storage can reduce costs and increase reliability, the heterogeneity in storage capacity, I/O…
This paper investigates adaptive streaming codes over a three-node relayed network. In this setting, a source transmits a sequence of message packets through a relay under a delay constraint of $T$ time slots per packet. The source-to-relay…
In many modern applications, data are received as infinite, rapid, unpredictable and time- variant data elements that are known as data streams. Systems which are able to process data streams with such properties are called Data Stream…
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…
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…
Maximum distance separable (MDS) are constructed to required specifications. The codes are explicitly given over finite fields with efficient encoding and decoding algorithms. Series of such codes over finite fields with ratio of distance…
The article addresses the problem of storing data in extreme environmental conditions with limited computing resources and memory. There is a requirement to create portable, fault-tolerant, modular database management systems (DBMS) that…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
In applications of distributed storage systems to distributed computing and implementation of key- value stores, the following property, usually referred to as consistency in computer science and engineering, is an important requirement: as…
In distributed storage systems, storage nodes intermittently go offline for numerous reasons. On coming back online, nodes need to update their contents to reflect any modifications to the data in the interim. In this paper, we consider a…