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11.
  • Agrell, Erik, 1965, et al. (författare)
  • Upper bounds for constant-weight codes
  • 2000
  • Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 46:7, s. 2373-2395
  • Tidskriftsartikel (refereegranskat)abstract
    • Let A(n,d,w) denote the maximum possible number of codewords in an (n,d,w) constant-weight binary code. We improve upon the best known upper bounds on A(n,d,w) in numerous instances for n⩽24 and d⩽12, which is the parameter range of existing tables. Most improvements occur for d=8, 10, where we reduce the upper bounds in more than half of the unresolved cases. We also extend the existing tables up to n⩽28 and d⩽14. To obtain these results, we develop new techniques and introduce new classes of codes. We derive a number of general bounds on A(n,d,w) by means of mapping constant-weight codes into Euclidean space. This approach produces, among other results, a bound on A(n,d,w) that is tighter than the Johnson bound. A similar improvement over the best known bounds for doubly-constant-weight codes, studied by Johnson and Levenshtein, is obtained in the same way. Furthermore, we introduce the concept of doubly-bounded-weight codes, which may be thought of as a generalization of the doubly-constant-weight codes. Subsequently, a class of Euclidean-space codes, called zonal codes, is introduced, and a bound on the size of such codes is established. This is used to derive bounds for doubly-bounded-weight codes, which are in turn used to derive bounds on A(n,d,w). We also develop a universal method to establish constraints that augment the Delsarte inequalities for constant-weight codes, used in the linear programming bound. In addition, we present a detailed survey of known upper bounds for constant-weight codes, and sharpen these bounds in several cases. All these bounds, along with all known dependencies among them, are then combined in a coherent framework that is amenable to analysis by computer. This improves the bounds on A(n,d,w) even further for a large number of instances of n, d, and w.
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12.
  • Agrell, Erik, 1965 (författare)
  • Voronoi regions for binary linear block codes
  • 1996
  • Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 42:1, s. 310-316
  • Tidskriftsartikel (refereegranskat)abstract
    • The Voronoi regions of a block code govern many aspects of the code's performance on a Gaussian channel, and they are fundamental instruments in, for example, error probability analysis and soft-decision decoding. The article presents an efficient method for finding the boundaries of the Voronoi regions for an arbitrary binary linear block code. Two theoretical results together lead to the Voronoi regions. First, it is shown that the question of the Voronoi neighborship can be reduced into testing a simpler relation, called the Gabriel neighborship. Second, a fast method of recognising Gabriel neighbors is proposed. These results are finally employed to describe the Voronoi regions for the Golay codes and several BCH codes, including Hamming codes.
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15.
  • Alvarado, A., et al. (författare)
  • High-SNR Asymptotics of Mutual Information for Discrete Constellations With Applications to BICM
  • 2014
  • Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 60:2, s. 1061-1076
  • Tidskriftsartikel (refereegranskat)abstract
    • Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity. Asymptotic expressions of the symbol-error probability (SEP) and the minimum mean-square error (MMSE) achieved by estimating the channel input given the channel output are also developed. It is shown that for any input distribution, the conditional entropy of the channel input given the output, MMSE, and SEP have an asymptotic behavior proportional to the Gaussian Q-function. The argument of the Q-function depends only on the minimum Euclidean distance (MED) of the constellation and the SNR, and the proportionality constants are functions of the MED and the probabilities of the pairs of constellation points at MED. The developed expressions are then generalized to study the high-SNR behavior of the generalized mutual information (GMI) for bit-interleaved coded modulation (BICM). By means of these asymptotic expressions, the long-standing conjecture that Gray codes are the binary labelings that maximize the BICM-GMI at high SNR is proven. It is further shown that for any equally spaced constellation whose size is a power of two, there always exists an anti-Gray code giving the lowest BICM-GMI at high SNR.
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16.
  • Anderson, John B, et al. (författare)
  • On the BCJR algorithm for rate-distortion source coding
  • 2007
  • Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 53:9, s. 3201-3207
  • Tidskriftsartikel (refereegranskat)abstract
    • The BCJR algorithm is an important channel decoding method. We extend it to trellis rate-distortion data compression. Beginning from source coding principles, the derivation of the algorithm avoids channel coding or soft output ideas. The encoder does not use entropy coding; equiprobable reproducer letters are emphasized since these maximize entropy. The BCJR method is demonstrated by tests of a tailbiting variant. It performs much better than the ordinary Viterbi algorithm for short and medium blocks. However, the improvement stems from tailbiting; the role of the BCJR is to achieve tailbiting in a relatively simple way. Some issues that arise with tailbiting are explored. It is shown that there is an optimal trellis state size for each block length.
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17.
  • Anderson, John B (författare)
  • On the complexity of bounded distance decoding for the AWGN channel
  • 2002
  • Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448. ; 48:5, s. 1046-1060
  • Tidskriftsartikel (refereegranskat)abstract
    • Earlier work has derived the storage complexity of the bounded distance decoder (BDD) for binary-channel convolutional codes. We extend this work to the Gaussian noise channel and to partial-response codes. We show that the storage requirement similar to(2(1-R) - 1)(-t) paths for rate-R convolutional codes over the binary channel becomes similar to2(2Rt) over the Gaussian channel, where the decoder must correct t errors. Thus, convolutional coding over the Gaussian channel is not only 3 dB more energy efficient, but its decoding is simpler as well. Next, we estimate the path storage for partial-response codes, i.e., real-number convolutional codes, over the Gaussian channel. The growth rate depends primarily on the bandwidth of the code. A new optimization procedure is devised to measure the maximum storage requirement in Gaussian noise for these two code types. An analysis based on difference equations predicts the asymptotic storage growth for partial response codes.
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18.
  • Andersson, Joel, et al. (författare)
  • On the Theorem of Uniform Recovery of Random Sampling Matrices
  • 2014
  • Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 60:3, s. 1700-1710
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an s-sparse signal from linear measurements (with high probability) is known to be m greater than or similar to s(ln s)(3) ln N. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of m x N-matrices, by considering what is called effective sparsity. We also present a condition on the so-called restricted isometry constants, delta s, ensuring sparse recovery via l(1)-minimization. We show that delta(2s) < 4/root 41 is sufficient and that this can be improved further to almost allow for a sufficient condition of the type delta(2s) < 2/3.
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19.
  • Andriyanova, Iryna, et al. (författare)
  • Threshold Saturation for Nonbinary SC-LDPC Codes on the Binary Erasure Channel
  • 2016
  • Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 62:5, s. 2622-2638
  • Tidskriftsartikel (refereegranskat)abstract
    • We analyze the asymptotic performance of nonbinary spatially coupled low-density parity-check (SC-LDPC) code ensembles defined over the general linear group on the binary erasure channel. In particular, we prove the threshold saturation of belief propagation decoding to the so-called potential threshold, using the proof technique based on potential functions introduced by Yedla et al., assuming that the potential function exists. We rewrite the density evolution of nonbinary SC-LDPC codes in an equivalent vector recursion form which is suited for the use of the potential function. We then discuss the existence of the potential function for the general case of vector recursions defined by multivariate polynomials, and give a method to construct it. We define a potential function in a slightly more general form than the one by Yedla et al., in order to make the technique based on potential functions applicable to the case of nonbinary LDPC codes. We show that the potential function exists if a solution to a carefully designed system of linear equations exists. Furthermore, we numerically show the existence of a solution to the system of linear equations for a large number of nonbinary LDPC code ensembles, which allows us to define their potential function and thus prove threshold saturation.
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20.
  • Angelakis, Vangelis, et al. (författare)
  • Minimum-Time Link Scheduling for Emptying Wireless Systems: Solution Characterization and Algorithmic Framework
  • 2014
  • Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 60:2, s. 1083-1100
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider a set of transmitter-receiver pairs, or links, that share a wireless medium and address the problem of emptying backlogged queues with given initial size at the transmitters in minimum time. The problem amounts to determining activation subsets of links, and their time durations, to form a minimum-time schedule. Scheduling in wireless networks has been studied under various formulations before. In this paper, we present fundamental insights and solution characterizations that include: 1) showing that the complexity of the problem remains high for any continuous and increasing rate function; 2) formulating and proving sufficient and necessary optimality conditions of two baseline scheduling strategies that correspond to emptying the queues using one-at-a-time or all-at-once strategies; and 3) presenting and proving the tractability of the special case in which the transmission rates are functions only of the cardinality of the link activation sets. These results are independent of physical-layer system specifications and are valid for any form of rate function. We then develop an algorithmic framework for the solution to this problem. The framework encompasses exact as well as sub-optimal, but fast, scheduling algorithms, all under a unified principle design. Through computational experiments, we finally investigate the performance of several specific algorithms from this framework.
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