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177
The Golden Code: A 2 × 2 fullrate spacetime code with nonvanishing determinants
 IEEE Transactions on Information Theory
, 2005
"... Abstract — In this paper we present the Golden ..."
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Perfect space–time block codes
 IEEE TRANS. INFORM. THEORY
, 2006
"... In this paper, we introduce the notion of perfect space–time block codes (STBCs). These codes have fullrate, fulldiversity, nonvanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping. We present algebraic construct ..."
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Cited by 101 (17 self)
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In this paper, we introduce the notion of perfect space–time block codes (STBCs). These codes have fullrate, fulldiversity, nonvanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping. We present algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas.
A unified framework for tree search decoding: rediscovering the sequential decoder,”
 IEEE Transactions on Information Theory,
, 2006
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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.
Low MLDecoding Complexity, Large Coding Gain, FullRate, FullDiversity STBCs for 2 x 2 and 4 × 2 MIMO systems
, 2009
"... This paper deals with low maximumlikelihood (ML)decoding complexity, fullrate and fulldiversity spacetime block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna (2 2) and the 4 transmit antenna, 2 receive antenna (4 2) MIMO systems. Presently, th ..."
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Cited by 47 (23 self)
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This paper deals with low maximumlikelihood (ML)decoding complexity, fullrate and fulldiversity spacetime block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna (2 2) and the 4 transmit antenna, 2 receive antenna (4 2) MIMO systems. Presently, the best known STBC for the 2 2 system is the Golden code and that for the 4 2 system is the DjABBA code. Following the approach by Biglieri, Hong, and Viterbo, a new STBC is presented in this paper for the 2 2 system. This code matches the Golden code in performance and MLdecoding complexity for square QAM constellations while it has lower MLdecoding complexity with the same performance for nonrectangular QAM constellations. This code is also shown to be informationlossless and diversitymultiplexing gain (DMG) tradeoff optimal. This design procedure is then extended to the 4 2 system and a code,
A LowComplexity Detector for Large MIMO Systems and Multicarrier CDMA Systems
"... Abstract — We consider large MIMO systems, where by ‘large’ we mean number of transmit and receive antennas of the order of tens to hundreds. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. We present a lowcomplexity detec ..."
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Cited by 43 (28 self)
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Abstract — We consider large MIMO systems, where by ‘large’ we mean number of transmit and receive antennas of the order of tens to hundreds. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. We present a lowcomplexity detector which achieves uncoded nearexponential diversity performance for hundreds of antennas (i.e., achieves near SISO AWGN performance in a large MIMO fading environment) with an average perbit complexity of just O(NtNr), whereNtand Nr denote the number of transmit and receive antennas, respectively. With an outer turbo code, the proposed detector achieves good coded bit error performance as well. For example, in a 600 transmit and 600 receive antennas VBLAST system with a high spectral efficiency of 450 bps/Hz (using BPSK and rate3/4 turbo code), our simulation results show that the proposed detector performs to within about 7 dB from capacity. This practical feasibility of the proposed highperformance, lowcomplexity detector could potentially trigger wide interest in the theory and implementation of large MIMO systems. We also illustrate the applicability of the proposed detector in the lowcomplexity detection of highrate, nonorthogonal spacetime block codes and large multicarrier CDMA (MCCDMA) systems. In large MCCDMA systems with hundreds of users, the proposed detector is shown to achieve near singleuser performance at an average perbit complexity linear in number of users, which is quite appealing for its use in practical CDMA systems. Index Terms — Large MIMO systems, VBLAST, lowcomplexity detection, nearexponential diversity, high spectral efficiency, spacetime block codes, multicarrier CDMA. 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.
Cyclic Division Algebras: A Tool for Space Time Coding
, 2007
"... Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been ..."
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Cited by 37 (3 self)
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Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of fulldiversity criterion requires that the difference of any two distinct codewords has full rank. Extensive work has been done on Space–Time coding, aiming at finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are noncommutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to improve the design of good codes. The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the nonvanishing determinant property, and the diversity multiplexing tradeoff. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes.