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We study network coding gaps for the problem of makespan minimization of multiple unicasts. In this problem distinct packets at different nodes in a network need to be delivered to a destination specific to each packet, as fast as possible.…
The problem of network function computation over a directed acyclic network is investigated in this paper. In such a network, a sink node desires to compute with zero error a {\em target function}, of which the inputs are generated at…
We consider communication over a noisy network under randomized linear network coding. Possible error mechanism include node- or link- failures, Byzantine behavior of nodes, or an over-estimate of the network min-cut. Building on the work…
In this paper, we investigate function computation problems under different secure conditions over a network with multiple source nodes and a single sink node which desires a function of all source messages without error. A wiretapper has…
A sum-network is a directed acyclic network in which all terminal nodes demand the `sum' of the independent information observed at the source nodes. Many characteristics of the well-studied multiple-unicast network communication problem…
Coding schemes for several problems in network information theory are constructed starting from point-to-point channel codes that are designed for symmetric channels. Given that the point-to-point codes satisfy certain properties pertaining…
We consider the communication capacity of wireline networks for a two-unicast traffic pattern. The network has two sources and two destinations with each source communicating a message to its own destination, subject to the capacity…
The problem of serving multicast flows in a crossbar switch is considered. Intra-flow linear network coding is shown to achieve a larger rate region than the case without coding. A traffic pattern is presented which is achievable with…
Cut-set bounds on achievable rates for network communication protocols are not in general tight. In this paper we introduce a new technique for proving converses for the problem of transmission of correlated sources in networks, that…
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…
We consider the problem of broadcast with common messages, and focus on the case that the common message rate $R_{\mathcal{A}}$, i.e., the rate of the message intended for all the receivers in the set $\mathcal{A}$, is the same for all the…
The decode-forward achievable region is studied for general networks. The region is subject to a fundamental tension in which nodes individually benefit at the expense of others. The complexity of the region depends on all the ways of…
The multi-way relay channel is a multicast network where L users exchange data through a relay. In this paper, the capacity region of a class of multi-way relay channels is derived, where the channel inputs and outputs take values over…
This paper considers a multi-source multi-relay network, in which relay nodes employ a coding scheme based on random linear network coding on source packets and generate coded packets. If a destination node collects enough coded packets, it…
The problem of finding network codes for general connections is inherently difficult in capacity constrained networks. Resource minimization for general connections with network coding is further complicated. Existing methods for…
One of the important unsolved problems in information theory is the conjecture that network coding has no rate benefit over routing in undirected unicast networks. Three known bounds on the symmetric rate in undirected unicast information…
It is common in the study of secure multicast network coding in the presence of an eavesdropper that has access to $z$ network links, to assume that the source node is the only node that generates random keys. In this setting, the secure…
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…
While network coding can be an efficient means of information dissemination in networks, it is highly susceptible to "pollution attacks," as the injection of even a single erroneous packet has the potential to corrupt each and every packet…
We study upper bounds on the sum-rate of multiple-unicasts. We approximate the Generalized Network Sharing Bound (GNS cut) of the multiple-unicasts network coding problem with $k$ independent sources. Our approximation algorithm runs in…