Related papers: Codes for Erasures over Directed Graphs
In this paper, we introduce a new model to study network reliability with node failures. This model, strongly connected node reliability, is the directed variant of node reliability and measures the probability that the operational vertices…
In this paper, we show that the single deletion correcting Varshamov-Tenengolts code, with minor modifications, can also correct an ordered deletion-erasure pattern where one deletion and at most one erasure occur and the deletion always…
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs…
Convolutional codes are a class of error-correcting codes that performs very well over erasure channels with low delay requirements. In particular, Maximum Distance Profile (MDP) convolutional codes, which are defined to have optimal column…
A graph is \emph{fan-crossing free} if it has a drawing in the plane so that each edge is crossed by independent edges, that is the crossing edges have distinct vertices. On the other hand, it is \emph{fan-crossing} if the crossing edges…
Binary code similarity detection is an important problem with applications in areas such as malware analysis, vulnerability research and license violation detection. This paper proposes a novel graph neural network architecture combined…
In extreme classification problems, learning algorithms are required to map instances to labels from an extremely large label set. We build on a recent extreme classification framework with logarithmic time and space, and on a general…
In the context of distributed storage systems, locally repairable codes have become important. In this paper we focus on codes that allow for multi-erasure pattern decoding with low computational effort. Different optimality requirements,…
We introduce a new construction of error-correcting codes from algebraic curves over finite fields. Modular curves of genus g -> infty over a field of size q0^2 yield nonlinear codes more efficient than the linear Goppa codes obtained from…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
The problem of securing data against eavesdropping in distributed storage systems is studied. The focus is on systems that use linear codes and implement exact repair to recover from node failures.The maximum file size that can be stored…
In this paper, we present a novel communication channel, called the absorption channel, inspired by information transmission in neurons. Our motivation comes from in-vivo nano-machines, emerging medical applications, and brain-machine…
Erasure codes have become an integral part of distributed storage systems as a tool for providing data reliability and durability under the constant threat of device failures. In such systems, an $[n, k]$ code over a finite field…
Production software oftentimes suffers from the issue of performance inefficiencies caused by inappropriate use of data structures, programming abstractions, and conservative compiler optimizations. It is desirable to avoid unnecessary…
We consider rank modulation codes for flash memories that allow for handling arbitrary charge-drop errors. Unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked…
Existing defects in software components is unavoidable and leads to not only a waste of time and money but also many serious consequences. To build predictive models, previous studies focus on manually extracting features or using tree…
We propose to use the concept of the Hamming bound to derive the optimal criteria for learning hash codes with a deep network. In particular, when the number of binary hash codes (typically the number of image categories) and code length…
The noise model of deletions poses significant challenges in coding theory, with basic questions like the capacity of the binary deletion channel still being open. In this paper, we study the harder model of worst-case deletions, with a…
Distributed data storage systems are essential to deal with the need to store massive volumes of data. In order to make such a system fault-tolerant, some form of redundancy becomes crucial, incurring various overheads - most prominently in…
We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…