Results 1  10
of
58
Resilient Network Coding in the Presence of Byzantine Adversaries
"... Network coding substantially increases network throughput. But since it involves mixing of information inside the network, a single corrupted packet generated by a malicious node can end up contaminating all the information reaching a destination, preventing decoding. This paper introduces distribu ..."
Abstract

Cited by 169 (32 self)
 Add to MetaCart
(Show Context)
Network coding substantially increases network throughput. But since it involves mixing of information inside the network, a single corrupted packet generated by a malicious node can end up contaminating all the information reaching a destination, preventing decoding. This paper introduces distributed polynomialtime rateoptimal network codes that work in the presence of Byzantine nodes. We present algorithms that target adversaries with different attacking capabilities. When the adversary can eavesdrop on all links and jam zO links, our first algorithm achieves a rate of C − 2zO, where C is the network capacity. In contrast, when the adversary has limited eavesdropping capabilities, we provide algorithms that achieve the higher rate of C − zO. Our algorithms attain the optimal rate given the strength of the adversary. They are informationtheoretically secure. They operate in a distributed manner, assume no knowledge of the topology, and can be designed and implemented in polynomialtime. Furthermore, only the source and destination need to be modified; nonmalicious nodes inside the network are oblivious to the presence of adversaries and implement a classical distributed network code. Finally, our algorithms work over wired and wireless networks.
Recent and Emerging Topics in Wireless Industrial Communications: A Selection
, 2007
"... In this paper we discuss a selection of promising and interesting research areas in the design of protocols and systemsforwirelessindustrialcommunications.Wehaveselected topicsthathaveeitheremergedashottopicsintheindustrial communicationscommunityinthelastfewyears(likewireless sensornetworks),orwhi ..."
Abstract

Cited by 96 (1 self)
 Add to MetaCart
(Show Context)
In this paper we discuss a selection of promising and interesting research areas in the design of protocols and systemsforwirelessindustrialcommunications.Wehaveselected topicsthathaveeitheremergedashottopicsintheindustrial communicationscommunityinthelastfewyears(likewireless sensornetworks),orwhichcouldbeworthwhileresearchtopicsin thenextfewyears(forexamplecooperativediversitytechniques for error control, cognitive radio/opportunistic spectrum access for mitigation of external interferences).
Network Coding: An Introduction
, 2008
"... The basic idea behind network coding is extraordinarily sim
ple. As it is defined in this book, network coding amounts to no more than performing coding operations on the contents of packetsâperforming arbitrary mappings on the contents of packets rather than the restricted functions of replicatio ..."
Abstract

Cited by 69 (3 self)
 Add to MetaCart
The basic idea behind network coding is extraordinarily sim
ple. As it is defined in this book, network coding amounts to no more than performing coding operations on the contents of packetsâperforming arbitrary mappings on the contents of packets rather than the restricted functions of replication and forwarding that are typically allowed in conventional,
storeandforward architectures. But, although simple, network coding has had little place in the history of networking. This is for good reason: in the traditional wireline technologies that have dominated networking
history, network coding is not very practical or advantageo
us.
Hence the motivation for this book: we feel that network coding may have a great deal to offer to the future design of packet networks, and we would like to help this potential be realized. We would like also to encourage more research in this burgeoning field. Thus, we have aimed the book at two (not necessarily distinct) audiences: first, the practi
tioner, whose main interest is applications; and, second, t
he theoretician, whose main interest is developing further understanding of the properties of network coding. Of these two audiences, we have tended to favor the first, though the content of the book is nevertheless theoretical. We have aimed to expound the theory in such a way that it is access
ible to those who would like to implement network coding, serving an important purpose that was, in our opinion, inadequately served. The theoretician, in contrast to the practitioner, is spoiled. Besides this book, a survey
of important theoretical results in network coding is provi
ded in Yeung et al.âs excellent review, Network Coding Theory [149, 150]. Because of our inclination toward applications, however, our presentation differs substantially from that of Yeung et al.
On the hardness of approximating the network coding capacity
 In Proc. IEEE Symp. on Inform. Theory (ISIT
, 2008
"... Abstract—This work addresses the computational complexity of achieving the capacity of a general network coding instance. We focus on the linear capacity, namely the capacity of the given instance when restricted to linear encoding functions. It has been shown [Lehman and Lehman, SODA 2005] that de ..."
Abstract

Cited by 32 (8 self)
 Add to MetaCart
(Show Context)
Abstract—This work addresses the computational complexity of achieving the capacity of a general network coding instance. We focus on the linear capacity, namely the capacity of the given instance when restricted to linear encoding functions. It has been shown [Lehman and Lehman, SODA 2005] that determining the (scalar) linear capacity of a general network coding instance is NPhard. In this work we initiate the study of approximation in this context. Namely, we show that given an instance to the general network coding problem of linear capacity C, constructing a linear code of rate αC for any universal (i.e., independent of the size of the instance) constant α ≤ 1 is “hard”. Specifically, finding such network codes would solve a long standing open problem in the field of graph coloring. In addition, we consider the problem of determining the (scalar) linear capacity of a planar network coding instance (i.e., a general instance in which the underlying graph is planar). We show that even for planar networks this problem remains NPhard. I.
The Wireless Control Network: A New Approach for Control Over Networks
, 2011
"... We present a method to stabilize a plant with a network of resource constrained wireless nodes. As opposed to traditional networked control schemes where the nodes simply route information to and from a dedicated controller (perhaps performing some encoding along the way), our approach treats the ne ..."
Abstract

Cited by 29 (6 self)
 Add to MetaCart
We present a method to stabilize a plant with a network of resource constrained wireless nodes. As opposed to traditional networked control schemes where the nodes simply route information to and from a dedicated controller (perhaps performing some encoding along the way), our approach treats the network itself as the controller. Specifically, we formulate a strategy for each node in the network to follow, where at each timestep, each node updates its internal state to be a linear combination of the states of the nodes in its neighborhood. We show that this causes the entire network to behave as a linear dynamical system, with sparsity constraints imposed by the network topology. We provide a numerical design procedure to determine appropriate linear combinations to be applied by each node so that the transmissions of the nodes closest to the actuators will stabilize the plant. We also show how our design procedure can be modified to maintain mean square stability under packet drops in the network, and presen ta distributed scheme that can handle node failures while preserving stability. We call this architecture a Wireless Control Network, and show that it introduces very low computational and communication overhead to the nodes in the network, allows the use of simple transmission scheduling algorithms, and enables compositional design (where the existing wireless control infrastructure can be easily extended to handle new plants that are brought online in the vicinity of the network).
Network coding for twoway relaying: rate region, sum rate and opportunistic scheduling
 in the Proc. of IEEE International Conf. on Comm. (ICC
, 2008
"... Abstract—Network coding for twoway relaying in a threenode network is considered. The achievable rate regions under both traditional fourslot multihopping (FSMH) and network coding (MACXOR) are characterized, showing a combination between the two is needed for a larger region. This is accomplis ..."
Abstract

Cited by 25 (1 self)
 Add to MetaCart
(Show Context)
Abstract—Network coding for twoway relaying in a threenode network is considered. The achievable rate regions under both traditional fourslot multihopping (FSMH) and network coding (MACXOR) are characterized, showing a combination between the two is needed for a larger region. This is accomplished by an opportunistic network coding scheduling which requires minimal information. Queuing analysis shows that for any pair of random Poisson arrivals with rates within the convex hull of FSMH and MACXOR regions is stabilizable. Next we consider how traffic pattern, described by the rate ratio between uplink and downlink, influences the sum rate. It is analyzed and compared with that of FSMH. It is shown that network coding achieves the maximum gain when traffic is symmetric, while it could be worse than FSMH when the traffic is very asymmetric. How multiple antennas influence the performance of network coding is also discussed. Finally, simulations based on Erceg fading model under a WiMAX setting are presented, which shows that the network coding gain (vs FSMH) improves further under MIMO. I.
Linear Network Codes and Systems of Polynomial Equations
 (SUBMITTED TO ISIT 2008)
, 2008
"... If β and γ are nonnegative integers and F is a field, then a polynomial collection {p1,..., pβ} ⊆ Z[α1,..., αγ] is said to be solvable over F if there exist ω1,..., ωγ ∈ F such that for all i = 1,..., β we have pi(ω1,..., ωγ) = 0. We say that a network and a polynomial collection are solvably equi ..."
Abstract

Cited by 25 (4 self)
 Add to MetaCart
(Show Context)
If β and γ are nonnegative integers and F is a field, then a polynomial collection {p1,..., pβ} ⊆ Z[α1,..., αγ] is said to be solvable over F if there exist ω1,..., ωγ ∈ F such that for all i = 1,..., β we have pi(ω1,..., ωγ) = 0. We say that a network and a polynomial collection are solvably equivalent if for each field F the network has a scalarlinear solution over F if and only if the polynomial collection is solvable over F. Koetter and Médard’s work implies that for any directed acyclic network, there exists a solvably equivalent polynomial collection. We provide the converse result, namely that for any polynomial collection there exists a solvably equivalent directed acyclic network. (Hence, the problems of network scalarlinear solvability and polynomial collection solvability have the same complexity.) The construction of the network is modeled on a matroid construction using finite projective planes, due to MacLane in 1936. A set Ψ of prime numbers is a set of characteristics of a network if for every q ∈ Ψ, the network has a scalarlinear solution over some finite field with characteristic q and does not have a scalarlinear solution over any finite field whose characteristic lies outside of Ψ. We show that a collection of primes is a set of characteristics of some network if and only if the collection is finite or cofinite. Two networks N and N ′ are lsequivalent if for any finite field F, N is scalarlinearly solvable over F if and only if N ′ is scalarlinearly solvable over F. We further show that every network is lsequivalent to a multipleunicast matroidal network.
An Equivalence between Network Coding and Index Coding
, 2014
"... We show that the network coding and index coding problems are equivalent. This equivalence holds in the general setting which includes linear and nonlinear codes. Specifically, we present an efficient reduction that maps a network coding instance to an index coding instance while preserving feasibi ..."
Abstract

Cited by 20 (3 self)
 Add to MetaCart
(Show Context)
We show that the network coding and index coding problems are equivalent. This equivalence holds in the general setting which includes linear and nonlinear codes. Specifically, we present an efficient reduction that maps a network coding instance to an index coding instance while preserving feasibility. Previous connections were restricted to the linear case.
On the Multiple Unicast Network Coding Conjecture
"... Abstract—In this paper, we study the multiple unicast network communication problem on undirected graphs. It has been conjectured by Li and Li [CISS 2004] that, for the problem at hand, the use of network coding does not allow any advantage over standard routing. Loosely speaking, we show that under ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
(Show Context)
Abstract—In this paper, we study the multiple unicast network communication problem on undirected graphs. It has been conjectured by Li and Li [CISS 2004] that, for the problem at hand, the use of network coding does not allow any advantage over standard routing. Loosely speaking, we show that under certain (strong) connectivity requirements the advantage of network coding is indeed bounded by 3. I.