Related papers: Linear Network Coding for Two-Unicast-$Z$ Networks…
In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast-Z network is a two-unicast network where the destination intending to decode the second message has apriori side…
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…
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…
This paper considers the problem of network coding for multiple unicast connections in networks represented by directed acyclic graphs. The concept of interference alignment, traditionally used in interference networks, is extended to…
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…
We establish a duality result between linear index coding and Locally Repairable Codes (LRCs). Specifically, we show that a natural extension of LRCs we call Generalized Locally Repairable Codes (GLCRs) are exactly dual to linear index…
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…
Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters…
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…
Network coding is a technique to maximize communication rates within a network, in communication protocols for simultaneous multi-party transmission of information. Linear network codes are examples of such protocols in which the local…
When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted…
It is known that there exists a multiple-unicast network which has a rate $1$ linear network coding solution if and only if the characteristic of the finite field belongs to a given finite or co-finite set of primes. In this paper, we show…
This paper characterizes the secret message capacity of three networks where two unicast sessions share some of the communication resources. Each network consists of erasure channels with state feedback. A passive eavesdropper is assumed to…
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…
A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a sum-network. It is shown that there exists a solvably (and linear solvably)…
This paper considers vector network coding based on rank-metric codes and subspace codes. Our main result is that vector network coding can significantly reduce the required field size compared to scalar linear network coding in the same…
We consider the energy savings that can be obtained by employing network coding instead of plain routing in wireless multiple unicast problems. We establish lower bounds on the benefit of network coding, defined as the maximum of the ratio…
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…
We take a unified view of network coding and decentralized control. Precisely speaking, we consider both as linear time-invariant systems by appropriately restricting channels and coding schemes of network coding to be linear…
The problem of maximum rate achievable with analog network coding for a unicast communication over a layered wireless relay network with directed links is considered. A relay node performing analog network coding scales and forwards the…