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147
Wireless Network Information Flow: A Deterministic Approach
, 2009
"... In contrast to wireline networks, not much is known about the flow of information over wireless networks. The main barrier is the complexity of the signal interaction in wireless channels in addition to the noise in the channel. A widely accepted model is the the additive Gaussian channel model, and ..."
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Cited by 298 (46 self)
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In contrast to wireline networks, not much is known about the flow of information over wireless networks. The main barrier is the complexity of the signal interaction in wireless channels in addition to the noise in the channel. A widely accepted model is the the additive Gaussian channel model, and for this model, the capacity of even a network with a single relay node is open for 30 years. In this paper, we present a deterministic approach to this problem by focusing on the signal interaction rather than the noise. To this end, we propose a deterministic channel model which is analytically simpler than the Gaussian model but still captures two key wireless channel properties of broadcast and superposition. We consider a model for a wireless relay network with nodes connected by such deterministic channels, and present an exact characterization of the endtoend capacity when there is a single source and one or more destinations (all interested in the same information) and an arbitrary number of relay nodes. This result is a natural generalization of the celebrated maxflow mincut theorem for wireline networks. We then use the insights obtained from the analysis of the deterministic model to study information flow for the Gaussian wireless relay network. We present an achievable rate for general Gaussian relay networks and show that it is within a constant number of bits from the cutset bound on the capacity of these networks. This constant depends on the number of nodes in the network, but not the values of the channel gains or the signaltonoise ratios. We show that existing strategies cannot achieve such a constantgap approximation for arbitrary networks and propose a new quantizemapandforward scheme that does. We also give several extensions of the approximation framework including robustness results (through compound channels), halfduplex constraints and ergodic channel variations.
Stochastic Geometry and Random Graphs for the Analysis and Design of Wireless Networks
"... Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communicationtheoretic results accoun ..."
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Cited by 231 (43 self)
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Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communicationtheoretic results accounting for the network’s geometrical configuration. Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process. In this case, different techniques based on stochastic geometry and the theory of random geometric graphs – including point process theory, percolation theory, and probabilistic combinatorics – have led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. This tutorial article surveys some of these techniques, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. It also serves as an introduction to the field for the other papers in this special issue.
On coding for reliable communication over packet networks
, 2008
"... We consider the use of random linear network coding in lossy packet networks. In particular, we consider the following simple strategy: nodes store the packets that they receive and, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of ..."
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Cited by 223 (37 self)
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We consider the use of random linear network coding in lossy packet networks. In particular, we consider the following simple strategy: nodes store the packets that they receive and, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of stored packets. In such a strategy, intermediate nodes perform additional coding yet do not decode nor wait for a block of packets before sending out coded packets. Moreover, all coding and decoding operations have polynomial complexity. We show that, provided packet headers can be used to carry an amount of sideinformation that grows arbitrarily large (but independently of payload size), random linear network coding achieves packetlevel capacity for both single unicast and single multicast connections and for both wireline and wireless networks. This result holds as long as packets received on links arrive according to processes that have average rates. Thus packet losses on links may exhibit correlations in time or with losses on other links. In the special case of Poisson traffic with i.i.d. losses, we give error exponents that quantify the rate of decay of the probability of error with coding delay. Our analysis of random linear network coding shows not only that it achieves packetlevel capacity, but also that the propagation of packets carrying “innovative ” information follows the propagation of jobs through a queueing network, thus implying that fluid flow models yield good approximations.
MinimumCost Multicast over Coded Packet Networks
 IEEE TRANS. ON INF. THE
, 2006
"... We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as b ..."
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Cited by 166 (29 self)
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We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomialtime solvable optimization problem, ... and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimumcost multicast. By contrast, establishing minimumcost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.
The Importance of Being Opportunistic: Practical Network Coding for Wireless Environments
"... This paper applies network coding to wireless mesh networks and presents the first implementation results. It introduces COPE, an opportunistic approach to network coding, where each node snoops on the medium, learns the status of its neighbors, detects coding opportunities, and codes as long as the ..."
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Cited by 130 (12 self)
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This paper applies network coding to wireless mesh networks and presents the first implementation results. It introduces COPE, an opportunistic approach to network coding, where each node snoops on the medium, learns the status of its neighbors, detects coding opportunities, and codes as long as the recipients can decode. This flexible design allows COPE to efficiently support multiple unicast flows, even when traffic demands are unknown and bursty, and the senders and receivers are dynamic. We evaluate COPE using both emulation and testbed implementation. Our results show that COPE substantially improves the network throughput, and as the number of flows and the contention level increases, COPE’s throughput becomes many times higher than current 802.11 mesh networks.
Byzantine Modification Detection in Multicast Networks using Randomized Network Coding
 IN IEEE PROC. INTL. SYM. INFORM. THEORY
, 2004
"... We show how distributed randomized network coding, a robust approach to multicasting in distributed network settings, can be extended to provide Byzantine modification detection without the use of cryptographic functions. ..."
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Cited by 118 (13 self)
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We show how distributed randomized network coding, a robust approach to multicasting in distributed network settings, can be extended to provide Byzantine modification detection without the use of cryptographic functions.
Wireless Ad hoc Networks: Strategies and Scaling Laws for the Fixed SNR Regime
, 2006
"... This paper deals with throughput scaling laws for random adhoc wireless networks in a rich scattering environment. We develop schemes to optimize the ratio, ρ(n) of achievable network sum capacity to the sum of the pointtopoint capacities of sourcedestinations pairs operating in isolation. For f ..."
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Cited by 60 (1 self)
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This paper deals with throughput scaling laws for random adhoc wireless networks in a rich scattering environment. We develop schemes to optimize the ratio, ρ(n) of achievable network sum capacity to the sum of the pointtopoint capacities of sourcedestinations pairs operating in isolation. For fixed SNR networks, i.e., where the worst case SNR over the sourcedestination pairs is fixed independent of n, we show that collaborative strategies yield a scaling law of ρ(n) = O ( 1 n 1/3) in contrast to multihop strategies which yield a scaling law of ρ(n) = O ( 1
Further results on coding for reliable communication over packet networks,” submitted to 2005
 IEEE International Symposium on Information Theory (ISIT
, 2005
"... capacityachieving coding scheme for unicast or multicast over lossy wireline or wireless packet networks is presented. We extend that paper’s results in two ways: First, we extend the network model to allow packets received on a link to arrive according to any process with an average rate, as oppos ..."
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Cited by 57 (10 self)
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capacityachieving coding scheme for unicast or multicast over lossy wireline or wireless packet networks is presented. We extend that paper’s results in two ways: First, we extend the network model to allow packets received on a link to arrive according to any process with an average rate, as opposed to the assumption of Poisson traffic with i.i.d. losses that was previously made. Second, in the case of Poisson traffic with i.i.d. losses, we derive error exponents that quantify the rate at which the probability of error decays with coding delay. I.
Reliable physical layer network coding
 Proceedings of the IEEE
, 2011
"... Abstract—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 interference. This property of the wireless medium is ..."
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Cited by 55 (6 self)
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Abstract—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 interference. This property of the wireless medium is typically viewed as a hindrance to reliable communication over a network. However, using a recently developed coding strategy, interference can in fact be harnessed for network coding. In a wired network, (linear) network coding refers to each intermediate node taking its received packets, computing a linear combination over a finite field, and forwarding the outcome towards the destinations. Then, given an appropriate set of linear combinations, a destination can solve for its desired packets. For certain topologies, this strategy can attain significantly higher throughputs over routingbased strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear errorcorrecting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals. Starting with some simple examples, this survey explores the core ideas behind this new technique and the possibilities it offers for communication over interferencelimited wireless networks. Index Terms—Digital communication, wireless networks, interference, network coding, channel coding, linear code, modulation, physical layer, fading, multiuser channels, multiple access, broadcast. I.