Related papers: Codes for Erasures over Directed Graphs
We consider regenerating codes in distributed storage systems where connections between the nodes are constrained by a graph. In this problem, the failed node downloads the information stored at a subset of vertices of the graph for the…
Storage codes on graphs are an instance of \emph{codes with locality}, which are used in distributed storage schemes to provide local repairability. Specifically, the nodes of the graph correspond to storage servers, and the neighbourhood…
In distributed storage systems that use coding, the issue of minimizing the communication required to rebuild a storage node after a failure arises. We consider the problem of repairing an erased node in a distributed storage system that…
This paper presents several algorithms for hashing directed graphs. The algorithms given are capable of hashing entire graphs as well as assigning hash values to specific nodes in a given graph. The notion of node symmetry is made precise…
Erasure codes have emerged as an efficient technology for providing data redundancy in distributed storage systems. However, it is a challenging task to repair the failed storage nodes in erasure-coded storage systems, which requires large…
We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a…
We continue our study of regenerating codes in distributed storage systems where connections between the nodes are constrained by a graph. In this problem, the failed node downloads the information stored at a subset of vertices of the…
In a distributed storage system based on erasure coding, an important problem is the \emph{repair problem}: If a node storing a coded piece fails, in order to maintain the same level of reliability, we need to create a new encoded piece and…
This paper investigates the use of redundancy and self repairing against node failures in distributed storage systems, using various strategies. In replication method, access to one replication node is sufficient to reconstruct a lost node,…
Peer-to-peer distributed storage systems provide reliable access to data through redundancy spread over nodes across the Internet. A key goal is to minimize the amount of bandwidth used to maintain that redundancy. Storing a file using an…
Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…
In large-scale distributed storage systems, erasure coding is employed to ensure reliability against disk failures. Recent work by Kadekodi et al. demonstrates that adapting code parameters to varying disk failure rates can lead to…
We consider the \emph{functional index coding problem} over an error-free broadcast network in which a source generates a set of messages and there are multiple receivers, each holding a set of functions of source messages in its cache,…
A new class of exact-repair regenerating codes is constructed by stitching together shorter erasure correction codes, where the stitching pattern can be viewed as block designs. The proposed codes have the "help-by-transfer" property where…
The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect…
Linear codes over finite extension fields have widespread applications in theory and practice. In some scenarios, the decoder has a sequential access to the codeword symbols, giving rise to a hierarchical erasure structure. In this paper we…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
Maximum distance separable (MDS) array codes are XOR-based optimal erasure codes that are particularly suitable for use in disk arrays. This paper develops an innovative method to build MDS array codes from an elegant class of nested…
\emph{Resistive memories}, such as \emph{phase change memories} and \emph{resistive random access memories} have attracted significant attention in recent years due to their better scalability, speed, rewritability, and yet non-volatility.…
We construct optimal secure coded distributed schemes that extend the known optimal constructions over fields of characteristic 0 to all fields. A serendipitous result is that we can encode \emph{all} functions over finite fields with a…