Related papers: Linear Network Error Correction Coding: A Revisit
Index coding, or broadcasting with side information, is a network coding problem of most fundamental importance. In this problem, given a directed graph, each vertex represents a user with a need of information, and the neighborhood of each…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
We consider uniquely-decodable coding for zero-error network function computation, where in a directed acyclic graph, the single sink node is required to compute with zero error a target function multiple times, whose arguments are the…
The problem of finding network codes for general connections is inherently difficult in capacity constrained networks. Resource minimization for general connections with network coding is further complicated. Existing methods for…
Assume that a graph $G$ models a detection system for a facility with a possible ``intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing detectors at a subset of vertices in $G$…
This paper studies the capacity of single-source single-sink noiseless networks under adversarial or arbitrary errors on no more than z edges. Unlike prior papers, which assume equal capacities on all links, arbitrary link capacities are…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close…
As parallelism becomes critically important in the semiconductor technology, high-performance computing, and cloud applications, parallel network systems will increasingly follow suit. Today, parallelism is an essential architectural…
Though deep learning has been applied successfully in many scenarios, malicious inputs with human-imperceptible perturbations can make it vulnerable in real applications. This paper proposes an error-correcting neural network (ECNN) that…
Deterministic linear network coding (DLNC) is an important family of network coding techniques for wireless packet broadcast. In this paper, we show that DLNC is strongly related to and can be effectively studied using matroid theory…
The relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable…
Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vectorspace. Ralf Koetter and Frank R. Kschischang in Coding for errors and erasures in…
Motivated by systems where the information is represented by a graph, such as neural networks, associative memories, and distributed systems, we present in this work a new class of codes, called codes over graphs. Under this paradigm, the…
To better understand the correlation between network topological features and the robustness of network controllability in a general setting, this paper suggests a practical approach to searching for optimal network topologies with given…
The problem of coding for networks experiencing worst-case symbol errors is considered. We argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network…
LDPC codes play a vital role in coding theory and practical error correction. A central problem in this direction is to understand their rate--distance tradeoff. In this paper, we introduce a new framework for estimating ball sizes in the…
This paper investigates the construction of linear network codes for broadcasting a set of data packets to a number of users. The links from the source to the users are modeled as independent erasure channels. Users are allowed to inform…
This paper investigates the performance of streaming codes in low-latency applications over a multi-link three-node relayed network. The source wishes to transmit a sequence of messages to the destination through a relay. Each message must…
For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of…