Related papers: Osculating Spaces of Varieties and Linear Network …
Minimal multicast networks are fascinating and efficient combinatorial objects, where the removal of a single link makes it impossible for all receivers to obtain all messages. We study the structure of such networks, and prove some…
Vector sets with optimal coherence according to the Welch bound cannot exist for all pairs of dimension and cardinality. If such an optimal vector set exists, it is an equiangular tight frame and represents the solution to a Grassmannian…
Following the approach by R. K\"otter and F. R. Kschischang, we study network codes as families of k-dimensional linear subspaces of a vector space F_q^n, q being a prime power and F_q the finite field with q elements. In particular,…
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to…
We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a…
We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have…
In this paper, convolutional network coding is formulated by means of matrix power series representation of the local encoding kernel (LEK) matrices and global encoding kernel (GEK) matrices to establish its theoretical fundamentals for…
We consider the problem of multicasting information from a source to a set of receivers over a network where intermediate network nodes perform randomized network coding operations on the source packets. We propose a channel model for the…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
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…
The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…
We propose a simple yet effective wireless network coding and decoding technique. It utilizes spatial diversity through cooperation between nodes which carry out distributed encoding operations dictated by generator matrices of linear block…
Vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted on every edge is an $L$-dimensional vector of data symbols over a base field GF($q$). Vector LNC enriches the choices…
Network coding is a technique to maximize communication rates within a network, in communication protocols for simultaneous multi-party transmission of information. Linear network codes are examples of such protocols in which the local…
This paper presents methods to compare high order networks, defined as weighted complete hypergraphs collecting relationship functions between elements of tuples. They can be considered as generalizations of conventional networks where only…
We introduce a discrete network corresponding to any Gaussian wireless network that is obtained by simply quantizing the received signals and restricting the transmitted signals to a finite precision. Since signals in the discrete network…
Subspace codes form the appropriate mathematical setting for investigating the Koetter-Kschischang model of fault-tolerant network coding. The Main Problem of Subspace Coding asks for the determination of a subspace code of maximum size…
Vector-space word representations obtained from neural network models have been shown to enable semantic operations based on vector arithmetic. In this paper, we explore the existence of similar information on vector representations of…
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…