Efficient Modulation for Band-Limited Channels

Forney, G. David; Gallager, Robert G.; Lang, G. R.; Longstaff, F.M.; Qureshi, Shahzad Ahmad

doi:10.1109/jsac.1984.1146101

Cited by 629 publications

(265 citation statements)

References 19 publications

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“…Similarly, we consider Q-HEX constellations [22] carved from the translated hexagonal lattice A 2 defined by the generator matrix [11] in the figures was optimized to mimic a Gray labeling as close as possible, in order to minimize bit error probability. The error probability performance is usually plotted as a function of SNR b = n t E b /N 0 , where E b = E s /q is the energy per bit.…”

Section: Modulations and Full-rate Codesmentioning

confidence: 99%

Cyclic Division Algebras: A Tool for Space-Time Coding

Oggier

Belfiore

Viterbo

2007

FNT in Communications and Information Theory

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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 full-diversity 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 non-commutative 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 non-vanishing determinant property, and the diversity multiplexing trade-off. 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.

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Section: Modulations and Full-rate Codesmentioning

confidence: 99%

Cyclic Division Algebras: A Tool for Space-Time Coding

Oggier

Belfiore

Viterbo

2007

FNT in Communications and Information Theory

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“…We now examine two important lattices: Lattices of squares (including square and rectangular QAM) and lattices of equilateral triangles (TRI) (including hexagonal constellations) [12]. The optimal rotation angles for these constellations are discussed in [10].…”

Section: A Qstbc With Lattice-based Constellationsmentioning

confidence: 99%

“…However, given a constellation, the optimum rotation angle must be chosen to minimize the symbol error rate (SER) or BER. Authors in references [6]- [11] provide some specific optimal rotation angles for quadrature amplitude modulation (QAM), phaseshift keying (PSK) and hexagonal constellations (or lattices of equilateral triangles) [12]. However, some results are not identical.…”

Section: Introductionmentioning

confidence: 99%

Optimal rotations for quasi-orthogonal STBC with two-dimensional constellations

Dao

Tellambura

2005

GLOBECOM '05. IEEE Global Telecommunications Conference, 2005.

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Abstract-Quasi-orthogonal space-time block codes (QSTBC) achieve full diversity by constellation rotations. Several authors have introduced optimal rotation angles, found either by computer search or by analytical derivation. However, existing analytical methods do not seem general enough to analyze optimal rotations for arbitrary constellations, and some previous results seem to conflict. We present a novel method to exactly derive the coding gain of QSTBC as a function of the rotation angle and the minimum Euclidean distance of two-dimensional constellations such as the ones carved from lattices of squares and triangles, and phase-shift keying (PSK) constellations. The upper bound of coding gain for amplitude PSK (APSK) is also obtained. We find the whole range of optimal rotations for maximizing the coding gain of QSTBC. Simulation results confirm the theoretical analysis.

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“…Trellis and lattice codes, which are special cases of coset codes, are particularly well suited for adaptive coded modulation since the code design and modulation design are separable [7], [8]. Thus, we can vary the size, power, and symbol time of the transmitted signal constellation to maximize the average data rate without affecting the bit-error rate (BER) or the coding gain.…”

Section: Introductionmentioning

confidence: 99%

Adaptive coded modulation for fading channels

Goldsmith

Chua²

1998

IEEE Trans. Commun.

746

331

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Abstract-We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive M-ary quadrature amplitude modulation (MQAM) to obtain trellis-coded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple four-state trellis code, and an effective 3.6-dB coding gain for an eight-state trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trellis-coded adaptive MQAM to that of coded modulation with built-in time diversity and fixed-rate modulation. The adaptive method exhibits a power savings of up to 20 dB.

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Efficient Modulation for Band-Limited Channels

Cited by 629 publications

References 19 publications

Cyclic Division Algebras: A Tool for Space-Time Coding

Cyclic Division Algebras: A Tool for Space-Time Coding

Optimal rotations for quasi-orthogonal STBC with two-dimensional constellations

Adaptive coded modulation for fading channels

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