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Sökning: L773:0018 9448 OR L773:0018 9448

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1.
  • Agrell, Erik, 1965, et al. (författare)
  • A table of upper bounds for binary codes
  • 2001
  • Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 47:7, s. 3004-3006
  • Tidskriftsartikel (refereegranskat)abstract
    • Let A(n, d) denote the maximum possible number of codewords in an (n, d) binary code. We establish four new bounds on A(n, d), namely, A(21, 4)⩽43689, A(22, 4)⩽87378, A(22, 6)⩽6941, and A(23, 4)⩽173491. Furthermore, using previous upper bounds on the size of constant-weight binary codes, we reapply known methods to generate a table of bounds on A(n, d) for all n⩽28. This table extends the range of parameters compared with previously known tables.
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2.
  • Agrell, Erik, 1965, et al. (författare)
  • Closest point search in lattices
  • 2002
  • Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 48:8, s. 2201-2214
  • Tidskriftsartikel (refereegranskat)abstract
    • In this semitutorial paper, a comprehensive survey of closest point search methods for lattices without a regular structure is presented. The existing search strategies are described in a unified framework, and differences between them are elucidated. An efficient closest point search algorithm, based on the Schnorr-Euchner variation of the Pohst method, is implemented. Given an arbitrary point x is an element of R-m and a generator matrix for a lattice A, the algorithm computes the point of A that is closest to x. The algorithm is shown to be substantially faster than other known methods, by means of a theoretical comparison with the Kannan algorithm and an experimental comparison with the Pohst algorithm and its variants, such as the recent Viterbo-Boutros decoder. Modifications of the algorithm are developed to solve a number of related search problems for lattices, such as finding a shortest vector, determining the kissing number, computing the Voronoi-relevant vectors, and finding. a Korkine-Zolotareff reduced basis.
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3.
  • Agrell, Erik, 1965, et al. (författare)
  • Gray coding for multilevel constellations in Gaussian noise
  • 2007
  • Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 53:1, s. 224-235
  • Tidskriftsartikel (refereegranskat)abstract
    • The problem of finding the optimal labeling (bit-to-symbol mapping) of multilevel coherent phase shift keying (PSK), pulse amplitude modulation (PAM), and quadrature amplitude modulation (QAM) constellations with respect to minimizing the bit-error probability (BEP) over a Gaussian channel is addressed. We show that using the binary reflected Gray code (BRGC) to label the signal constellation results in the lowest possible BEP for high enough signal energy-to-noise ratios and analyze what is "high enough"in this sense. It turns out that the BRGC is optimal for PSK and PAM systems whenever the target BEP is at most a few percent, which covers most systems of practical interest. New and simple closed-form expressions are presented for the BEP of PSK, PAM, and QAM using the BRGC. © 2007 IEEE.
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4.
  • Agrell, Erik, 1965, et al. (författare)
  • On the Best Lattice Quantizers
  • 2023
  • Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 69:12, s. 7650-7658
  • Tidskriftsartikel (refereegranskat)abstract
    • A lattice quantizer approximates an arbitrary real-valued source vector with a vector taken from a specific discrete lattice. The quantization error is the difference between the source vector and the lattice vector. In a classic 1996 paper, Zamir and Feder show that the globally optimal lattice quantizer (which minimizes the mean square error) has white quantization error: for a uniformly distributed source, the covariance of the error is the identity matrix, multiplied by a positive real factor. We generalize the theorem, showing that the same property holds (i) for any lattice whose mean square error cannot be decreased by a small perturbation of the generator matrix, and (ii) for an optimal product of lattices that are themselves locally optimal in the sense of (i). We derive an upper bound on the normalized second moment (NSM) of the optimal lattice in any dimension, by proving that any lower- or upper-triangular modification to the generator matrix of a product lattice reduces the NSM. Using these tools and employing the best currently known lattice quantizers to build product lattices, we construct improved lattice quantizers in dimensions 13 to 15, 17 to 23, and 25 to 48. In some dimensions, these are the first reported lattices with normalized second moments below the best known upper bound.
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5.
  • Agrell, Erik, 1965, et al. (författare)
  • On the optimality of the binary reflected Gray code
  • 2004
  • Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 50:12, s. 3170-3182
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper concerns the problem of selecting a binary labeling for the signal constellation in M-PSK, M-PAM, and M-QAM communication systems. Gray labelings are discussed and the original work by Frank Gray is analyzed. As is noted, the number of distinct Gray labelings that result in different bit-error probability grows rapidly with increasing constellation size. By introducing a recursive Gray labeling construction method called expansion, the paper answers the natural question of what labeling, among all possible constellation labelings, will give the lowest possible average probability of bit errors for the considered constellations. Under certain assumptions on the channel, the answer is that the labeling proposed by Gray, the binary reflected Gray code, is the optimal labeling for all three constellations, which has, surprisingly, never been proved before.
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6.
  • Agrell, Erik, 1965, et al. (författare)
  • On the symbol error probability of regular polytopes
  • 2011
  • Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 57:6, s. 3411-3415
  • Tidskriftsartikel (refereegranskat)abstract
    • An exact expression is derived for the symbol error probability when the vertices of the four-dimensional 24-cell are used for digital transmission in Gaussian noise. Corresponding expressions for other regular convex polytopes are summarized. Numerically stable versions of these error probabilities are also obtained. © 2011 IEEE.
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7.
  • Agrell, Erik, 1965 (författare)
  • On the Voronoi neighbor ratio for binary linear block codes
  • 1998
  • Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 44:7, s. 3064-3072
  • Tidskriftsartikel (refereegranskat)abstract
    • Soft-decision decoding of block codes is regarded as the geometrical problem of identifying the Voronoi region within which a given input vector lies. A measure, called the neighbor ratio, is proposed to characterize how many facets a Voronoi region has. Theory and algorithms are presented to determine the neighbor ratio for binary linear block codes and results are given for several types of codes. An asymptotic analysis for long codes reveals that the neighbor ratio depends on whether the code rate is less than 1/2 or not. For rates below this threshold, all pairs of codewords tend to share a Voronoi facet; for higher rates, a relatively small fraction of them do.
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8.
  • Agrell, Erik, 1965, et al. (författare)
  • Optimal Alphabets and Binary Labelings for BICM at Low SNR
  • 2011
  • Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 57:10, s. 6650-6672
  • Tidskriftsartikel (refereegranskat)abstract
    • Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit $-1.59 \tr{dB}$. It is shown that the $\Eb/N_0$ required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.
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9.
  • Agrell, Erik, 1965, et al. (författare)
  • Optimization of lattices for quantization
  • 1998
  • Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 44:5, s. 1814-1828
  • Tidskriftsartikel (refereegranskat)abstract
    • A training algorithm for the design of lattices for vector quantization is presented. The algorithm uses a steepest descent method to adjust a generator matrix, in the search for a lattice whose Voronoi regions have minimal normalized second moment. The numerical elements of the found generator matrices are interpreted and translated into exact values. Experiments show that the algorithm is stable, in the sense that several independent runs reach equivalent lattices. The obtained lattices reach as low second moments as the best previously reported lattices, or even lower. Specifically, we report lattices in nine and ten dimensions with normalized second moments of 0.0716 and 0.0708, respectively, and nonlattice tessellations in seven and nine dimensions with 0.0727 and 0.0711, which improves on previously known values. The new nine- and ten-dimensional lattices suggest that Conway and Sloane's (1993) conjecture on the duality between the optimal lattices for packing and quantization might be false. A discussion of the application of lattices in vector quantizer design for various sources, uniform and nonuniform, is included.
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10.
  • Agrell, Erik, 1965, et al. (författare)
  • Signal Shaping for BICM at Low SNR
  • 2013
  • Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 59:4, s. 2396-2410
  • Tidskriftsartikel (refereegranskat)abstract
    • The generalized mutual information (GMI) of bit-interleaved coded modulation (BICM) systems, sometimes called the BICM capacity, is investigated at low signal-to-noise ratio (SNR). The combinations of input alphabet, input distribution, and binary labeling that achieve the Shannon limit are completely characterized. The main conclusion is that a BICM system with probabilistic shaping achieves the Shannon limit at low SNR if and only if it can be represented as a zero-mean linear projection of a hypercube. Hence, probabilistic shaping offers no extra degrees of freedom to optimize the low-SNR BICM-GMI, in addition to what is provided by geometrical shaping. The analytical conclusions are confirmed by numerical results, which also show that for a fixed input alphabet, probabilistic shaping can improve the BICM-GMI in the low and medium SNR range.
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