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Information Theory, IEEE Transactions on

Issue 5 • Date Sep 1994

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Displaying Results 1 - 25 of 48
  • General principles for the algebraic decoding of cyclic codes

    Publication Year: 1994 , Page(s): 1661 - 1663
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (280 KB)  

    This paper provides two theorems for decoding all types of cyclic codes. It is shown that from a polynomial ideal point of view, the decoding problems of cyclic codes are closely related to the monic generators of certain polynomial ideals. This conclusion is also generalized to the decoding problems of algebraic geometry codes. View full abstract»

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  • Six new binary quasi-cyclic codes

    Publication Year: 1994 , Page(s): 1666 - 1667
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (184 KB)  

    Six new quasi-cyclic codes are presented, which improve the lower bounds on the minimum distance for a binary code. A local exhaustive search is used to find these codes and many other quasi-cyclic codes which attain the lower bounds. View full abstract»

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  • On restoring band-limited signals

    Publication Year: 1994 , Page(s): 1490 - 1503
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (809 KB)  

    The problem of reconstruction of band-limited signals from discrete and noisy data is studied. The reconstruction schemes employing cardinal expansions are proposed and their asymptotical properties are examined. In particular, the conditions for the convergence of the mean integrated squared error are found and the rate of convergence is evaluated. The main difference between the proposed reconstruction scheme and the classical one is in treating the sampling rate and the reconstruction rate differently. This distinction is necessary to ensure consistency of the reconstruction scheme in the presence of noise View full abstract»

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  • Performance of nonuniform constellations on the Gaussian channel

    Publication Year: 1994 , Page(s): 1633 - 1638
    Cited by:  Papers (8)  |  Patents (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (476 KB)  

    Testing of high-speed voiceband modems has revealed a significant increase in distortion for points near the perimeter of a QAM signal constellation. This distortion increases with distance from the center of the constellation and limits performance at data rates above 19.2 kb/s. The perimeter distortion can be reduced by transforming the signal constellation so that points near the center are closer together, and points near the perimeter are further apart. When the channel SNR is high, such a transformation reduces immunity to Gaussian noise because points near the center of the transformed constellation are closer together than in a uniformly spaced constellation with the same average power. This paper demonstrates theoretically that for channel SNRs of practical interest. There is actually a small gain in immunity to Gaussian noise. In fact, an appropriate coded modulation scheme can produce gains of about 0.25 dB View full abstract»

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  • Maximum likelihood sequence estimation from the lattice viewpoint

    Publication Year: 1994 , Page(s): 1591 - 1600
    Cited by:  Papers (25)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (876 KB)  

    Considers the problem of data detection in multilevel lattice-type modulation systems in the presence of intersymbol interference and additive white Gaussian noise. The conventional maximum likelihood sequence estimator using the Viterbi algorithm has a time complexity of O(mν+1) operations per symbol and a space complexity of O(δmν) storage elements, where m is the size of input alphabet, ν is the length of channel memory, and δ is the truncation depth. By revising the truncation scheme and viewing the channel as a linear transform, the authors identify the problem of maximum likelihood sequence estimation with that of finding the nearest lattice point. From this lattice viewpoint, the lattice sequence estimator for PAM systems is developed, which has the following desired properties: 1) its expected time-complexity grows as δ2 as SNR→∞; 2) its space complexity grow as δ; and 3) its error performance is effectively optimal for sufficiently large m. A tight upper bound on the symbol error probability of the new estimator is derived, and is confirmed by the simulation results of an example channel. It turns out that the estimator is effectively optimal for m⩾4 and the loss in signal-to-noise ratio is less than 0.5 dB even for m=2. Finally, limitations of the proposed estimator are also discussed View full abstract»

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  • Suboptimum decoding of decomposable block codes

    Publication Year: 1994 , Page(s): 1392 - 1405
    Cited by:  Papers (9)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1040 KB)  

    To decode a long block code with a large minimum distance by maximum likelihood decoding is practically impossible because the decoding complexity is simply enormous. However, if a code can be decomposed into constituent codes with smaller dimensions and simpler structure, it is possible to devise a practical and yet efficient scheme to decode the code. This paper investigates a class of decomposable codes, their distance and structural properties. It is shown that this class includes several classes of well-known and efficient codes as subclasses. Several methods for constructing decomposable codes or decomposing codes are presented. A two-stage (soft-decision or hard-decision) decoding scheme for decomposable codes, their translates or unions of translates is devised, and its error performance is analyzed for an AWGN channel. The two-stage soft-decision decoding is suboptimum. Error performances of some specific decomposable codes based on the proposed two-stage soft-decision decoding are evaluated. It is shown that the proposed two-stage suboptimum decoding scheme provides an excellent trade-off between the error performance and decoding complexity for codes of moderate and long block length View full abstract»

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  • Asymptotically robust detection of known signals in nonadditive noise

    Publication Year: 1994 , Page(s): 1612 - 1619
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (688 KB)  

    Robust detection of known weak signals of unknown amplitude is considered for a class of combined additive and nonadditive noise models and an asymptotically large set of independent observations. This class includes observation models that may have combinations of multiplicative and signal-dependent noise terms. Sufficient conditions are given for robust detection schemes for cases where the general form of the observation model is known but the additive noise distribution is known only to be a member of a general convex uncertainty class. Robust schemes satisfying these conditions are found for some example cases where additive signals and noise have been processed by memoryless nonlinearities. Some interesting example cases of combined multiplicative and signal-dependent noise are shown to use redescending nonlinearities, instead of the limiter nonlinearities typically found for similar additive noise cases View full abstract»

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  • A generalisation of the discrete Fourier transform: determining the minimal polynomial of a periodic sequence

    Publication Year: 1994 , Page(s): 1702 - 1704
    Cited by:  Papers (7)
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    Let s be a periodic sequence whose elements lie in a finite field. The authors present an algorithm that calculates the minimal polynomial of s, assuming that a period of s is known. The algorithm generalises both the discrete Fourier transform and the Games-Chan algorithm View full abstract»

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  • Optimal robust signaling with pseudonoise-modulated orthogonal signals

    Publication Year: 1994 , Page(s): 1619 - 1624
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (496 KB)  

    It is well known that orthogonal signal sets approach the channel capacity and reliability function of the infinite bandwidth additive white Gaussian noise channel. It is shown that pseudonoise-modulated orthogonal signals play a similar role for the infinite bandwidth Gaussian arbitrarily varying channel View full abstract»

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  • On the optimal transmission of non-Gaussian signals through a noisy channel with feedback

    Publication Year: 1994 , Page(s): 1624 - 1629
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (444 KB)  

    This paper is concerned with the optimal transmission of a non-Gaussian signal (a non-Gaussian message) through a channel with Gaussian white noise. The coding is assumed to be linear in the signal, but nonlinear in the observation (the channel output). Also, we assume that the signal is a square integrable process which is independent of the noise. It is shown that the optimal transmission which maximizes the mutual information between the signal and the observation is achieved by a coding scheme which generates the least-squares estimation error for the signal multiplied by a deterministic coefficient. Namely, it is shown that, for a fixed deterministic coefficient, the estimation error process has the same mutual information as the original signal, and when it is sent, the mean power of the signal is minimized over the codings with the same mutual information. On the other hand, the mutual information is maximized by taking the coefficient in such a way that the mean power of the encoded signal takes the maximum admissible value. It is seen that the well-known result for Gaussian signals is also valid for square integrable non-Gaussian signals View full abstract»

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  • A trellis coded modulation scheme constructed from block coded modulation with interblock memory

    Publication Year: 1994 , Page(s): 1348 - 1363
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1092 KB)  

    Proposes a new trellis coded modulation scheme which is constructed by combining a convolutional code and a variation of block coded modulation called block coded modulation with interblock memory. In the proposed scheme, each coded multidimensional signal point has a kind of two-fold dependency on other coded multidimensional signal points. In addition to the dependency on other coded multidimensional signal points described by the trellis of a convolutional code, each coded multidimensional signal point has another form of dependency on one previously coded multidimensional signal point. The additional dependency comes from the design of block coded modulation with interblock memory View full abstract»

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  • A determination of the parameters of a large class of Goppa codes

    Publication Year: 1994 , Page(s): 1678 - 1681
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (372 KB)  

    We determine the code parameters of a large class of Goppa codes, constructed from certain curves described by Stichtenoth (see Arch. Math., vol.XXIV, pp.615-631, 1973), in terms of the genus and the Weierstrass gap sequence of a given chosen point on each tune. Examples are codes from Hermitian, Artin-Schreier, and hyperelliptic curves View full abstract»

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  • Optimal waveform selection for tracking systems

    Publication Year: 1994 , Page(s): 1536 - 1550
    Cited by:  Papers (49)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1188 KB)  

    Investigates adaptive waveform selection schemes where selection is based on overall target tracking system performance. Optimal receiver assumptions allow the inclusion of transmitted waveform specification parameters in the tracking subsystem defining equations. The authors give explicit expressions for two one-step ahead optimization problems for a single target in white Gaussian noise when the tracker is a conventional Kalman filter. These problems may be solved to yield the most improvement possible in tracking performance for each new transmitted pulse. In cases where target motion is restricted to one dimension, closed-form solutions to the local (one step ahead) waveform optimization problem have been obtained. The optimal waveform selection algorithms in the paper may be included with conventional Kalman filtering equations to form an enhanced Kalman tracker. Simulation examples are presented to illustrate the potential of the waveform selection schemes for the optimal utilization of the capabilities of modern digital waveform generators, including multiple waveform classes. The extension of the basic waveform optimization scheme to more complex tracking scenarios is also discussed View full abstract»

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  • Dynamic system identification with order statistics

    Publication Year: 1994 , Page(s): 1474 - 1489
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (956 KB)  

    Systems consisting of linear dynamic and memory-less nonlinear subsystems are identified. The paper deals with systems in which the nonlinear element is followed by a linear element, as well as systems in which the subsystems are connected in parallel. The goal of the identification is to recover the nonlinearity from noisy input-output observations of the whole system; signals interconnecting the elements are not measured. Observed values of the input signal are rearranged in increasing order, and coefficients for the expansion of the nonlinearity in trigonometric series are estimated from the new sequence of observations obtained in this way. Two algorithms are presented, and their mean integrated square error is examined. Conditions for pointwise convergence are also established. For the nonlinearity satisfying the Lipschitz condition, the error converges to zero. The rate of convergence derived for differentiable nonlinear characteristics is insensitive to the roughness of the probability density of the input signal. Results of numerical simulation are also presented View full abstract»

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  • On sequential delay estimation in wideband digital communication systems

    Publication Year: 1994 , Page(s): 1327 - 1333
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (432 KB)  

    The problem of estimating the symbol timing in wideband data communication signals is considered. Conventional approaches to this problem suffer from several drawbacks, including possible lack of consistency due to multiple extrema in the error surface, and very slow convergence due to exceedingly sharp waveform correlation functions. In the paper sequential detection-estimation algorithms that alleviate these problems are constructed and analyzed. These algorithms are based on two techniques: the use of regularization (i.e., prefiltering) to produce a consistent initial estimate at the expense of higher mean-square error, and the coupling of recursive maximum-likelihood with this consistent estimator to produce the desired goal-a recursive consistent and efficient estimator View full abstract»

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  • Malfunction in the Peterson-Gorenstein-Zierler decoder

    Publication Year: 1994 , Page(s): 1649 - 1653
    Cited by:  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (460 KB)  

    Most versions of the Peterson-Gorenstein-Zierler (PGZ) decoding algorithm are not true bounded distance decoding algorithms in the sense that when a received vector is not in the decoding sphere of any codeword, the algorithm does not always declare a decoding failure. For a t-error-correcting BCH code, if the received vector is at distance i, i⩽t from a codeword in a supercode with BCH distance t+i+1, the decoder will output that codeword from the supercede. If that codeword is not a member of the t-error-correcting code, then decoder malfunction is said to have occurred. We describe the necessary and sufficient conditions for decoder malfunction, and show that malfunction can be avoided in the PGZ decoder by checking t-ν equations, where ν is the number of errors hypothesized by the decoder. A formula for the probability of decoder malfunction is also given, and the significance of decoder malfunction is considered for PGZ decoders and high-speed Berlekamp-Massey decoders View full abstract»

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  • Use of Grobner bases to decode binary cyclic codes up to the true minimum distance

    Publication Year: 1994 , Page(s): 1654 - 1661
    Cited by:  Papers (17)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (740 KB)  

    A general algebraic method for decoding all types of binary cyclic codes is presented. It is shown that such a method can correct t=[(d-1)/2] errors, where d is the true minimum distance of the given cyclic code. The key idea behind this decoding technique is a systematic application of the algorithmic procedures of Grobner bases to obtain the error-locator polynomial L(z). The discussion begins from a set of syndrome polynomials F and the ideal T(F) generated by F. It is proved here that the process of transforming F to the normalized reduced Grobner basis of I(F) with respect to the “purely lexicographical” ordering automatically converges to L(z). Furthermore, it is shown that L(z) can be derived from any normalized Grobner basis of I(F) with respect to any admissible total ordering. To illustrate this new approach, the procedures for decoding certain BCH codes and quadratic residue codes are demonstrated View full abstract»

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  • On the structure of linear codes with covering radius two and three

    Publication Year: 1994 , Page(s): 1406 - 1416
    Cited by:  Papers (1)
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    We obtain new bounds on l(m,r), the minimum length of a linear code with codimension m and covering radius r. All bounds are derived in a uniform way. We employ results from coding theory, some earlier results on covering codes, and combinatorial arguments. We prove the following bounds: l(6, 2)=13, l(7,2)=19, l(8,2)⩾25, l(9,2)⩾34, l(2m-l,2)⩾2m+1 for m⩾3, l(14,2)⩾182, l(16,2)⩾363, l(18,2)⩾725, l(20,2)⩾1449, l(22,2)⩾2897, l(24,2)⩾5794, l(9,3)⩾17, l(10,3)⩾21, l(12,3)⩾31, l(13,3)⩾38 View full abstract»

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  • On the number of digital convex polygons inscribed into an (m,m)-grid

    Publication Year: 1994 , Page(s): 1681 - 1686
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (500 KB)  

    Binary images of objects are digitized by coloring a pixel cell black if more than half of its area is within the interior of the object. For simplicity, the digitization is often modified by looking only at the center point of a cell to determine its pixel value. The digitized boundary curve consists of a sequence of 4-directional links, sometimes called a "crack" code since it follows the cracks or edges of the pixel cells. Of interest here is the entropy of digitized binary objects or planar curves on an m×m integer grid. Let D(m) denote the number of digital convex polygons which can be inscribed into an integer grid of size m×m. The asymptotic estimation of log D(m) is of interest in determining the entropy of digitized convex shapes. It is shown that log D(m) is of the order m2/3 View full abstract»

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  • On the correlation structure of the wavelet coefficients of fractional Brownian motion

    Publication Year: 1994 , Page(s): 1609 - 1612
    Cited by:  Papers (16)
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    Shows that the interdependence of the discrete wavelet coefficients of fractional Brownian motion, defined by normalized correlation, decays exponentially fast across scales and hyperbolically fast along time View full abstract»

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  • Block-based eigensystem of the 1±D and 1-D2 partial response channels

    Publication Year: 1994 , Page(s): 1645 - 1647
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    We find analytical expressions for the block-based input and output eigenvectors and eigenvalues of the systems with responses 1±d and 1-D2. The input eigenvectors form an orthonormal basis which is the optimum modulator for a channel with that transfer function. The output eigenvectors form an orthonormal basis with the same spectral nulls as the corresponding system. This basis can be used to produce line codes with spectral nulls. The eigenvectors are sinusoids. This reduces the computational complexity by allowing for fast transform algorithms to perform the modulation for a block of data View full abstract»

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  • Binary coding by integration of polynomials

    Publication Year: 1994 , Page(s): 1417 - 1424
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (616 KB)  

    Based on the idea of integration and differentiation of polynomials, a large class of linear unequal error-protection (LUEP) codes is constructed. Many of these codes are optimal. A codeword is generated by binary discrete integration of an all-zero vector, using the information bits as integration constants. Decoding is performed by discrete differentiation of the received word. For special designs, all information bits are equally protected and in this case all classes of Reed-Muller codes are obtained. Thus, a new and very comprehensive description of these codes is given. The described codes are decoded by majority decisions over corresponding derivatives, based on the structure of Pascal's triangle reduced modulo 2 View full abstract»

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  • The performance of convolutional codes on the block erasure channel using various finite interleaving techniques

    Publication Year: 1994 , Page(s): 1459 - 1473
    Cited by:  Papers (26)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1252 KB)  

    Consider the transmission of a finitely interleaved rate 1/n convolutionally encoded message over a channel with memory having two internal states Ξ0 and Ξ1 where when in state Ξ0, the channel resembles a noiseless binary symmetric channel (BSC), whereas when in state Ξ1, the channel is totally blocked and is well approximated by a binary-input single-output channel. Assume that the channel's internal state is drawn at random once every h channel uses, and then remains constant for the following h channel uses. Further assume that the message is short in comparison to h, and that due to delay constraints, the message must be decoded within Nh channel uses, where N need not be large in comparison to the code's constraint length. Such a model is appropriate for describing a convolutionally coded slow frequency hopping system with non-ideal interleaving, in which every frequency is either totally erased or else noiseless. The probability of a message error, the normalized expected number of bits in error, and the bit error rate (BER) are analytically computed for the periodic N×h bit and word interleavers, where a bit refers to a binary code symbol, and a word refers to a n-tuple of consecutive bits. An analytic expression for the BER is also given for pseudo-random word and bit interleavers and for the corresponding limiting cases of infinite interleaving, i.e., N→∞. As an example for the use of our methods, we analyze the performance of the GSM system with various interleaving depths and methods. We introduce the notion of “matched” code and interleaver pairs, and argue that this is a desirable property. Several exhaustive searches are carried out for matched codes and interleavers View full abstract»

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  • New bounds for the sizes of radar arrays

    Publication Year: 1994 , Page(s): 1672 - 1678
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (500 KB)  

    Improved upper bounds for the size of radar arrays are found by using the window method. New general constructions and computer-searched examples are presented. The radar array problem is generalized to include arrays with sidelobes greater than 1 View full abstract»

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  • Decoding of convolutional codes using a syndrome trellis

    Publication Year: 1994 , Page(s): 1663 - 1666
    Cited by:  Papers (26)  |  Patents (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (348 KB)  

    Soft-decision maximum-likelihood decoding of convolutional codes using the Viterbi algorithm with a syndrome trellis is proposed. The parity check matrix of a convolutional code is used to construct the trellis. This trellis is minimal. The number of operations for the decoding of one block of a q-ary rate k/n convolutional code is ~nqmin(k,n-k)qν, where ν is the memory size of the code. When the code rate satisfies k/n>½, the proposed algorithm is simpler than the classical Viterbi algorithm that has complexity ~nqkqν View full abstract»

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Aims & Scope

IEEE Transactions on Information Theory publishes papers concerned with the transmission, processing, and utilization of information.

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Editor-in-Chief
Frank R. Kschischang

Department of Electrical and Computer Engineering