Related papers: Scalar Solvability of Network Computation Problems…
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…
This article studies two notions of generalized matroid representations motivated by algorithmic information theory and cryptographic secret sharing. The first (entropic representability) involves discrete random variables, while the second…
We consider the vector linear solvability of networks over a field $\mathbb{F}_q.$ It is well known that a scalar linear solution over $\mathbb{F}_q$ exists for a network if and only if the network is \textit{matroidal} with respect to a…
This paper provides a new duality between entropy functions and network codes. Given a function $g\geq 0$ defined on all proper subsets of $N$ random variables, we provide a construction for a network multicast problem which is solvable if…
We present different classes of solutions to the Firing Squad Synchronization Problem on networks of different shapes. The nodes are finite state processors that work at unison discrete steps. The networks considered are the line, the ring…
We are interested in how to best communicate a (usually real valued) source to a number of destinations (sinks) over a network with capacity constraints in a collective fidelity metric over all the sinks, a problem which we call joint…
Problems related to network coding for acyclic, instantaneous networks (where the edges of the acyclic graph representing the network are assumed to have zero-delay) have been extensively dealt with in the recent past. The most prominent of…
We investigate linear network coding in the context of robust function computation, where a sink node is tasked with computing a target function of messages generated at multiple source nodes. In a previous work, a new distance measure was…
In this work, we explore the problem of multi-user linearly-separable distributed computation, where $N$ servers help compute the desired functions (jobs) of $K$ users, and where each desired function can be written as a linear combination…
Random linear network coding is a particularly decentralized approach to the multicast problem. Use of random network codes introduces a non-zero probability however that some sinks will not be able to successfully decode the required…
The problem of network coding for multicasting a single source to multiple sinks has first been studied by Ahlswede, Cai, Li and Yeung in 2000, in which they have established the celebrated max-flow mini-cut theorem on non-physical…
We consider the distributed function computation problem in asymmetric communication scenarios, where the sink computes some deterministic function of the data split among N correlated informants. The distributed function computation…
In the algebraic view, the solution to a network coding problem is seen as a variety specified by a system of polynomial equations typically derived by using edge-to-edge gains as variables. The output from each sink is equated to its…
Distributed computing is fundamental to multi-agent systems, with solving distributed linear equations as a typical example. In this paper, we study distributed solvers for network linear equations over a network with node-to-node…
Increasing network utilization is often considered as the holy grail of communications. In this article, the concept of sub-rate coding and decoding in the framework of linear network coding (LNC) is discussed for single-source…
We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The…
The connection between index coding and matroid theory have been well studied in the recent past. El Rouayheb et al. established a connection between multilinear representation of matroids and wireless index coding. Muralidharan and Rajan…
The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer…
One open problem in source coding is to characterize the limits of representing losslessly a non-identity discrete function of the data encoded independently by the encoders of several correlated sources with memory. This paper investigates…
We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A special case of this correspondence identifies the problem of…