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Search Results: 1 - 10 of 14476 matches for " Ankit Singh Rawat "
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On Locality in Distributed Storage Systems
Ankit Singh Rawat,Sriram Vishwanath
Mathematics , 2012,
Abstract: This paper studies the design of codes for distributed storage systems (DSS) that enable local repair in the event of node failure. This paper presents locally repairable codes based on low degree multivariate polynomials. Its code construction mechanism extends work on Noisy Interpolating Set by Dvir et al. \cite{dvir2011}. The paper presents two classes of codes that allow node repair to be performed by contacting 2 and 3 surviving nodes respectively. It further shows that both classes are good in terms of their rate and minimum distance, and allow their rate to be bartered for greater flexibility in the repair process.
Cooperative Local Repair in Distributed Storage
Ankit Singh Rawat,Arya Mazumdar,Sriram Vishwanath
Mathematics , 2014,
Abstract: Erasure-correcting codes, that support {\em local repair} of codeword symbols, have attracted substantial attention recently for their application in distributed storage systems. This paper investigates a generalization of the usual locally recoverable codes. In particular, this paper studies a class of codes with the following property: any small set of codeword symbols is recoverable from a small number of other symbols. This is referred to as {\em cooperative local repair}. The main contribution of this paper is bounds on the trade-off of minimum distance and the dimension of such codes, as well as explicit constructions of families of codes that enable cooperative local repair. Some other results regarding cooperative local repair are also presented, including an analysis for the well-known Hadamard codes.
Error Resilience in Distributed Storage via Rank-Metric Codes
Natalia Silberstein,Ankit Singh Rawat,Sriram Vishwanath
Mathematics , 2012,
Abstract: This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the system during a node repair process. This paper presents a concatenated coding scheme which is based on two types of codes: maximum rank distance (MRD) code as an outer code and optimal repair maximal distance separable (MDS) array code as an inner code. Given this, two different types of adversarial errors are considered: the first type considers an adversary that can replace the content of an affected node only once; while the second attack-type considers an adversary that can pollute data an unbounded number of times. This paper proves that the proposed coding scheme attains a suitable upper bound on resilience capacity for the first type of error. Further, the paper presents mechanisms that combine this code with subspace signatures to achieve error resilience for the second type of errors. Finally, the paper concludes by presenting a construction based on MRD codes for optimal locally repairable scalar codes that can tolerate adversarial errors.
Error-Correcting Regenerating and Locally Repairable Codes via Rank-Metric Codes
Natalia Silberstein,Ankit Singh Rawat,Sriram Vishwanath
Computer Science , 2013,
Abstract: 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 codes. The concatenated coding scheme brings together a maximum rank distance (MRD) code as an outer code and either a globally regenerating or a locally repairable code as an inner code. Also, error resilience for combination of locally repairable codes with regenerating codes is considered. This concatenated coding system is designed to handle two different types of adversarial errors: the first type includes an adversary that can replace the content of an affected node only once; while the second type studies an adversary that is capable of polluting data an unbounded number of times. The paper establishes an upper bound on the resilience capacity for a locally repairable code and proves that this concatenated coding coding scheme attains the upper bound on resilience capacity for the first type of adversary. Further, the paper presents mechanisms that combine the presented concatenated coding scheme with subspace signatures to achieve error resilience for the second type of errors.
Optimal Locally Repairable and Secure Codes for Distributed Storage Systems
Ankit Singh Rawat,O. Ozan Koyluoglu,Natalia Silberstein,Sriram Vishwanath
Mathematics , 2012,
Abstract: This paper aims to go beyond resilience into the study of security and local-repairability for distributed storage systems (DSS). Security and local-repairability are both important as features of an efficient storage system, and this paper aims to understand the trade-offs between resilience, security, and local-repairability in these systems. In particular, this paper first investigates security in the presence of colluding eavesdroppers, where eavesdroppers are assumed to work together in decoding stored information. Second, the paper focuses on coding schemes that enable optimal local repairs. It further brings these two concepts together, to develop locally repairable coding schemes for DSS that are secure against eavesdroppers. The main results of this paper include: a. An improved bound on the secrecy capacity for minimum storage regenerating codes, b. secure coding schemes that achieve the bound for some special cases, c. a new bound on minimum distance for locally repairable codes, d. code construction for locally repairable codes that attain the minimum distance bound, and e. repair-bandwidth-efficient locally repairable codes with and without security constraints.
Secure Cooperative Regenerating Codes for Distributed Storage Systems
O. Ozan Koyluoglu,Ankit Singh Rawat,Sriram Vishwanath
Mathematics , 2012,
Abstract: Regenerating codes enable trading off repair bandwidth for storage in distributed storage systems (DSS). Due to their distributed nature, these systems are intrinsically susceptible to attacks, and they may also be subject to multiple simultaneous node failures. Cooperative regenerating codes allow bandwidth efficient repair of multiple simultaneous node failures. This paper analyzes storage systems that employ cooperative regenerating codes that are robust to (passive) eavesdroppers. The analysis is divided into two parts, studying both minimum bandwidth and minimum storage cooperative regenerating scenarios. First, the secrecy capacity for minimum bandwidth cooperative regenerating codes is characterized. Second, for minimum storage cooperative regenerating codes, a secure file size upper bound and achievability results are provided. These results establish the secrecy capacity for the minimum storage scenario for certain special cases. In all scenarios, the achievability results correspond to exact repair, and secure file size upper bounds are obtained using min-cut analyses over a suitable secrecy graph representation of DSS. The main achievability argument is based on an appropriate pre-coding of the data to eliminate the information leakage to the eavesdropper.
Optimal Locally Repairable Codes via Rank-Metric Codes
Natalia Silberstein,Ankit Singh Rawat,O. Ozan Koyluoglu,Sriram Vishwanath
Mathematics , 2013,
Abstract: 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 of node failures. This construction, based on maximum rank distance (MRD) Gabidulin codes, provides new optimal vector and scalar LRCs. In addition, the paper also discusses mechanisms by which codes obtained using this construction can be used to construct LRCs with efficient repair of failed nodes by combination of LRC with regenerating codes.
Batch Codes through Dense Graphs without Short Cycles
Alexandros G. Dimakis,Anna Gal,Ankit Singh Rawat,Zhao Song
Mathematics , 2014,
Abstract: Consider a large database of $n$ data items that need to be stored using $m$ servers. We study how to encode information so that a large number $k$ of read requests can be performed in parallel while the rate remains constant (and ideally approaches one). This problem is equivalent to the design of multiset Batch Codes introduced by Ishai, Kushilevitz, Ostrovsky and Sahai [17]. We give families of multiset batch codes with asymptotically optimal rates of the form $1-1/\text{poly}(k)$ and a number of servers $m$ scaling polynomially in the number of read requests $k$. An advantage of our batch code constructions over most previously known multiset batch codes is explicit and deterministic decoding algorithms and asymptotically optimal fault tolerance. Our main technical innovation is a graph-theoretic method of designing multiset batch codes using dense bipartite graphs with no small cycles. We modify prior graph constructions of dense, high-girth graphs to obtain our batch code results. We achieve close to optimal tradeoffs between the parameters for bipartite graph based batch codes.
Locality and Availability in Distributed Storage
Ankit Singh Rawat,Dimitris S. Papailiopoulos,Alexandros G. Dimakis,Sriram Vishwanath
Computer Science , 2014,
Abstract: This paper studies the problem of code symbol availability: a code symbol is said to have $(r, t)$-availability if it can be reconstructed from $t$ disjoint groups of other symbols, each of size at most $r$. For example, $3$-replication supports $(1, 2)$-availability as each symbol can be read from its $t= 2$ other (disjoint) replicas, i.e., $r=1$. However, the rate of replication must vanish like $\frac{1}{t+1}$ as the availability increases. This paper shows that it is possible to construct codes that can support a scaling number of parallel reads while keeping the rate to be an arbitrarily high constant. It further shows that this is possible with the minimum distance arbitrarily close to the Singleton bound. This paper also presents a bound demonstrating a trade-off between minimum distance, availability and locality. Our codes match the aforementioned bound and their construction relies on combinatorial objects called resolvable designs. From a practical standpoint, our codes seem useful for distributed storage applications involving hot data, i.e., the information which is frequently accessed by multiple processes in parallel.
Van Panchayats as an Effective Tool in Conserving Biodiversity at Local Level  [PDF]
Vardan Singh Rawat, Yashwant Singh Rawat
Journal of Environmental Protection (JEP) , 2010, DOI: 10.4236/jep.2010.13033
Abstract: Forest vegetation of a community managed forest was studied along four aspects. Quercus leucotrichophora and Pinus roxburghii was the dominant species on each of the two aspects. Across the aspects the total tree density ranged between 193 to 324.3 ind/ha, sapling density between 119 to 258.6 ind/ha and seedling density from 249.98 to 845 ind/ha. The shrub density varied from 199.99 to 406.32 ind/ha and herb density from 9466.66 to 52483.33 ind/ha. The total basal area varied from 0.06 to 7.15 m2/ha at eastern and north facing aspect for Quercus leucotrichophora and Pinus roxburghii respectively showing that the forest is in young stage. Species diversity value for tree layer varied from 0.21 to 1.23 while concentration of dominance value ranged from 0.56 to 0.94. It was noticed that with an increase in species diversity concentration of dominance value decreases indicating inverse relationship between diversity and dominance.
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