Related papers: Locality in Crisscross Error Correction
In an $[n,k,d]$ linear code, a code symbol is said to have locality $r$ if it can be repaired by accessing at most $r$ other code symbols. For an $(n,k,r)$ \emph{locally repairable code} (LRC), the minimum distance satisfies the well-known…
Codes in the sum-rank metric have received many attentions in recent years, since they have wide applications in the multishot network coding, the space-time coding and the distributed storage. In this paper, by constructing covering codes…
Locally repairable codes (LRC) have recently been a subject of intense research due to theoretical appeal and their application in distributed storage systems. In an LRC, any coordinate of a codeword can be recovered by accessing only few…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
In error-correcting codes, locality refers to several different ways of quantifying how easily a small amount of information can be recovered from encoded data. In this work, we study a notion of locality called the s-Disjoint-Repair-Group…
We give a centralized deterministic algorithm for constructing linear network error-correcting codes that attain the Singleton bound of network error-correcting codes. The proposed algorithm is based on the algorithm by Jaggi et al. We give…
This paper develops a new family of locally recoverable codes for distributed storage systems, Sequential Locally Recoverable Codes (SLRCs) constructed to handle multiple erasures in a sequential recovery approach. We propose a new…
In this paper, a link between polymatroid theory and locally repairable codes (LRCs) is established. The codes considered here are completely general in that they are subsets of $A^n$, where $A$ is an arbitrary finite set. Three classes of…
Spatially-Coupled (SC)-LDPC codes are known to have outstanding error-correction performance and low decoding latency. Whereas previous works on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length design approach, in…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these…
Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes…
The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…
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…
An $[n,k]$ code $\mathcal{C}$ is said to be locally recoverable in the presence of a single erasure, and with locality parameter $r$, if each of the $n$ code symbols of $\mathcal{C}$ can be recovered by accessing at most $r$ other code…
In this paper, we discuss codes for distributed storage systems with hierarchical repair properties. Specifically, we devote attention to the repair problem of the rack-aware storage model with locality, aiming to enhance the system's…
Symbol-pair codes were proposed for the application in high density storage systems, where it is not possible to read individual symbols. Yaakobi, Bruck and Siegel proved that the minimum pair-distance of binary linear cyclic codes…
We investigate one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable…
Local Reconstruction Codes (LRCs) allow for recovery from a small number of erasures in a local manner based on just a few other codeword symbols. A maximally recoverable (MR) LRC offers the best possible blend of such local and global…
A locally repairable code (LRC) with locality $r$ allows for the recovery of any erased codeword symbol using only $r$ other codeword symbols. A Singleton-type bound dictates the best possible trade-off between the dimension and distance of…
In this paper motivated from subspace coding we introduce subspace-metric codes and subset-metric codes. These are coordinate-position independent pseudometrics and suitable for the folded codes. The half-Singleton upper bounds for linear…