Related papers: On Vector Linear Solvability of Multicast Networks
Network embedding is a highly effective method to learn low-dimensional node vector representations with original network structures being well preserved. However, existing network embedding algorithms are mostly developed for a single…
While it is known that using network coding can significantly improve the throughput of directed networks, it is a notorious open problem whether coding yields any advantage over the multicommodity flow (MCF) rate in undirected networks. It…
In this paper we give network coding algorithms for multi-layered video streaming. The problem is motivated by video broadcasting in a communication network to users with varying demands. We give a polynomial time algorithm for deciding…
Direct application of network coding at the physical layer - physical layer network coding (PNC) - is a promising technique for two-way relay wireless networks. In a two-way relay network, relay nodes are used to relay two-way information…
In this work, we study the problem of index coding from graph homomorphism perspective. We show that the minimum broadcast rate of an index coding problem for different variations of the problem such as non-linear, scalar, and vector index…
One of the main theoretical motivations for the emerging area of network coding is the achievability of the max-flow/min-cut rate for single source multicast. This can exceed the rate achievable with routing alone, and is achievable with…
In this paper we show that the Index Coding problem captures several important properties of the more general Network Coding problem. An instance of the Index Coding problem includes a server that holds a set of information messages…
The graph convolution network (GCN) is a widely-used facility to realize graph-based semi-supervised learning, which usually integrates node features and graph topologic information to build learning models. However, as for multi-label…
Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem…
A general lossless joint source-channel coding (JSCC) scheme based on linear codes and random interleavers for multiple-access channels (MACs) is presented and then analyzed in this paper. By the information-spectrum approach and the…
This paper proposes Fulcrum network codes, a network coding framework that achieves three seemingly conflicting objectives: (i) to reduce the coding coefficient overhead to almost n bits per packet in a generation of n packets; (ii) to…
A main distinguishing feature of a wireless network compared with a wired network is its broadcast nature, in which the signal transmitted by a node may reach several other nodes, and a node may receive signals from several other nodes,…
This paper investigates the problem of single-source multicasting over a communication network in the presence of restricted adversaries. When the adversary is constrained to operate only on a prescribed subset of edges, classical cut-set…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, semi-injective, and linear target functions over…
In recent years, deep neural network is widely used in machine learning. The multi-class classification problem is a class of important problem in machine learning. However, in order to solve those types of multi-class classification…
Most state-of-the-art Graph Neural Networks (GNNs) can be defined as a form of graph convolution which can be realized by message passing between direct neighbors or beyond. To scale such GNNs to large graphs, various neighbor-, layer-, or…
Linear computation broadcast (LCBC) refers to a setting with $d$ dimensional data stored at a central server, where $K$ users, each with some prior linear side-information, wish to retrieve various linear combinations of the data. For each…
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…
Several types of AL-FEC (Application-Level FEC) codes for the Packet Erasure Channel exist. Random Linear Codes (RLC), where redundancy packets consist of random linear combinations of source packets over a certain finite field, are a…