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Information Theory, IEEE Transactions on

Issue 5 • Date Sep 1994

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Displaying Results 1 - 25 of 48
  • 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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  • 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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  • On restoring band-limited signals

    Publication Year: 1994 , Page(s): 1490 - 1503
    Cited by:  Papers (13)
    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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  • Data fusion with minimal communication

    Publication Year: 1994 , Page(s): 1551 - 1563
    Cited by:  Papers (25)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1096 KB)  

    Two sensors obtain data vectors x and y, respectively, and transmit real vectors m&oarr;1(x) and m&oarr;2(y), respectively, to a fusion center. The authors obtain tight lower bounds on the number of messages (the sum of the dimensions of m&oarr;1 and m&oarr;2) that have to be transmitted for the fusion center to be able to evaluate a given function f&oarr;(x,y). When the function f&oarr; is linear, they show that these bounds are effectively computable. Certain decentralized estimation problems can be cast in the framework and are discussed in some detail. In particular, the authors consider the case where x and y are random variables representing noisy measurements and f&oarr;(x,y)=E[z|x,y], where z is a random variable to be estimated. Furthermore, it is established that a standard method for combining decentralized estimates of Gaussian random variables has nearly optimal communication requirements View full abstract»

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  • Irreducible components of canonical diagrams for spectral nulls

    Publication Year: 1994 , Page(s): 1375 - 1391
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1256 KB)  

    Irreducible components of canonical diagrams for spectral null constraints at f=fsk/n are studied, where k and n are integers and fs is the symbol frequency. To identify systematically all irreducible components of the canonical diagrams for first-order spectral nulls at f, we give a set of channel symbol sequences specifying all of them. If n is a prime number, then each sequence in the set corresponds to exactly one label-preserving graph isomorphism class of irreducible components. We also give a set of channel symbol sequences specifying all irreducible components of canonical diagrams for second-order spectral nulls at DC (i.e., f=0) View full abstract»

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  • Modulation and coding for throughput-efficient optical systems

    Publication Year: 1994 , Page(s): 1313 - 1326
    Cited by:  Papers (27)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1136 KB)  

    Optical direct-detection systems are currently being considered for some high-speed intersatellite links, where data rates of a few hundred megabits per second are envisioned under power and pulsewidth constraints. The authors investigate the capacity, cutoff rate, and error-probability performance of uncoded and trellis-coded systems for various modulation schemes and under throughput and power constraints. Modulation schemes considered are on-off keying, pulse-position modulation (PPM), overlapping PPM, and multipulse (combinatorial) PPM 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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  • 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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  • Two new rate 2/p binary quasi-cyclic codes

    Publication Year: 1994 , Page(s): 1667 - 1668
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (168 KB)  

    A class of rate 2/P quasi-cyclic codes can be characterized in terms of m×m circulant matrices. In this correspondence, two new codes with parameters (80, 10, 35) and (95, 10, 42) are presented which improve the known lower bound on the maximum possible minimum distance. The former code can be extended with an even parity check bit to an (81, 10, 36) code that establishes that d2(81, 10)=36 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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  • 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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  • Lower bounds on the probability of deception in authentication with arbitration

    Publication Year: 1994 , Page(s): 1573 - 1585
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1008 KB)  

    The paper investigates a model for authentication in which not only an outsider, but also the transmitter or the receiver, may cheat. Lower bounds on the probability of success for different types of deception as well as on the parameters of secure authentication codes are derived. The latter bounds are shown to be tight by demonstrating codes in projective space that meet the bounds with equality View full abstract»

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  • Symmetry properties of multilevel coded modulation

    Publication Year: 1994 , Page(s): 1630 - 1632
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (292 KB)  

    We consider the geometrical uniformity properties of signal space codes generated by multilevel coded modulation. First we examine multilevel schemes based on 2L-ary PSK signal sets, and we derive conditions on the binary component codes which lead to geometrically uniform signal space codes. Next we study the geometrical uniformity of multilevel schemes based on signal sets having a generating group isomorphic to a direct product. Finally, we provide an easy-to-test criterion for finding if a given signal set (or signal space code) obtained as the union of two orbits of the same generating group has the uniform distance property 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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  • Estimation for discrete Markov random fields observed in Gaussian noise

    Publication Year: 1994 , Page(s): 1600 - 1603
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB)  

    A finite state Markov random field is observed in Gaussian noise. Changes of measures are defined under which all random variables of the signal are independent and uniformly distributed over the finite state space and all random variables of the observation are independent and N(0,1). The problem of estimating the most likely signal given the observations is treated in a related form by introducing probabilities over the possible signals View full abstract»

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  • Weight distributions of cosets of two-error-correcting binary BCH codes, extended or not

    Publication Year: 1994 , Page(s): 1425 - 1442
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1264 KB)  

    Let B be the binary two-error-correcting BCH code of length 2m-1 and let Bˆ be the extended code of B. We give formal expressions of weight distributions of the cosets of the codes Bˆ only depending on m. We can then deduce the weight distributions of the cosets of B. When m is odd, it is well known that there are four distinct weight distributions for the cosets of B. So our main result is about the even case. Camion, Courteau, and Montpetit (see ibid., vol.38, no.7, p.1353, 1992) observe that for the lengths 15, 63, and 255 there are eight distinct weight distributions. We prove that this property holds for the codes Bˆ and B for all even m View full abstract»

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  • A lower bound on the expected length of one-to-one codes

    Publication Year: 1994 , Page(s): 1670 - 1672
    Cited by:  Papers (18)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (220 KB)  

    We show that the expected length of any one-to-one encoding of a discrete random variable X is at least H(X)-log(H(X)+1)-log e and that this bound is asymptotically achievable View full abstract»

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  • On the efficiency of on-line density estimators

    Publication Year: 1994 , Page(s): 1504 - 1512
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (568 KB)  

    An on-line density estimator may be defined to be one where each update, following the arrival of a new data value, may be accomplished after no more than a fixed number of calculations. This definition should also apply to any empirical bandwidth selection rule for such an estimator. Recursive estimators comprise only a special case of on-line estimators, but even there, on-line bandwidth formulas have not been developed. The authors introduce a class of on-line estimators, and discuss efficiency in this context. It is shown that some nonrecursive members of the class achieve greater efficiency than any recursive estimators, and that efficiency increases to 100% as the order of the estimated derivative increases. On-line bandwidth selection rules, enabling these high orders of efficiency to be achieved asymptotically, are introduced 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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  • 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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  • 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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  • Nonparametric density estimation for classes of positive random variables

    Publication Year: 1994 , Page(s): 1513 - 1535
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1480 KB)  

    A kernel-based density estimator for positive random variables is proposed and analyzed. In particular, a nonparametric estimator is developed which takes advantage of the fact that positive random variables can be represented as the norms of random vectors. By appropriately choosing the dimension of the assumed vector space, the estimator can be structured to exploit a priori knowledge about the density to be estimated. The asymptotic properties (e.g., pointwise and L1-consistency) of this density estimator are investigated and found to be similar to the desirable features of the standard kernel estimator. An upper bound on the expected value of the L1 error is also derived which provides insight into the behavior of the estimator. Upon using this upper bound, the optimal form for the estimator (i.e., the kernel function, the smoothing factor, etc.) is selected via a minimax strategy. In addition, this upper bound is used to compare the asymptotic performance of the proposed estimator to that of the standard kernel estimator and to boundary-corrected kernel estimators. Numerical examples illustrate that the proposed scheme outperforms the standard and boundary-corrected estimators for a variety of density types View full abstract»

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  • A random coding bound for fixed convolutional codes of rate 1/n

    Publication Year: 1994 , Page(s): 1668 - 1670
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (228 KB)  

    We show that the ensemble average of the block error probability for the ensemble of terminated rate 1/n fixed convolutional codes, used on the binary symmetric channel with a maximum likelihood decoder, is bounded by exp2-NEr(1-K/N), where N=(L+m)n is the block length, L being the message length, K the constraint length, and E r() is the random coding exponent for block codes. Hence, E r(1-K/N)>0 for H(p)<K/N⩽1, where H() is the binary entropy function and p is the cross-over probability of the binary symmetric channel View full abstract»

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  • Good multi-T phase codes under bandwidth and complexity constraints

    Publication Year: 1994 , Page(s): 1699 - 1702
    Cited by:  Papers (1)  |  Patents (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (324 KB)  

    Multi-T phase codes are an equivalent realization of multi-h phase codes within the class of continuous phase modulations (CPM). The authors present, in the form of code tables, the results of a systematic search for binary and quaternary multi-T phase codes which maximize the free Euclidean distance under given bandwidth and complexity constraints View full abstract»

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  • Joint transmitter-receiver optimization for multi-input multi-output systems with decision feedback

    Publication Year: 1994 , Page(s): 1334 - 1347
    Cited by:  Papers (66)  |  Patents (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (964 KB)  

    The joint transmit-receive optimization problem for multiuser communication systems with decision feedback is investigated. It is shown that minimization of the geometric mean-squared error (defined as the determinant of the error covariance matrix) leads to a tractable transmitter optimization problem for general multi-input multi-output decision-feedback systems. Several computational results are included that highlight system performance for a variety of useful transmission scenarios View full abstract»

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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