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Perfect SpaceTime Codes for Any Number of Antennas
"... In a recent paper, perfect (n × n) spacetime codes were introduced as the class of linear dispersion spacetime codes having full rate, nonvanishing determinant, a signal constellation isomorphic to either the rectangular or hexagonal lattices in 2n 2 dimensions and uniform average transmitted en ..."
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Cited by 37 (3 self)
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In a recent paper, perfect (n × n) spacetime codes were introduced as the class of linear dispersion spacetime codes having full rate, nonvanishing determinant, a signal constellation isomorphic to either the rectangular or hexagonal lattices in 2n 2 dimensions and uniform average transmitted energy per antenna. Consequence of these conditions include optimality of perfect codes with respect to the ZhengTse DiversityMultiplexing Gain tradeoff (DMT), as well as excellent lowSNR performance. Yet perfect spacetime codes have been constructed only for 2, 3, 4 and 6 transmit antennas. In this paper, we construct perfect codes for all channel dimensions, present some additional attributes of this class of spacetime codes and extend the notion of a perfect code to the rectangular case.
An algebraic coding scheme for wireless relay networks with multipleantenna nodes
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2008
"... We consider the problem of coding over a halfduplex wireless relay network where both the transmitter and the receiver have respectively several transmit and receive antennas, whereas each relay is a small device with only a single antenna. Since, in this scenario, requiring the relays to decode r ..."
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Cited by 14 (4 self)
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We consider the problem of coding over a halfduplex wireless relay network where both the transmitter and the receiver have respectively several transmit and receive antennas, whereas each relay is a small device with only a single antenna. Since, in this scenario, requiring the relays to decode results in severe rate hits, we propose a full rate strategy where the relays do a simple operation before forwarding the signal, based on the idea of distributed spacetime coding. Our scheme relies on division algebras, an algebraic object which allows the design of fully diverse matrices. The code construction is applicable to systems with any number of transmit/receive antennas and relays, and has better performance than random code constructions, with much less encoding complexity. Finally, the robustness of the proposed distributed spacetime codes to node failures is considered.
Asymptotically Optimal Cooperative Wireless Networks with Reduced Signaling Complexity
 IEEE J. Select. Areas Commun
, 2007
"... Abstract — This paper considers an orthogonal amplifyandforward (OAF) protocol for cooperative relay communication over Rayleighfading channels in which the intermediate relays are permitted to linearly transform the received signal and where the source and relays transmit for equal time durations ..."
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Cited by 11 (2 self)
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Abstract — This paper considers an orthogonal amplifyandforward (OAF) protocol for cooperative relay communication over Rayleighfading channels in which the intermediate relays are permitted to linearly transform the received signal and where the source and relays transmit for equal time durations. The diversitymultiplexing gain (DMG) tradeoff of the equivalent spacetime channel associated to this protocol is determined and a cyclicdivisionalgebrabased DMG optimal code constructed. The transmission or signaling alphabet of this code is the union of the QAM constellation and a rotated version of QAM. The size of this signaling alphabet is small in comparison with prior DMG optimal constructions in the literature and is independent of the number of participating nodes in the network. Index Terms — cooperative diversity, distributed spacetime code, orthogonal amplify and forward, diversitymultiplexing gain tradeoff, spacetime codes, cyclic division algebra codes. I.
spacetime codes that achieve the diversitymultiplexing gain tradeoff
 in Proc. IEEE Int. Symp. Inf. Theory
, 2005
"... Abstract — In the recent landmark paper of Zheng and Tse it is shown for the quasistatic, Rayleighfading MIMO channel with nt transmit and nr receive antennas, that there exists a fundamental tradeoff between diversity gain and multiplexing gain, referred to as the DiversityMultiplexing Gain (DM ..."
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Cited by 8 (2 self)
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Abstract — In the recent landmark paper of Zheng and Tse it is shown for the quasistatic, Rayleighfading MIMO channel with nt transmit and nr receive antennas, that there exists a fundamental tradeoff between diversity gain and multiplexing gain, referred to as the DiversityMultiplexing Gain (DMG) tradeoff. This paper presents the first explicit construction of spacetime (ST) codes for an arbitrary number of transmit and/or receive antennas that achieve the DMG tradeoff. It is shown here that ST codes constructed from cyclicdivisionalgebras (CDA) and satisfying a certain nonvanishing determinant (NVD) property, are optimal under the DMG tradeoff for any nt,nr. Furthermore, this optimality is achieved with minimum possible value of the delay or blocklength parameter T = nt. CDAbased ST codes with NVD have previously been constructed for restricted values of nt. A unified construction of DMG optimal CDAbased ST codes with NVD is given here, for any number nt of transmit antennas. The CDAbased constructions are also extended to provide DMG optimal codes for all T ≥ nt, again for any number nt of transmit antennas. This extension thus presents rectangular DMG optimal spacetime codes that achieve the DMG tradeoff. Taken together, the above constructions also extend the region of T for which the DMG tradeoff is precisely known from T ≥ nt + nr − 1 to T ≥ nt.
DiversityMultiplexing Gain Tradeoff and DMTOptimal Distributed SpaceTime . . .
 GENOME RES
"... This paper considers protocols for fading, wireless relay networks that aim to achieve cooperative diversity through the use of distributed spacetime codes. All pointtopoint communication is modeled as taking place over quasistatic, Rayleighfading channels with each node in the network operati ..."
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Cited by 5 (1 self)
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This paper considers protocols for fading, wireless relay networks that aim to achieve cooperative diversity through the use of distributed spacetime codes. All pointtopoint communication is modeled as taking place over quasistatic, Rayleighfading channels with each node in the network operating in halfduplex mode. Channelstate information is assumed to be present only at the receiver. The diversitymultiplexing gain tradeoff (DMT) is taken to be the measure of performance. Prior work in this area relating to the identification of the DMT of various protocols as well as to DMToptimal code construction is first reviewed. This is followed by a description of our recent results in this area. These include determination of the DMT of the orthogonal amplifyandforward and selection decodeandforward protocols as well as some simplydescribed, DMToptimal code constructions based on cyclic division algebras.
Embedded Orthogonal SpaceTime Codes for High Rate and Low Decoding Complexity,” to appear
 IEEE Global Communications Conference (Globecom 2009
"... Abstract — We propose a new family of highrate spacetime block codes called embedded orthogonal spacetime (EOS) codes. The family is parameterized by the number of transmit antennas, which can be any positive integer, and by the rate, which can be as high as half the number of transmit antennas. ..."
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Cited by 3 (1 self)
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Abstract — We propose a new family of highrate spacetime block codes called embedded orthogonal spacetime (EOS) codes. The family is parameterized by the number of transmit antennas, which can be any positive integer, and by the rate, which can be as high as half the number of transmit antennas. The proposed codes are based on a new concept called embedding, whereby information symbols of a traditional spacetime code are replaced by codewords from a second spacetime code. The EOS codes use orthogonal designs as this second code, which induces orthogonality in an effective channel matrix and leads to reducedcomplexity decoding. The EOS codes have lower decoding complexity than previously reported spacetime codes for any number of transmit antennas, and for any rate. Furthermore, simulation results show that the EOS codes outperform previous constructions for certain number of antennas and certain rates, when performance is measured by error probability in quasistatic Rayleigh fading. Index Terms — transmit diversity, spacetime coding. I.
An Elementary Condition for NonNorm Elements
"... Abstract—Cyclic division algebra (CDA) has recently become a major technique to construct space–time block codes with nonvanishing determinant (NVD). One of the key steps in this technique is the determination of nonnorm elements and a sufficient condition for the determination has been given by Ki ..."
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Cited by 2 (1 self)
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Abstract—Cyclic division algebra (CDA) has recently become a major technique to construct space–time block codes with nonvanishing determinant (NVD). One of the key steps in this technique is the determination of nonnorm elements and a sufficient condition for the determination has been given by Kiran and Rajan lately based on algebraic number theory. In this paper, based on Kiran and Rajan’s condition, we present a more elementary condition for nonnorm elements when signals are QAM or HEX, which is easier to check. With this elementary condition, nonnorm elements with smaller absolute values than the existing ones can be found. Index Terms—Algebraic number theory, cyclic division algebra, nonnorm elements, nonvanishing determinant, space–time block codes. I.