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We define a notion of network capacity region of networks that generalizes the notion of network capacity defined by Cannons et al. and prove its notable properties such as closedness, boundedness and convexity when the finite field is…
We consider the multiple unicast problem under network coding over directed acyclic networks when there are two source-terminal pairs, $s_1-t_1$ and $s_2-t_2$. Current characterizations of the multiple unicast capacity region in this…
This work considers the problem of transmitting multiple compressible sources over a network at minimum cost. The aim is to find the optimal rates at which the sources should be compressed and the network flows using which they should be…
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 investigate the two unicast flow problem over layered linear deterministic networks with arbitrary number of nodes. When the minimum cut value between each source-destination pair is constrained to be 1, it is obvious that the triangular…
We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, semi-injective, and linear target functions over…
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…
In this work we study zero vs. epsilon-error capacity in network coding instances. For multicast network coding it is well known that all rates that can be delivered with arbitrarily small error probability can also be delivered with zero…
A new inner bound on the capacity region of a general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound is built on a random coding scheme and optimal decoding,…
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 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…
The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
This paper studies the capacity of single-source single-sink noiseless networks under adversarial or arbitrary errors on no more than z edges. Unlike prior papers, which assume equal capacities on all links, arbitrary link capacities are…
In this paper, we consider different aspects of the network functional compression problem where computation of a function (or, some functions) of sources located at certain nodes in a network is desired at receiver(s). The rate region of…
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 the capacity problem for wireless networks. Networks are modeled as random unit-disk graphs, and the capacity problem is formulated as one of finding the maximum value of a multicommodity flow. In this paper, we develop a proof…
This work considers the multiple-access multicast error-correction scenario over a packetized network with $z$ malicious edge adversaries. The network has min-cut $m$ and packets of length $\ell$, and each sink demands all information from…
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 consider a communication network with a single source that has a set of messages and two terminals where each terminal is interested in an arbitrary subset of messages at the source. A tight capacity region for this problem is…