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Lying at the interface between Network Science and Machine Learning, node embedding algorithms take a graph as input and encode its structure onto output vectors that represent nodes in an abstract geometric space, enabling various…
In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to…
Linear codes are widely studied due to their applications in communication, cryptography, quantum codes, distributed storage and many other fields. In this paper, we use the trace and norm functions over finite fields to construct a family…
Differential linear network coding (DLNC) is a precoding scheme for information transmission over random linear networks. By using differential encoding and decoding, the conventional approach of lifting, required for inherent channel…
The performance of many network learning applications crucially hinges on the success of network embedding algorithms, which aim to encode rich network information into low-dimensional vertex-based vector representations. This paper…
Phylogenetic networks are used to represent the evolutionary history of species. Recently, the new class of orchard networks was introduced, which were later shown to be interpretable as trees with additional horizontal arcs. This makes the…
We consider the problem of information flow over Gaussian relay networks. Similar to the recent work by Avestimehr \emph{et al.} [1], we propose network codes that achieve up to a constant gap from the capacity of such networks. However,…
In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of…
In this paper, we develop a new aligned vertex convolutional network model to learn multi-scale local-level vertex features for graph classification. Our idea is to transform the graphs of arbitrary sizes into fixed-sized aligned vertex…
Neural network-based language models deal with data sparsity problems by mapping the large discrete space of words into a smaller continuous space of real-valued vectors. By learning distributed vector representations for words, each…
Wireless communications using light waves are called visible light communication. A technique called Physical-layer Network coding allows several users to communicate simultaneously over the same channel in a distributed space-time Coding…
A subspace code is a nonempty set of subspaces of a vector space $\mathbb F^n_q$. Linear codes with complementary duals, or LCD codes, are linear codes whose intersection with their duals is trivial. In this paper, we introduce a notion of…
Network coding is studied when an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than when the adversary controls a given number of edges in the…
We introduce and explore a new concept of evasive subspace with respect to a collection of subspaces sharing a common dimension, most notably partial spreads. We show that this concept generalises known notions of subspace scatteredness and…
Variational auto-encoders (VAEs) have proven to be a well suited tool for performing dimensionality reduction by extracting latent variables lying in a potentially much smaller dimensional space than the data. Their ability to capture…
Convolutional neural networks have been highly successful in image-based learning tasks due to their translation equivariance property. Recent work has generalized the traditional convolutional layer of a convolutional neural network to…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
We consider a problem in which a source is encoded into N packets, an unknown number of which are subject to adversarial errors en route to the decoder. We seek code designs for which the decoder is guaranteed to be able to reproduce the…
This paper proves the separation between source-network coding and channel coding in networks of noisy, discrete, memoryless channels. We show that the set of achievable distortion matrices in delivering a family of dependent sources across…
We investigate techniques for designing modulation/coding schemes for the wireless two-way relaying channel. The relay is assumed to have perfect channel state information, but the transmitters are assumed to have no channel state…