Related papers: On Vector Linear Solvability of Multicast Networks
Recent research indicates that packet transmission employing random linear network coding can be regarded as transmitting subspaces over a linear operator channel (LOC). In this paper we propose the framework of linear operator broadcast…
Sparse random linear network coding (SRLNC) used as a class of erasure codes to ensure the reliability of multicast communications has been widely investigated. However, an exact expression for the decoding success probability of SRLNC is…
Random linear network coding (RLNC) is asymptotically throughput optimal in the wireless broadcast of a block of packets from a sender to a set of receivers, but suffers from heavy computational load and packet decoding delay. To mitigate…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
A class of network codes have been proposed in the literature where the symbols transmitted on network edges are binary vectors and the coding operation performed in network nodes consists of the application of (possibly several)…
Vector perturbation is an encoding method for broadcast channels in which the transmitter solves a shortest vector problem in a lattice to create a perturbation vector, which is then added to the data before transmission. In this work, we…
The capacity of the AWGN broadcast channel is achieved by superposition coding, but superposition of individual coded modulations expands the modulation alphabet and distorts its configuration. Coded modulation over a broadcast channel…
The problem of scalar multiplication applied to vectors is considered in the Lee metric. Unlike in other metrics, the Lee weight of a vector may be increased or decreased by the product with a nonzero, nontrivial scalar. This problem is of…
Large Language Models (LLMs) have demonstrated strong reasoning abilities, making them suitable for complex tasks such as graph computation. Traditional reasoning steps paradigm for graph problems is hindered by unverifiable steps, limited…
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…
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…
We consider multi-resolution streaming in fully-connected peer-to-peer networks, where transmission rates are constrained by arbitrarily specified upload capacities of the source and peers. We fully characterize the capacity region of rate…
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…
In this exploratory numerical study, we assess the suitability of Quantum Linear Solvers(QLSs)toward providing a quantum advantage for Networks-based Linear System Problems (NLSPs). NLSPs naturally arise from graphs, and are of importance…
The rate regions of multilevel diversity coding systems (MDCS), a sub-class of the broader family of multi-source multi-sink networks with special structure, are investigated. After showing how to enumerate all non-isomorphic MDCS instances…
For data streaming applications, existing solutions are not yet able to close the gap between high data rates and low delay. This work considers the problem of data streaming under mixed delay constraints over a single communication channel…
Convolutional neural networks (CNNs) leverage the great power in representation learning on regular grid data such as image and video. Recently, increasing attention has been paid on generalizing CNNs to graph or network data which is…
An index coding (IC) problem consisting of a server and multiple receivers with different side-information and demand sets can be equivalently represented using a fitting matrix. A scalar linear index code to a given IC problem is a matrix…
A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver…
We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…