90 research outputs found

    Fast-Decodable Asymmetric Space-Time Codes from Division Algebras

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    Multiple-input double-output (MIDO) codes are important in the near-future wireless communications, where the portable end-user device is physically small and will typically contain at most two receive antennas. Especially tempting is the 4 x 2 channel due to its immediate applicability in the digital video broadcasting (DVB). Such channels optimally employ rate-two space-time (ST) codes consisting of (4 x 4) matrices. Unfortunately, such codes are in general very complex to decode, hence setting forth a call for constructions with reduced complexity. Recently, some reduced complexity constructions have been proposed, but they have mainly been based on different ad hoc methods and have resulted in isolated examples rather than in a more general class of codes. In this paper, it will be shown that a family of division algebra based MIDO codes will always result in at least 37.5% worst-case complexity reduction, while maintaining full diversity and, for the first time, the non-vanishing determinant (NVD) property. The reduction follows from the fact that, similarly to the Alamouti code, the codes will be subsets of matrix rings of the Hamiltonian quaternions, hence allowing simplified decoding. At the moment, such reductions are among the best known for rate-two MIDO codes. Several explicit constructions are presented and shown to have excellent performance through computer simulations.Comment: 26 pages, 1 figure, submitted to IEEE Trans. Inf. Theory, October 201

    Algebraic number theory and code design for Rayleigh fading channels

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    Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems. Extended work has been done on single antenna fading channels, and algebraic lattice codes have been proven to be an effective tool. The general framework has been settled in the last ten years and many explicit code constructions based on algebraic number theory are now available. The aim of this work is to provide both an overview on algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory. The basic facts of this mathematical field will be illustrated by many examples and by the use of a computer algebra freeware in order to make it more accessible to a large audience

    Maximum-likelihood decoding and integer least-squares: the expected complexity

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    The problem of finding the least-squares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The problem is equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In communications applications, however, the given vector is not arbitrary, but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known. Therefore in this paper, rather than dwell on the worst-case complexity of the integer-least-squares problem, we study its expected complexity, averaged over the noise and over the lattice. For the “sphere decoding” algorithm of Fincke and Pohst we find a closed-form expression for the expected complexity and show that, for a wide range of noise variances and dimensions, the expected complexity is polynomial, in fact often roughly cubic. Since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial, this suggests that maximum-likelihood decoding, which was hitherto thought to be computationally intractable, can in fact be implemented in real-time—a result with many practical implications

    Low-Complexity Voronoi Shaping for the Gaussian Channel

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    Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up version of the coding lattice. In this paper, we design low-complexity VCs with a cubic coding lattice of up to 32 dimensions, in which pseudo-Gray labeling is applied to minimize the bit error rate. The designed VCs have considerable shaping gains of up to 1.03 dB and finer choices of spectral efficiencies in practice compared with conventional VCs. A mutual information estimation method and a log-likelihood approximation method based on importance sampling for very large constellations are proposed and applied to the designed VCs. With error-control coding, the proposed VCs can have higher information rates than the conventional scaled VCs because of their inherently good pseudo-Gray labeling feature, with a lower decoding complexity

    Statistical Pruning for Near-Maximum Likelihood Decoding

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    In many communications problems, maximum-likelihood (ML) decoding reduces to finding the closest (skewed) lattice point in N-dimensions to a given point xisin CN. In its full generality, this problem is known to be NP-complete. Recently, the expected complexity of the sphere decoder, a particular algorithm that solves the ML problem exactly, has been computed. An asymptotic analysis of this complexity has also been done where it is shown that the required computations grow exponentially in N for any fixed SNR. At the same time, numerical computations of the expected complexity show that there are certain ranges of rates, SNRs and dimensions N for which the expected computation (counted as the number of scalar multiplications) involves no more than N3 computations. However, when the dimension of the problem grows too large, the required computations become prohibitively large, as expected from the asymptotic exponential complexity. In this paper, we propose an algorithm that, for large N, offers substantial computational savings over the sphere decoder, while maintaining performance arbitrarily close to ML. We statistically prune the search space to a subset that, with high probability, contains the optimal solution, thereby reducing the complexity of the search. Bounds on the error performance of the new method are proposed. The complexity of the new algorithm is analyzed through an upper bound. The asymptotic behavior of the upper bound for large N is also analyzed which shows that the upper bound is also exponential but much lower than the sphere decoder. Simulation results show that the algorithm is much more efficient than the original sphere decoder for smaller dimensions as well, and does not sacrifice much in terms of performance

    Advanced constellation and demapper schemes for next generation digital terrestrial television broadcasting systems

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    206 p.Esta tesis presenta un nuevo tipo de constelaciones llamadas no uniformes. Estos esquemas presentan una eficacia de hasta 1,8 dB superior a las utilizadas en los últimos sistemas de comunicaciones de televisión digital terrestre y son extrapolables a cualquier otro sistema de comunicaciones (satélite, móvil, cable¿). Además, este trabajo contribuye al diseño de constelaciones con una nueva metodología que reduce el tiempo de optimización de días/horas (metodologías actuales) a horas/minutos con la misma eficiencia. Todas las constelaciones diseñadas se testean bajo una plataforma creada en esta tesis que simula el estándar de radiodifusión terrestre más avanzado hasta la fecha (ATSC 3.0) bajo condiciones reales de funcionamiento.Por otro lado, para disminuir la latencia de decodificación de estas constelaciones esta tesis propone dos técnicas de detección/demapeo. Una es para constelaciones no uniformes de dos dimensiones la cual disminuye hasta en un 99,7% la complejidad del demapeo sin empeorar el funcionamiento del sistema. La segunda técnica de detección se centra en las constelaciones no uniformes de una dimensión y presenta hasta un 87,5% de reducción de la complejidad del receptor sin pérdidas en el rendimiento.Por último, este trabajo expone un completo estado del arte sobre tipos de constelaciones, modelos de sistema, y diseño/demapeo de constelaciones. Este estudio es el primero realizado en este campo

    Multidimensional Optimized Optical Modulation Formats

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    This chapter overviews the relatively large body of work (experimental and theoretical) on modulation formats for optical coherent links. It first gives basic definitions and performance metrics for modulation formats that are common in the literature. Then, the chapter discusses optimization of modulation formats in coded systems. It distinguishes between three cases, depending on the type of decoder employed, which pose quite different requirements on the choice of modulation format. The three cases are soft-decision decoding, hard-decision decoding, and iterative decoding, which loosely correspond to weak, medium, and strong coding, respectively. The chapter also discusses the realizations of the transmitter and transmission link properties and the receiver algorithms, including DSP and decoding. It further explains how to simply determine the transmitted symbol from the received 4D vector, without resorting to a full search of the Euclidean distances to all points in the whole constellation

    An optimum geometric decoder for MIMO systems

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    In this paper, we propose a simple implementation of an optimum Geometric decoder (GD) for use in MIMO systems. The decoder uses the channel matrix to construct a hyper paraboloid and then restricts the symbol vectors to be searched to a hyper ellipsoid projected from the hyper paraboloid. Computer simulation results on 4Ă—4 different MIMO systems transmitting 16QAM and 64QAM show that the proposed GD can achieve the same bit-error-rate (BER) performances as those of the Maximum Likelihood (ML) decoder, yet having much less complexity.published_or_final_versionThe 5th IEEE GCC Conference & Exhibition, Kuwait City, Kuwait, 17-19 March 2009. In Proceedings of the IEEE GCC Conference & Exhibition, 2009, p. 1-
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