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53
Approximately universal codes over slow fading channels
 IEEE Trans. Inform. Theory
, 2006
"... Performance of reliable communication over a coherent slow fading channel at high SNR is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains. We study the problem of designing codes that optimally tradeoff the diversity and multiplexing gains. Our main contribution ..."
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Cited by 107 (1 self)
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Performance of reliable communication over a coherent slow fading channel at high SNR is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains. We study the problem of designing codes that optimally tradeoff the diversity and multiplexing gains. Our main contribution is a precise characterization of codes that are universally tradeoffoptimal, i.e., they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel. We denote this characterization as one of approximate universality where the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains, respectively. The characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the spacetime coding literature. 1
Explicit spacetime codes achieving the diversitymultiplexing gain tradeoff
 IEEE Trans. Inf. Theory
, 2006
"... Abstract — A recent result of Zheng and Tse states that over a quasistatic channel, there exists a fundamental tradeoff, referred to as the diversitymultiplexing gain (DMG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a spacetime ( ..."
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Cited by 59 (8 self)
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Abstract — A recent result of Zheng and Tse states that over a quasistatic channel, there exists a fundamental tradeoff, referred to as the diversitymultiplexing gain (DMG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a spacetime (ST) block code. This tradeoff is precisely known in the case of i.i.d. Rayleighfading, for T ≥ nt + nr − 1 where T is the number of time slots over which coding takes place and nt, nr are the number of transmit and receive antennas respectively. For T < nt + nr − 1, only upper and lower bounds on the DMG tradeoff are available. In this paper, we present a complete solution to the problem of explicitly constructing DMG optimal ST codes, i.e., codes that achieve the DMG tradeoff for any number of receive antennas. We do this by showing that for the square minimumdelay case when T = nt = n, cyclicdivisionalgebra (CDA) based ST codes having the nonvanishing determinant property are DMG optimal. While constructions of such codes were previously known for restricted values of n, we provide here a construction for such codes that is valid for all n. For the rectangular, T> nt case, we present two general techniques for building DMGoptimal rectangular ST codes from their square counterparts. A byproduct of our results establishes that the DMG tradeoff for all T ≥ nt is the same as that previously known to hold for T ≥ nt + nr − 1. Index Terms — diversitymultiplexing gain tradeoff, spacetime codes, explicit construction, cyclic division algebra. I.
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.
DMT optimality of LRaided linear decoders for a general class of channels, lattice designs, and system models
 IEEE Trans. Infom. Theory
, 2010
"... Abstract—The work identifies the first general, explicit, and nonrandom MIMO encoderdecoder structures that guarantee optimality with respect to the diversitymultiplexing tradeoff (DMT), without employing a computationally expensive maximumlikelihood (ML) receiver. Specifically, the work establi ..."
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Cited by 33 (4 self)
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Abstract—The work identifies the first general, explicit, and nonrandom MIMO encoderdecoder structures that guarantee optimality with respect to the diversitymultiplexing tradeoff (DMT), without employing a computationally expensive maximumlikelihood (ML) receiver. Specifically, the work establishes the DMT optimality of a class of regularized lattice decoders, and more importantly the DMT optimality of their latticereduction (LR)aided linear counterparts. The results hold for all channel statistics, for all channel dimensions, and most interestingly, irrespective of the particular latticecode applied. As a special case, it is established that the LLLbased LRaided linear implementation of the MMSEGDFE lattice decoder facilitates DMT optimal decoding of any lattice code at a worstcase complexity that grows at most linearly in the data rate. This represents a fundamental reduction in the decoding complexity when compared to ML decoding whose complexity is generally exponential in rate. The results ’ generality lends them applicable to a plethora of pertinent communication scenarios such as quasistatic MIMO, MIMOOFDM, ISI, cooperativerelaying, and MIMOARQ channels, in all of which the DMT optimality of the LRaided linear decoder is guaranteed. The adopted approach yields insight, and motivates further study, into joint transceiver designs with an improved SNR gap to ML decoding. Index Terms—Diversitymultiplexing tradeoff, lattice decoding, linear decoding, lattice reduction, regularization, multipleinput multipleoutput (MIMO), spacetime codersdecoders. I.
Multigroup ML Decodable Collocated and Distributed Space Time Block Codes
"... In this paper, collocated and distributed spacetime block codes (DSTBCs) which admit multigroup maximum likelihood (ML) decoding are studied. First the collocated case is considered and the problem of constructing spacetime block codes (STBCs) which optimally tradeoff rate and ML decoding complexi ..."
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Cited by 26 (18 self)
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In this paper, collocated and distributed spacetime block codes (DSTBCs) which admit multigroup maximum likelihood (ML) decoding are studied. First the collocated case is considered and the problem of constructing spacetime block codes (STBCs) which optimally tradeoff rate and ML decoding complexity is posed. Recently, sufficient conditions for multigroup ML decodability have been provided in the literature and codes meeting these sufficient conditions were called Clifford Unitary Weight (CUW) STBCs. An algebraic framework based on extended Clifford algebras is proposed to study CUW STBCs and using this framework, the optimal tradeoff between rate and ML decoding complexity of CUW STBCs is obtained for few specific cases. Code constructions meeting this tradeoff optimally are also provided. The paper then focuses on multigroup ML decodable DSTBCs for application in synchronous wireless relay networks and three constructions of fourgroup ML decodable DSTBCs are provided. Finally, the OFDM based Alamouti spacetime coded scheme proposed by LiXia for a 2 relay asynchronous relay network is extended to a more general transmission scheme that can achieve full asynchronous cooperative diversity for arbitrary number of relays. It is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node. Fourgroup decodable DSTBCs applicable in the proposed OFDM based transmission scheme are also given.
Perfect spacetime codes with minimum and nonminimum delay for any number of antennas
 IEEE Trans. Inform. Theory
, 2005
"... Abstract — Perfect spacetime codes were first introduced by Oggier et. al. to be the spacetime codes that have full rate, full diversitygain, nonvanishing determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping of the constellation. These d ..."
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Cited by 26 (8 self)
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Abstract — Perfect spacetime codes were first introduced by Oggier et. al. to be the spacetime codes that have full rate, full diversitygain, nonvanishing determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping of the constellation. These defining conditions jointly correspond to optimality with respect to the ZhengTse DMG tradeoff, independent of channel statistics, as well as to near optimality in maximizing mutual information. All the above traits endow the code with error performance that is currently unmatched. Yet perfect spacetime codes have been constructed only for 2, 3,4 and 6 transmit antennas. We construct minimum and nonminimum delay perfect codes for all channel dimensions. A. Definition of Perfect Codes I.
On Optimal Multilayer Cyclotomic Space–Time Code Designs
, 2005
"... High rate and large diversity product (or coding advantage, or coding gain, or determinant distance, or minimum product distance) are two of the most important criteria often used for good space–time code designs. In recent (linear) latticebased space–time code designs, more attention is paid to t ..."
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Cited by 23 (7 self)
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High rate and large diversity product (or coding advantage, or coding gain, or determinant distance, or minimum product distance) are two of the most important criteria often used for good space–time code designs. In recent (linear) latticebased space–time code designs, more attention is paid to the high rate criterion but less to the large diversity product criterion. In this paper, we consider these two criteria together for multilayer cyclotomic space–time code designs. In a previous paper, we recently proposed a systematic cyclotomic diagonal space–time code design over a general cyclotomic number ring that has infinitely many designs for a fixed number of transmit antennas, where diagonal codes correspond to singlelayer codes in this paper. In this paper, we first propose a general multilayer cyclotomic space–time codes. We present a general optimality theorem for these infinitely many cyclotomic diagonal (or singlelayer) space–time codes over general cyclotomic number rings for a general number of transmit antennas. We then present optimal multilayer (fullrate) cyclotomic space–time code designs for two and three transmit antennas. We also present an optimal twolayer cyclotomic space–time code design for three and four transmit antennas. The optimality here is in the sense that, for a fixed mean transmission signal power, its diversity product is maximized, or equivalently, for a fixed diversity product, its mean transmission signal power is minimized. It should be emphasized that all the optimal multilayer cyclotomic space–time codes presented in this paper have the nonvanishing determinant property.
A new fullrate fulldiversity spacetime block code with nonvanishing determinants and simplified maximumlikelihood decoding
, 2008
"... A new 2 x 2 fullrate fulldiversity linear dispersion spacetime block code (STBC) is designed by augmenting the generator of the lattice of the Alamouti’s orthogonal STBC and optimizing it according to the criterion of the maximal worst codeword difference determinant. The proposed STBC is prove ..."
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Cited by 20 (0 self)
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A new 2 x 2 fullrate fulldiversity linear dispersion spacetime block code (STBC) is designed by augmenting the generator of the lattice of the Alamouti’s orthogonal STBC and optimizing it according to the criterion of the maximal worst codeword difference determinant. The proposed STBC is proved to satisfy the nonvanishing determinant property and, therefore, to achieve the optimal diversitymultiplexing gain (DMG) tradeoff, while offering a reduced computational complexity of maximumlikelihood (ML) decoding as compared to other existing fullrate STBCs. The performance of our new code is shown to be comparable to that of the best fullrate STBCs known so far.
InformationLossless SpaceTime Block Codes from CrossedProduct Algebras
 IEEE TRANS. INFORM. THEORY
, 2006
"... It is known that the Alamouti code is the only complex orthogonal design (COD) which achieves capacity and that too for the case of two transmit and one receive antenna only. Damen et al. proposed a design for two transmit antennas, which achieves capacity for any number of receive antennas, callin ..."
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Cited by 17 (11 self)
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It is known that the Alamouti code is the only complex orthogonal design (COD) which achieves capacity and that too for the case of two transmit and one receive antenna only. Damen et al. proposed a design for two transmit antennas, which achieves capacity for any number of receive antennas, calling the resulting space–time block code (STBC) when used with a signal set an informationlossless STBC. In this paper, using crossedproduct central simple algebras, we construct STBCs for arbitrary number of transmit antennas over an a priori specified signal set. Alamouti code and quasiorthogonal designs are the simplest special cases of our constructions. We obtain a condition under which these STBCs from crossedproduct algebras are informationlossless. We give some classes of crossedproduct algebras, from which the STBCs obtained are informationlossless and also of full rank. We present some simulation results for two, three, and four transmit antennas to show that our STBCs perform better than some of the best known STBCs and also that these STBCs are approximately 1 dB away from the capacity of the channel with quadrature amplitude modulation (QAM) symbols as input.