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133
Cooperative diversity in wireless networks: efficient protocols and outage behavior
 IEEE TRANS. INFORM. THEORY
, 2004
"... We develop and analyze lowcomplexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals’ relaying signals for one another. We outline several strategies ..."
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Cited by 1940 (31 self)
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We develop and analyze lowcomplexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals’ relaying signals for one another. We outline several strategies employed by the cooperating radios, including fixed relaying schemes such as amplifyandforward and decodeandforward, selection relaying schemes that adapt based upon channel measurements between the cooperating terminals, and incremental relaying schemes that adapt based upon limited feedback from the destination terminal. We develop performance characterizations in terms of outage events and associated outage probabilities, which measure robustness of the transmissions to fading, focusing on the high signaltonoise ratio (SNR) regime. Except for fixed decodeandforward, all of our cooperative diversity protocols are efficient in the sense that they achieve full diversity (i.e., secondorder diversity in the case of two terminals), and, moreover, are close to optimum (within 1.5 dB) in certain regimes. Thus, using distributed antennas, we can provide the powerful benefits of space diversity without need for physical arrays, though at a loss of spectral efficiency due to halfduplex operation and possibly at the cost of additional receive hardware. Applicable to any wireless setting, including cellular or ad hoc networks—wherever space constraints preclude the use of physical arrays—the performance characterizations reveal that large power or energy savings result from the use of these protocols.
An algebraic approach to network coding
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 2003
"... We take a new look at the issue of network capacity. It is shown that network coding is an essential ingredient in achieving the capacity of a network. Building on recent work by Li et al., who examined the network capacity of multicast networks, we extend the network coding framework to arbitrary n ..."
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Cited by 864 (85 self)
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We take a new look at the issue of network capacity. It is shown that network coding is an essential ingredient in achieving the capacity of a network. Building on recent work by Li et al., who examined the network capacity of multicast networks, we extend the network coding framework to arbitrary networks and robust networking. For networks which are restricted to using linear network codes, we find necessary and sufficient conditions for the feasibility of any given set of connections over a given network. We also consider the problem of network recovery for nonergodic link failures. For the multicast setup we prove that there exist coding strategies that provide maximally robust networks and that do not require adaptation of the network interior to the failure pattern in question. The results are derived for both delayfree networks and networks with delays.
Cooperative strategies and capacity theorems for relay networks
 IEEE Trans. Inform. Theory
, 2005
"... Abstract—Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decodeandforward the source message to the destination, or they compressandforward their channel outputs to the destination. The decodeandforward scheme is a va ..."
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Cited by 733 (19 self)
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Abstract—Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decodeandforward the source message to the destination, or they compressandforward their channel outputs to the destination. The decodeandforward scheme is a variant of multihopping, but in addition to having the relays successively decode the message, the transmitters cooperate and each receiver uses several or all of its past channel output blocks to decode. For the compressandforward scheme, the relays take advantage of the statistical dependence between their channel outputs and the destination’s channel output. The strategies are applied to wireless channels, and it is shown that decodeandforward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides with the rate of a distributed antenna array with full cooperation even though the transmitting antennas are not colocated. The capacity results generalize broadly, including to multiantenna transmission with Rayleigh fading, singlebounce fading, certain quasistatic fading problems, cases where partial channel knowledge is available at the transmitters, and cases where local user cooperation is permitted. The results further extend to multisource and multidestination networks such as multiaccess and broadcast relay channels. Index Terms—Antenna arrays, capacity, coding, multiuser channels, relay channels. I.
A Network Information Theory for Wireless Communication: Scaling Laws and Optimal Operation
 IEEE Transactions on Information Theory
, 2002
"... How much information can be carried over a wireless network with a multiplicity of nodes? What are the optimal strategies for information transmission and cooperation among the nodes? We obtain sharp information theoretic scaling laws under some conditions. ..."
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Cited by 369 (18 self)
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How much information can be carried over a wireless network with a multiplicity of nodes? What are the optimal strategies for information transmission and cooperation among the nodes? We obtain sharp information theoretic scaling laws under some conditions.
Capacity bounds and power allocation for wireless relay channels
 IEEE TRANS. INF. THEORY
, 2005
"... We consider threenode wireless relay channels in a Rayleighfading environment. Assuming transmitter channel state information (CSI), we study upper bounds and lower bounds on the outage capacity and the ergodic capacity. Our studies take into account practical constraints on the transmission/rece ..."
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Cited by 317 (6 self)
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We consider threenode wireless relay channels in a Rayleighfading environment. Assuming transmitter channel state information (CSI), we study upper bounds and lower bounds on the outage capacity and the ergodic capacity. Our studies take into account practical constraints on the transmission/reception duplexing at the relay node and on the synchronization between the source node and the relay node. We also explore power allocation. Compared to the direct transmission and traditional multihop protocols, our results reveal that optimum relay channel signaling can significantly outperform multihop protocols, and that power allocation has a significant impact on the performance.
Towards an Information Theory of Large Networks: An Achievable Rate Region
 IEEE Trans. Inform. Theory
, 2003
"... Abstract — We study communication networks of arbitrary size and topology and communicating over a general vector discrete memoryless channel. We propose an informationtheoretic constructive scheme for obtaining an achievable rate region in such networks. Many wellknown capacitydefining achievabl ..."
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Cited by 204 (12 self)
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Abstract — We study communication networks of arbitrary size and topology and communicating over a general vector discrete memoryless channel. We propose an informationtheoretic constructive scheme for obtaining an achievable rate region in such networks. Many wellknown capacitydefining achievable rate regions can be derived as special cases of the proposed scheme. A few such examples are the physically degraded and reverselydegraded relay channels, the Gaussian multipleaccess channel, and the Gaussian broadcast channel. The proposed scheme also leads to inner bounds for the multicast and allcast capacities. Applying the proposed scheme to a specific wireless network of nodes located in a region of unit area, we show that a transport capacity of ¡£ ¢ bitmeters/sec is feasible in a certain family of networks, as compared to the best possible transport capacity ¡£¢§ ¦ ¨ ¤ of bitmeters/sec in [16] where the receiver capabilities were limited. Even though the improvement is shown for a specific class of networks, a clear implication is that designing and employing more sophisticated multiuser coding schemes can provide sizable gains in at least some large wireless networks. Index Terms — Discrete memoryless channels, Gaussian channels, multiuser communications, network information theory,
Computeandforward: Harnessing interference through structured codes
 IEEE TRANS. INF. THEORY
, 2009
"... ..."
On the capacity of large Gaussian relay networks
 IEEE TRANS. INF. THEORY
, 2005
"... The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cutset arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and ..."
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Cited by 149 (6 self)
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The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cutset arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and lower bounds coincide in the limit as the number of relays tends to infinity. Hence, this paper provides a new example where a simple cutset upper bound is achievable, and one more example where uncoded transmission achieves optimal performance. The findings are illustrated by geometric interpretations. The techniques developed in this paper are then applied to a sensor network situation. This is a network joint source–channel coding problem, and it is well known that the source–channel separation theorem does not extend to this case. The present paper extends this insight by providing an example where separating source from channel coding does not only lead to suboptimal performance—it leads to an exponential penalty in performance scaling behavior (as a function of the number of nodes). Finally, the techniques developed in this paper are extended to include certain models of ad hoc wireless networks, where a capacity scaling law can be established: When all nodes act purely as relays for a single source–destination pair, capacity grows with the logarithm of the number of nodes.
Practical Relay Networks: A Generalization of HybridARQ
 IEEE J. SEL. AREAS COMM
, 2005
"... Wireless networks contain an inherent distributed spatial diversity that can be exploited by the use of relaying. Relay networks take advantage of the broadcastoriented nature of radio and require nodebased, rather than linkbased protocols. Prior work on relay networks has studied performance li ..."
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Cited by 141 (2 self)
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Wireless networks contain an inherent distributed spatial diversity that can be exploited by the use of relaying. Relay networks take advantage of the broadcastoriented nature of radio and require nodebased, rather than linkbased protocols. Prior work on relay networks has studied performance limits either with unrealistic assumptions, complicated protocols, or only a single relay. In this paper, a practical approach to networks comprising multiple relays operating over orthogonal time slots is proposed based on a generalization of hybridautomatic repeat request (ARQ). In contrast with conventional hybridARQ, retransmitted packets do not need to come from the original source radio but could instead be sent by relays that overhear the transmission. An information theoretic framework is exposed that establishes the performance limits of such systems in a block fading environment, and numerical results are presented for some representative topologies and protocols. The results indicate a significant improvement in the energylatency tradeoff when compared with conventional multihop protocols implemented as a cascade of pointtopoint links.
Bounds on capacity and minimum energyperbit for AWGN relay channels
 IEEE TRANS. INF. THEORY
, 2006
"... Upper and lower bounds on the capacity and minimum energyperbit for general additive white Gaussian noise (AWGN) and frequencydivision AWGN (FDAWGN) relay channel models are established. First, the maxflow mincut bound and the generalized blockMarkov coding scheme are used to derive upper an ..."
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Cited by 108 (2 self)
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Upper and lower bounds on the capacity and minimum energyperbit for general additive white Gaussian noise (AWGN) and frequencydivision AWGN (FDAWGN) relay channel models are established. First, the maxflow mincut bound and the generalized blockMarkov coding scheme are used to derive upper and lower bounds on capacity. These bounds are never tight for the general AWGN model and are tight only under certain conditions for the FDAWGN model. Two coding schemes that do not require the relay to decode any part of the message are then investigated. First, it is shown that the “sideinformation coding scheme ” can outperform the blockMarkov coding scheme. It is also shown that the achievable rate of the sideinformation coding scheme can be improved via time sharing. In the second scheme, the relaying functions are restricted to be linear. The problem is reduced to a “singleletter ” nonconvex optimization problem for the FDAWGN model. The paper also establishes a relationship between the minimum energyperbit and capacity of the AWGN relay channel. This relationship together with the lower and upper bounds on capacity are used to establish corresponding lower and upper bounds on the minimum energyperbit that do not differ by more than a factor of 1 45 for the FDAWGN relay channel model and 1 7 for the general AWGN model.