Related papers: Codes for Graph Erasures
Coding schemes with extremely low computational complexity are required for particular applications, such as wireless body area networks, in which case both very high data accuracy and very low power-consumption are required features. In…
Codes defined on graphs and their properties have been subjects of intense recent research. On the practical side, constructions for capacity-approaching codes are graphical. On the theoretical side, codes on graphs provide several…
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
Graph codes play an important role in photonic quantum technologies as they provide significant protection against qubit loss, a dominant noise mechanism. Here, we develop methods to analyse and optimise measurement-based tolerance to qubit…
The repair bandwidth of a code is the minimum amount of data required to repair one or several failed nodes (erasures). For MDS codes, the repair bandwidth is bounded below by the so-called cut-set bound, and codes that meet this bound with…
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…
MDS array codes are widely used in storage systems to protect data against erasures. We address the \emph{rebuilding ratio} problem, namely, in the case of erasures, what is the the fraction of the remaining information that needs to be…
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
We consider the problem of information aggregation in sensor networks, where one is interested in computing a function of the sensor measurements. We allow for block processing and study in-network function computation in directed graphs…
A linear graph code is a family $\mathcal{C}$ of graphs on $n$ vertices with the property that the symmetric difference of the edge sets of any two graphs in $\mathcal{C}$ is also the edge set of a graph in $\mathcal{C}$. In this article,…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Yet, the codes being deployed in practice are fairly short. In this work, we address what we…
Graph neural networks operate on graph-structured data via exchanging messages along edges. One limitation of this message passing paradigm is the over-squashing problem. Over-squashing occurs when messages from a node's expanded receptive…
Protecting against link failures in communication networks is essential to increase robustness, accessibility, and reliability of data transmission. Recently, network coding has been proposed as a solution to provide agile and cost…
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…
Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a…
In this paper, we construct Error-Correcting Graph Codes. An error-correcting graph code of distance $\delta$ is a family $C$ of graphs on a common vertex set of size $n$, such that if we start with any graph in $C$, we would have to modify…
We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…
An identifying code in a graph is a set of vertices which intersects all the symmetric differences between pairs of neighbourhoods of vertices. Not all graphs have identifying codes; those that do are referred to as twin-free. In this…