Related papers: Coding for Locality in Reconstructing Permutations
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…
Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node,…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
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…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
Combinatorial designs provide an interesting source of optimization problems. Among them, permutation codes are particularly interesting given their applications in powerline communications, flash memories, and block ciphers. This paper…
Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of $n$…
In this paper we prove new lower bounds for the maximal size of permutation codes by connecting the theory of permutation codes with the theory of linear block codes. More specifically, using the columns of a parity check matrix of an…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
In this paper, we study three applications of recursion to problems in coding and random permutations. First, we consider locally recoverable codes with partial locality and use recursion to estimate the minimum distance of such codes. Next…
This paper investigates data compression that simultaneously allows local decoding and local update. The main result is a universal compression scheme for memoryless sources with the following features. The rate can be made arbitrarily…
In this work, we study the codes over the integers with locality constraints. We introduce a weighted notion of locality over $\mathbb{Z}/q_1\mathbb{Z} \times \cdots \times \mathbb{Z}/q_n\mathbb{Z}$ and derive a Singleton-like bound for…
A major issue of locally repairable codes is their robustness. If a local repair group is not able to perform the repair process, this will result in increasing the repair cost. Therefore, it is critical for a locally repairable code to…
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…
An index code is said to be locally decodable if each receiver can decode its demand using its side information and by querying only a subset of the transmitted codeword symbols instead of observing the entire codeword. Local decodability…
Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
We examine the problem of allocating a given total storage budget in a distributed storage system for maximum reliability. A source has a single data object that is to be coded and stored over a set of storage nodes; it is allowed to store…
Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted…
The {\em repair locality} of a distributed storage code is the maximum number of nodes that ever needs to be contacted during the repair of a failed node. Having small repair locality is desirable, since it is proportional to the number of…