Results 1  10
of
18
An Upper Bound On the Size of Locally Recoverable Codes
"... Abstract—In a locally recoverable or 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 storage where a most frequent errorevent is a single storage node fa ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
(Show Context)
Abstract—In a locally recoverable or 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 storage where a most frequent errorevent is a single storage node failure (erasure). A common objective is to repair the node by downloading data from as few other storage node as possible. In this paper, we bound the minimum distance of a code in terms of of its length, size and locality. Unlike previous bounds, our bound follows from a significantly simple analysis and depends on the size of the alphabet being used. I.
On a duality between recoverable distributed storage and index coding
 in IEEE International Symposium on Information Theory (ISIT
, 2003
"... Abstract—In this paper, we introduce a model of a singlefailure locally recoverable distributed storage system. This model appears to give rise to a problem seemingly dual of the wellstudied index coding problem. The relation between the dimensions of an optimal index code and optimal distributed ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Abstract—In this paper, we introduce a model of a singlefailure locally recoverable distributed storage system. This model appears to give rise to a problem seemingly dual of the wellstudied index coding problem. The relation between the dimensions of an optimal index code and optimal distributed storage code of our model has been established in this paper. We also show some extensions to vector codes. I.
Locality and availability in distributed storage
 IN PROCEEDINGS OF THE IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT
, 2014
"... 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, 3replication supports (1, 2)availability as each symbol can be read from its t = 2 ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
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, 3replication 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 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 tradeoff 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.
1 Coding with Constraints: Minimum Distance Bounds and Systematic Constructions
"... ar ..."
(Show Context)
Batch Codes through Dense Graphs without Short Cycles
, 2014
"... 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 multis ..."
Abstract
 Add to MetaCart
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/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 graphtheoretic method of designing multiset batch codes using dense bipartite graphs with no small cycles. We modify prior graph constructions of dense, highgirth graphs to obtain our batch code results. We achieve close to optimal tradeoffs between the parameters for bipartite graph based batch codes.
Linear Locally Repairable Codes with Random Matrices
, 2014
"... In this paper, locally repairable codes with allsymbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the locality property, is a generator matrix for a locally repaira ..."
Abstract
 Add to MetaCart
In this paper, locally repairable codes with allsymbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the locality property, is a generator matrix for a locally repairable code with a good minimum distance. The proof of this gives also a constructive method to find locally repairable codes.