Quarternary signal sets for digital communications with nonuniform sources

Nguyen, Ha H.; Nechiporenko, T.

doi:10.1109/ccece.2005.1557398

Cited by 6 publications

(6 citation statements)

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“…In Fig. 1, it is clear that the pairwise optimized constellation PO4 performs identically to the optimized M = 4 constellation of [10]. Both constellations perform considerably better than quaternary phase shift keying (QPSK) for highly non-uniform sources, with nearly 5 dB gain at any SNR.…”

Section: Iiic1 Binary and Quaternary Constellationsmentioning

confidence: 80%

“…The method, which is simple to implement, consists of iteratively improving the performance of a constellation by re-arranging its points two at a time, while keeping the other points fixed. We verify our work by comparing it to the known optimal constellations in [7] for M = 2, and in [10] for M = 4, before considering larger constellations. Other related works on constellation design include [4,6,12,14].…”

mentioning

confidence: 90%

“…We next consider the constellations found in [10] for M = 4. When the pairwise optimization stabilizes, the resulting constellation is very similar to those arrived at in [10] for the given design SNR (in this case SN R = 0 dB), up to a rotation and/or reflection.…”

Section: Iiic1 Binary and Quaternary Constellationsmentioning

confidence: 99%

“…For M = 2, the optimal constellation was found analytically in [7], but as the constellation size grows, this quickly becomes difficult. In [10], the authors design optimal constellations for M = 4 by numerically evaluating tight error bounds developed in [8]. Our goal is to design signal point arrangements that are near-optimal for larger constellation sizes, such as M = 16, 64, 256, under MAP decoding.…”

Section: Problem Statementmentioning

confidence: 99%

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Pairwise optimization of modulation constellations for non-uniform sources

Moore

Takahara

Alajaji

2009

Can. J. Electr. Comput. Eng.

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The design of two-dimensional signal constellations for the transmission of binary non-uniform memoryless sources over additive white Gaussian noise channels is investigated. The main application of this problem is the implementation of improved constellations where transmitted data is highly non-uniform. A simple algorithm, which optimizes a constellation by re-arranging its points in a pairwise fashion (i.e., two points are modified at a time, with all other points remaining fixed), is presented. In general, the optimized constellations depend on both the source statistics and the signal-to-noise ratio (SNR) in the channel. We show that constellations designed with source statistics considered can yield symbol error rate (SER) performance that is substantially better than rectangular quadrature amplitude modulation signal sets used with either Gray mapping or more recently developed maps. SER gains as high as 5 dB in E b /N0 SNR are obtained for highly non-uniform sources. Symbol mappings are also developed for the new constellations using a similar pairwise optimization method whereby we assign and compare a weighted score for each pair. These maps, when compared to the mappings used in conjunction with the standard rectangular QAM constellation, again achieve considerable performance gains in terms of bit error rate (BER). Gains as high as 4 dB were achieved over rectangular QAM with Gray mapping, or more than 1 dB better than previously improved mappings. Finally, the uncoded pairwise optimized system is compared to a standard tandem (separate) source and channel coding system. Although neither system is universally better, the uncoded system with optimized constellations outperforms the tandem coding system for low-to-mid SNRs. Performance/complexity trade-offs between the two systems are also discussed. I IntroductionFor uniformly distributed sources, rectangular quadrature amplitude modulation (QAM) using Gray mapping is known to perform well, and is shown as optimal in terms of bit error rate (BER) for high enough signal-to-noise ratios (SNR) [1]. As noted in [13], however, there are many real-world examples of data sources which are highly nonuniform, such as text (email and instant/short messages), medical images and encoded voice data [2]. Compression will often have residual redundancy in the output due to non-ideal coding methods [3]. Rather than using traditional separate source and channel coding (which may be sensitive to noise-related errors in decoding if optimal variablelength source coding is used, as we later illustrate in Section VI), we can choose instead to directly exploit the non-uniformity of the source via the modulation scheme, while gaining noise-resiliency in many cases and significantly reducing system complexity and delay [3]. Such an approach, which can be characterized as a joint source-channel coding approach, is quite attractive for complexity-constrained and delaysensitive applications such as wireless sensor networks. In these nonuniform situations, the performance of Gray...

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Section: Iiic1 Binary and Quaternary Constellationsmentioning

confidence: 80%

mentioning

confidence: 90%

Section: Iiic1 Binary and Quaternary Constellationsmentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

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Pairwise optimization of modulation constellations for non-uniform sources

Moore

Takahara

Alajaji

2009

Can. J. Electr. Comput. Eng.

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“…Optimal quaternary constellation design could also be studied as in [21] for STOB coded channels using the error bounds of [8]. Another direction is to use (12) to find trellis encoders and signal mappings which, when used with the MAP decoding rule in (2), will reduce the FER and/or BER of a trellis-coded system.…”

Section: Discussionmentioning

confidence: 99%

MAP decoding for multi-antenna systems with non-uniform sources: exact pairwise error probability and applications

Behnamfar

Alajaji

Linder

2009

IEEE Trans. Commun.

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Abstract-We study the maximum a posteriori (MAP) decoding of memoryless non-uniform sources over multiple-antenna channels. Our model is general enough to include space-time coding, BLAST architectures, and single-transmit multi-receive antenna systems which employ any type of channel coding. We derive a closed-form expression for the codeword pairwise error probability (PEP) of general multi-antenna codes using moment generating function and Laplace transform arguments. We then consider space-time orthogonal block (STOB) coding and prove that, similar to the maximum likelihood (ML) decoding case, detection of symbols is decoupled in MAP decoding. We also derive the symbol PEP in closed-form for STOB codes. We apply these results in several scenarios. First, we design a binary antipodal signaling scheme which minimizes the system bit error rate (BER) under STOB coding. At a BER of 10 −6 , this constellation has a channel signal-to-noise ratio (CSNR) gain of 4.7 dB over conventional BPSK signaling for a binary nonuniform source with p0 = P (0) = 0.9. We next design space-time linear dispersion (LD) codes which are optimized for the source distribution under the criterion of minimizing the union upper bound on the frame error rate (FER). Two codes are given here: one outperforms V-BLAST by 3.5 dB and Alamouti's code by 12.3 dB at an FER of 10 −2 for a binary source with p0 = 0.9, and the other outperforms V-BLAST by 4.2 dB at an FER of 10 −3 for a uniform source. These codes also outperform the LD codes of [13] constructed under a different criteria. Finally, the problem of bit-to-signal mapping is studied. It is shown that for a binary source with p0 = 0.9, 64-QAM signaling, and SER = 10 −3 , a gain of 3.7 dB can be achieved using a better-thanGray mapping. For a system with one transmit and two receive antennas that uses trellis coding with 16-QAM signaling, a 1.8 dB gain over quasi-Gray mapping and ML decoding is observed when MAP decoding is used for binary sources with p0 = 0.9.

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Optimized M-ary Orthogonal and Bi-Orthogonal Signaling using Coherent Receiver with Non-Equal Symbol Probabilities

Wei

2012

IEEE Commun. Lett.

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Quarternary signal sets for digital communications with nonuniform sources

Cited by 6 publications

References 5 publications

Pairwise optimization of modulation constellations for non-uniform sources

Pairwise optimization of modulation constellations for non-uniform sources

MAP decoding for multi-antenna systems with non-uniform sources: exact pairwise error probability and applications

Optimized M-ary Orthogonal and Bi-Orthogonal Signaling using Coherent Receiver with Non-Equal Symbol Probabilities

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