Related papers: Linear Network Error Correction Coding: A Revisit
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem ($k$-ECSS), as well as nonuniform…
We consider the problem of linear network coding over communication networks, representable by directed acyclic graphs, with multiple groupcast sessions: the network comprises of multiple destination nodes, each desiring messages from…
In the modern era of large-scale computing systems, a crucial use of error correcting codes is to judiciously introduce redundancy to ensure recoverability from failure. To get the most out of every byte, practitioners and theorists have…
The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with…
Graph Convolutional Networks (GCNs) have received increasing attention in the machine learning community for effectively leveraging both the content features of nodes and the linkage patterns across graphs in various applications. As…
The distance of a graph from being triangle-free is a fundamental graph parameter, counting the number of edges that need to be removed from a graph in order for it to become triangle-free. Its corresponding computational problem is the…
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…
We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations consist of only circular-shifts and bit-wise additions (XOR). Formulated as a special vector linear code over GF($2$), an…
This paper addresses the issue of design of low-rate sparse-graph codes with linear minimum distance in the blocklength. First, we define a necessary condition which needs to be satisfied when the linear minimum distance is to be ensured.…
We consider network coding for a noiseless broadcast channel where each receiver demands a subset of messages available at the transmitter and is equipped with noisy side information in the form an erroneous version of the message symbols…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
We study the problem of erasure correction (node repair) for regenerating codes defined on graphs wherein the cost of transmitting the information to the failed node depends on the graphical distance from this node to the helper vertices of…
Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…
Error correction codes are an integral part of communication applications, boosting the reliability of transmission. The optimal decoding of transmitted codewords is the maximum likelihood rule, which is NP-hard due to the curse of…
Link and node failures are common two fundamental problems that affect operational networks. Hence, protection of communication networks is essential to increase their reliability, performance, and operations. Much research work has been…
Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its…
Recently, physical layer security in the optical layer has gained significant traction. Security treats in optical networks generally impact the reliability of optical transmission. Linear Network Coding (LNC) can protect from both the…
Random linear network coding (RLNC) in theory achieves the max-flow capacity of multicast networks, at the cost of high decoding complexity. To improve the performance-complexity tradeoff, we consider the design of sparse network codes. A…
Increasing network utilization is often considered as the holy grail of communications. In this article, the concept of sub-rate coding and decoding in the framework of linear network coding (LNC) is discussed for single-source…
Physical-layer network coding (PNC) is a communications paradigm that exploits overlapped transmissions to boost the throughput of wireless relay networks. A high point of PNC research was a theoretical proof that PNC that makes use of…