Related papers: Network Coding for Computing: Cut-Set Bounds
A function computation problem in directed acyclic networks has been considered in the literature, where a sink node wants to compute a target function with the inputs generated at multiple source nodes. The network links are error-free but…
We consider uniquely-decodable coding for zero-error network function computation, where in a directed acyclic graph, the single sink node is required to compute with zero error a target function multiple times, whose arguments are the…
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…
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 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…
We study the limits of communication efficiency for function computation in collocated networks within the framework of multi-terminal block source coding theory. With the goal of computing a desired function of sources at a sink, nodes…
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…
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…
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…
We investigate linear network coding in the context of robust function computation, where a sink node is tasked with computing a target function of messages generated at multiple source nodes. In a previous work, a new distance measure was…
Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general.…
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 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…
In this paper we show that the Index Coding problem captures several important properties of the more general Network Coding problem. An instance of the Index Coding problem includes a server that holds a set of information messages…
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…
In the All-Reduce problem, each one of the K nodes holds an input and wishes to compute the sum of all K inputs through a communication network where each pair of nodes is connected by a parallel link with arbitrary bandwidth. The…
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…
Secure network function computation is a critical research direction in network coding, which aims to ensure that the target function is correctly computed at the sink node while preventing the wiretapper from obtaining any information…
We introduce a new technique to certify lower bounds on the multicut size using network coding. In directed networks the network coding rate is not a lower bound on the multicut, but we identify a class of networks on which the rate is…
In a single hop broadcast packet erasure network, we demonstrate that it is possible to provide multirate packet delivery outside of what is given by the network min-cut. This is achieved by using a deterministic non-block-based network…