Related papers: Network coding and spherical buildings
When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted…
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…
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…
We extend the notion of locality from the Hamming metric to the rank and subspace metrics. Our main contribution is to construct a class of array codes with locality constraints in the rank metric. Our motivation for constructing such codes…
To address growth challenges facing large Data Centers and supercomputing clusters a new construction is presented for scalable, high throughput, low latency networks. The resulting networks require 1.5-5 times fewer switches, 2-6 times…
A subspace code is defined as a collection of subspaces of an ambient vector space, where each information-encoding codeword is a subspace. This paper studies a class of spatial sensing problems, notably direction of arrival (DoA)…
Upper bounds are derived for codes in Stiefel and Grassmann manifolds with given minimal chordal distance. They stem from upper bounds for codes in products of unit spheres and projective spaces. The new bounds are asymptotically better…
Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
A concept of higher order neighborhood in complex networks, introduced previously (PRE \textbf{73}, 046101, (2006)), is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each…
We define and study a class of codes obtained from scrolls over curves of any genus over finite fields. These codes generalize Goppa codes in a natural way, and the orthogonal complements of these codes belong to the same class. We show how…
Secure network coding realizes the secrecy of the message when the message is transmitted via noiseless network and a part of edges or a part of intermediate nodes are eavesdropped. In this framework, if the channels of the network has…
We propose a new class of space-time block codes based on finite-field rank-metric codes in combination with a rank-metric-preserving mapping to the set of Eisenstein integers. It is shown that these codes achieve maximum diversity order…
We consider linear error correcting codes associated to higher dimensional projective varieties defined over a finite field. The problem of determining the basic parameters of such codes often leads to some interesting and difficult…
In this paper, we show how to construct a factor graph from a network code. This provides a systematic framework for decoding using message passing algorithms. The proposed message passing decoder exploits knowledge of the underlying…
In recent years, network coding has emerged as an innovative method that helps wireless network approaches its maximum capacity, by combining multiple unicasts in one broadcast. However, the majority of research conducted in this area is…
Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…
A novel implementation of a special class of Galois ring, in which the multiplication can be realized by a cyclic convolution, is applied to the construction of network codes. The primitive operations involved are byte-wise shifts and…
Traditional network security protocols depend mainly on developing cryptographic schemes and on using biometric methods. These have led to several network security protocols that are unbreakable based on difficulty of solving untractable…
Subspace codes have important applications in random network coding. It is interesting to construct subspace codes with both sizes, and the minimum distances are as large as possible. In particular, cyclic constant dimension subspaces codes…