Related papers: On Base Field of Linear Network Coding
It is known that for any finite/co-finite set of primes there exists a network which has a rate $1$ solution if and only if the characteristic of the finite field belongs to the given set. We generalize this result to show that for any…
We introduce a new technique to certify lower bounds on the multicut size using network coding. In directed networks the network coding rate is not a lower bound on the multicut, but we identify a class of networks on which the rate is…
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…
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…
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…
One fundamental problem in the field of network coding is to determine the network coding capacity of networks under various network coding schemes. In this thesis, we address the problem with two approaches: matroidal networks and capacity…
The network coding problem asks whether data throughput in a network can be increased using coding (compared to treating bits as commodities in a flow). While it is well-known that a network coding advantage exists in directed graphs, the…
We consider a lossy multicast network in which the reliability is provided by means of Random Linear Network Coding. Our goal is to characterise the performance of such network in terms of the probability that a source message is delivered…
Characterizing the capacity region of multi-source wireless relay networks is one of the fundamental issues in network information theory. The problem is, however, quite challenging due to inter-user interference when there exist multiple…
We consider a network multicast example that relates the solvability of the multicast problem with the existence of an entropy function. As a result, we provide an alternative approach to the proving of the insufficiency of linear (and…
We study scalar-linear and vector-linear solutions of the generalized combination network. We derive new upper and lower bounds on the maximum number of nodes in the middle layer, depending on the network parameters and the alphabet size.…
We study matroidal networks introduced by Dougherty et al. We prove the converse of the following theorem: If a network is scalar-linearly solvable over some finite field, then the network is a matroidal network associated with a…
In the practical network communications, many internal nodes in the network are required to not only transmit messages but decode source messages. For different applications, four important classes of linear network codes in network coding…
We consider the problem of linear network coding over communication networks, representable by directed acyclic graphs, with multiple groupcast sessions: the network comprises of multiple destination nodes, each desiring messages from…
A linear Fractional Network Coding (FNC) solution over $\mathbb{F}_q$ is a linear network coding solution over $\mathbb{F}_q$ in which the message dimensions need not necessarily be the same and need not be the same as the edge vector…
Network coding is a new technique to transmit data through a network by letting the intermediate nodes combine the packets they receive. Given a network, the network coding solvability problem decides whether all the packets requested by…
The empirical results suggest that the learnability of a neural network is directly related to its size. To mathematically prove this, we borrow a tool in topological algebra: Betti numbers to measure the topological geometric complexity of…
In this paper, we propose a subnetwork decomposition/combination approach to investigate the single rate $2$-pair unicast problem. It is shown that the solvability of a $2$-pair unicast problem is completely determined by four specific link…
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…
We examine the issue of separation and code design for networks that operate over finite fields. We demonstrate that source-channel (or source-network) separation holds for several canonical network examples like the noisy multiple access…