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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…
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…
In this paper, we use entropy functions to characterise the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding error, for general network coding problems. We show that when sources are colocated,…
For any given channel $W$ with classical inputs and possibly quantum outputs, a dual classical-input channel $W^\perp$ can be defined by embedding the original into a channel $\mathcal N$ with quantum inputs and outputs. Here we give new…
Explicit characterization and computation of the multi-source network coding capacity region (or even bounds) is long standing open problem. In fact, finding the capacity region requires determination of the set of all entropic vectors…
The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over…
Characterizing the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterizing all information inequalities. The majority of…
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…
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…
Characterising the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterising all information inequalities. The majority of…
We approach the problem of linear network coding for multicast networks from different perspectives. We introduce the notion of the coding points of a network, which are edges of the network where messages combine and coding occurs. We give…
One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…
This paper considers a base station that delivers packets to multiple receivers through a sequence of coded transmissions. All receivers overhear the same transmissions. Each receiver may already have some of the packets as side…
This paper investigates the problem of single-source multicasting over a communication network in the presence of restricted adversaries. When the adversary is constrained to operate only on a prescribed subset of edges, classical cut-set…
We consider the following \textit{network computation problem}. In an acyclic network, there are multiple source nodes, each generating multiple messages, and there are multiple sink nodes, each demanding a function of the source messages.…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
We introduce a formal framework to study the multiple unicast problem for a coded network in which the network code is linear over a finite field and fixed. We show that the problem corresponds to an interference alignment problem over a…
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 the problem of error control in a coded, multicast network, focusing on the scenario where the errors can occur only on a proper subset of the network edges. We model this problem via an adversarial noise, presenting a formal…