Related papers: Linear Network Coding for Two-Unicast-$Z$ Networks…
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…
Vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted on every edge is an $L$-dimensional vector of data symbols over a base field GF($q$). Vector LNC enriches the choices…
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…
We present a heuristic for designing vector non-linear network codes for non-multicast networks, which we call quasi-linear network codes. The method presented has two phases: finding an approximate linear network code over the reals, and…
When there exists a malicious attacker in the network, we need to consider the possibilities of eavesdropping and the contamination simultaneously. Under an acyclic broadcast network, the optimality of linear codes was shown when Eve is…
In this paper, we consider networks with multiple unicast sessions. Generally, non-linear network coding is needed to achieve the whole rate region of network coding. Yet, there exist networks for which routing is sufficient to achieve the…
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…
This paper considers the communication over a quantum multiple-unicast network where r sender-receiver pairs communicate independent quantum states. We concretely construct a quantum network code for the quantum multiple-unicast network as…
We prove the following results regarding the linear solvability of networks over various alphabets. For any network, the following are equivalent: (i) vector linear solvability over some finite field, (ii) scalar linear solvability over…
This paper addresses network code design for robust transmission of sources over an orthogonal two-hop wireless network with a broadcasting relay. The network consists of multiple sources and destinations in which each destination,…
For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of…
In this paper, a class of relay networks is considered. We assume that, at a node, outgoing channels to its neighbors are orthogonal, while incoming signals from neighbors can interfere with each other. We are interested in the multicast…
Not only is network coding essential to achieve the capacity of a single-session multicast network, it can also help to improve the throughput of wireless networks with multiple unicast sessions when overheard information is available. Most…
In this paper, we present a new technique to obtain upper bounds on undirected unicast network information capacity. Using this technique, we characterize an upper bound, called partition bound, on the symmetric rate of information flow in…
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…
This paper considers vector network coding solutions based on rank-metric codes and subspace codes. The main result of this paper is that vector solutions can significantly reduce the required alphabet size compared to the optimal scalar…
The index coding problem is studied from an interference alignment perspective, providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between multiple unicast…
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…
The capacity of line networks with buffer size constraints is an open, but practically important problem. In this paper, the upper bound on the achievable rate of a class of codes, called batched codes, is studied for line networks. Batched…
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…