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Cooperative diversity in wireless networks: efficient protocols and outage behavior
 IEEE Trans. Inform. Theory
, 2004
"... Abstract—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 str ..."
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Cited by 1013 (25 self)
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Abstract—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. Index Terms—Diversity techniques, fading channels, outage probability, relay channel, user cooperation, wireless networks. I.
Distributed spacetimecoded protocols for exploiting cooperative diversity in wireless networks
 IEEE Trans. Inf. Theory
, 2003
"... Abstract—We develop and analyze space–time coded cooperative diversity protocols for combating multipath fading across multiple protocol layers in a wireless network. The protocols exploit spatial diversity available among a collection of distributed terminals that relay messages for one another in ..."
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Cited by 328 (5 self)
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Abstract—We develop and analyze space–time coded cooperative diversity protocols for combating multipath fading across multiple protocol layers in a wireless network. The protocols exploit spatial diversity available among a collection of distributed terminals that relay messages for one another in such a manner that the destination terminal can average the fading, even though it is unknown a priori which terminals will be involved. In particular, a source initiates transmission to its destination, and many relays potentially receive the transmission. Those terminals that can fully decode the transmission utilize a spacetime code to cooperatively relay to the destination. We demonstrate that these protocols achieve full spatial diversity in the number of cooperating terminals, not just the number of decoding relays, and can be used effectively for higher spectral efficiencies than repetitionbased schemes. We discuss issues related to space–time code design for these protocols, emphasizing codes that readily allow for appealing distributed versions. Index Terms—Diversity techniques, fading channels, outage probability, relay channel, user cooperation, wireless networks. I.
Learning and Value Function Approximation in Complex Decision Processes
, 1998
"... In principle, a wide variety of sequential decision problems  ranging from dynamic resource allocation in telecommunication networks to financial risk management  can be formulated in terms of stochastic control and solved by the algorithms of dynamic programming. Such algorithms compute and sto ..."
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Cited by 36 (4 self)
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In principle, a wide variety of sequential decision problems  ranging from dynamic resource allocation in telecommunication networks to financial risk management  can be formulated in terms of stochastic control and solved by the algorithms of dynamic programming. Such algorithms compute and store a value function, which evaluates expected future reward as a function of current state. Unfortunately, exact computation of the value function typically requires time and storage that grow proportionately with the number of states, and consequently, the enormous state spaces that arise in practical applications render the algorithms intractable. In this thesis, we study tractable methods that approximate the value function. Our work builds on research in an area of artificial intelligence known as reinforcement learning. A point of focus of this thesis is temporaldifference learning  a stochastic algorithm inspired to some extent by phenomena observed in animal behavior. Given a selection of...
Secure broadcasting over fading channels
 IEEE Transactions on Information Theory
, 2008
"... Abstract—We study a problem of broadcasting confidential messages to multiple receivers under an informationtheoretic secrecy constraint. Two scenarios are considered: 1) all receivers are to obtain a common message; and 2) each receiver is to obtain an independent message. Moreover, two models are ..."
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Cited by 28 (5 self)
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Abstract—We study a problem of broadcasting confidential messages to multiple receivers under an informationtheoretic secrecy constraint. Two scenarios are considered: 1) all receivers are to obtain a common message; and 2) each receiver is to obtain an independent message. Moreover, two models are considered: parallel channels and fastfading channels. For the case of reversely degraded parallel channels, one eavesdropper, and an arbitrary number of legitimate receivers, we determine the secrecy capacity for transmitting a common message, and the secrecy sumcapacity for transmitting independent messages. For the case of fastfading channels, we assume that the channel state information of the legitimate receivers is known to all the terminals, while that of the eavesdropper is known only to itself. We show that, using a suitable binning strategy, a common message can be reliably and securely transmitted at a rate independent of the number of receivers. We also show that a simple opportunistic transmission strategy is optimal for the reliable and secure transmission of independent messages in the limit of large number of receivers. Index Terms—Confidential messages, cryptography, fading channels, informationtheoretic secrecy, key distribution, multicasting, multiuser diversity, parallel channels, wiretap channel. I.
Finding Collisions on a Public Road, or Do Secure Hash Functions Need Secret Coins
 In Proc. Crypto ’04
, 2004
"... Abstract. Many cryptographic primitives begin with parameter generation, which picks a primitive from a family. Such generation can use public coins (e.g., in the discretelogarithmbased case) or secret coins (e.g., in the factoringbased case). We study the relationship between publiccoin and secr ..."
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Cited by 22 (0 self)
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Abstract. Many cryptographic primitives begin with parameter generation, which picks a primitive from a family. Such generation can use public coins (e.g., in the discretelogarithmbased case) or secret coins (e.g., in the factoringbased case). We study the relationship between publiccoin and secretcoin collisionresistant hash function families (CRHFs). Specifically, we demonstrate that: – there is a lack ofattention to the distinction between secretcoin and publiccoin definitions in the literature, which has led to some problems in the case ofCRHFs; – in some cases, publiccoin CRHFs can be built out ofsecretcoin CRHFs; – the distinction between the two notions is meaningful, because in general secretcoin CRHFs are unlikely to imply publiccoin CRHFs. The last statement above is our main result, which states that there is no blackbox reduction from publiccoin CRHFs to secretcoin CRHFs. Our prooffor this result, while employing oracle separations, uses a novel approach, which demonstrates that there is no blackbox reduction without demonstrating that there is no relativizing reduction.
Geometric Theory of Images
, 1998
"... space whose dimension is measured A measure F A field V A vector space U Open sets H s Hausdor# measure Appendix B # A Gaussian probability density function # # A Gaussian distribution tangent to a manifold ## A Gaussian distribution normal to a manifold # Sample covariance matrix E, ..."
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Cited by 5 (0 self)
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space whose dimension is measured A measure F A field V A vector space U Open sets H s Hausdor# measure Appendix B # A Gaussian probability density function # # A Gaussian distribution tangent to a manifold ## A Gaussian distribution normal to a manifold # Sample covariance matrix E, E Error cost functions x x Center of a#ne subspace x Sample mean X A shifted data matrix Appendix C No special symbols Appendix D # Set of all images I An image I(x) Pixel brightness of image I at x P() A morph between two images Z(, , ) A general morph between images # A control line # Unit vector along the control line # # Vector perpendicular to the control line # # 1 ,# 0 The destination and source endpoints of # # The perpendicular proportion of a point to a control line # The signed perpendicular distance of a point to a control line d The Euclidean distance of a point to a control line #(#, , x) The point with the same relation to the control line # as ...
Cooperative Diversity in Wireless Networks: LowComplexity Protocols and Outage Behavior
"... 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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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 (SNR) ratio regime. Except for fixed decodeandforward, all of our cooperative diversity protocols achieve full diversity (i.e., secondorder diversity in the case of two terminals), and are close to optimum Manuscript submitted January 22, 2002; revised Mar. 30, 2004.