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Information Theory, IEEE Transactions on

Issue 3 • Date May 2000

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Displaying Results 1 - 25 of 46
  • Fundamentals of Convolutional Coding [Book Reviews]

    Publication Year: 2000 , Page(s): 1178 - 1179
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    Freely Available from IEEE
  • Contributors

    Publication Year: 2000 , Page(s): 1180 - 1189
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    Freely Available from IEEE
  • Quantum error detection .II. Bounds

    Publication Year: 2000 , Page(s): 789 - 800
    Cited by:  Papers (13)
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    For pt.I see ibid., vol.46, no.3, p.778-88 (2000). In Part I of this paper we formulated the problem of error detection with quantum codes on the depolarizing channel and gave an expression for the probability of undetected error via the weight enumerators of the code. In this part we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent. The lower (existence) bound is proved for stabilizer codes by a counting argument for classical self-orthogonal quaternary codes. Upper bounds are proved by linear programming. First we formulate two linear programming problems that are convenient for the analysis of specific short codes. Next we give a relaxed formulation of the problem in terms of optimization on the cone of polynomials in the Krawtchouk basis. We present two general solutions of the problem. Together they give an upper bound on the exponent of undetected error. The upper and lower asymptotic bounds coincide for a certain interval of code rates close to 1 View full abstract»

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  • Sphere-bound-achieving coset codes and multilevel coset codes

    Publication Year: 2000 , Page(s): 820 - 850
    Cited by:  Papers (75)  |  Patents (2)
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    A simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array L and its error probability on an additive white Gaussian noise (AWGN) channel. It is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding, including certain binary lattices. These codes have structure of the kind that has been found to be useful in practice. Capacity curves and design guidance for practical codes are given. Exponential error bounds for coset codes are developed, generalizing Poltyrev's (1994) bounds for lattices. These results are based on the channel coding theorems of information theory, rather than the Minkowski-Hlawka theorem of lattice theory View full abstract»

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  • The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel

    Publication Year: 2000 , Page(s): 933 - 946
    Cited by:  Papers (320)  |  Patents (32)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (316 KB)  

    We present a model for time-varying communication single-access and multiple-access channels without feedback. We consider the difference between mutual information when the receiver knows the channel perfectly and mutual information when the receiver only has an estimate of the channel. We relate the variance of the channel measurement error at the receiver to upper and lower bounds for this difference in mutual information. We illustrate the use of our bounds on a channel modeled by a Gauss-Markov process, measured by a pilot tone. We relate the rate of time variation of the channel to the loss in mutual information due to imperfect knowledge of the measured channel View full abstract»

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  • Reversible arithmetic coding for quantum data compression

    Publication Year: 2000 , Page(s): 1104 - 1116
    Cited by:  Papers (10)
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    We study the problem of compressing a block of symbols (a block quantum state) emitted by a memoryless quantum Bernoulli source. We present a simple-to-implement quantum algorithm for projecting, with high probability, the block quantum state onto the typical subspace spanned by the lending eigenstates of its density matrix. We propose a fixed-rate quantum Shannon-Fano code to compress the projected block quantum state using a per-symbol code rate that is slightly higher than the von Neumann (1955) entropy limit. Finally, we propose quantum arithmetic codes to efficiently implement quantum Shannon-Fano (1948) codes. Our arithmetic encoder and decoder have a cubic circuit and a cubic computational complexity in the block size. Both the encoder and decoder are quantum-mechanical inverses of each other, and constitute an elegant example of reversible quantum computation View full abstract»

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  • Interference estimation with applications to blind multiple-access communication over fading channels

    Publication Year: 2000 , Page(s): 947 - 961
    Cited by:  Papers (20)
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    We consider the detection of nonorthogonal multipulse signals on multiple-access fading channels. The generalized maximum-likelihood rule is employed to decode users whose complex fading gains are unknown. We develop geometrical interpretations for the resulting detectors and their corresponding asymptotic efficiencies. The generalized maximum-likelihood detection rule is then applied to find a matched subspace detector for the frequency-selective fading channel, under the assumption of a short coherence time (or long coherence time without the computational power to track the fading parameters). We propose blind implementations of these detectors for nonorthogonal multipulse signaling on both frequency-nonselective and frequency-selective multiple-access fading channels. These blind detectors extend the results of Wang and Poor (see ibid., vol.44, p.677-89, 1998) to multipulse modulation and fast frequency selective fading. For comparison, the minimum mean-squared error decision rules for these channels are derived and blind implementations of their corresponding detectors are developed View full abstract»

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  • Minimum Chernoff entropy and exponential bounds for locating changes

    Publication Year: 2000 , Page(s): 1168 - 1170
    Cited by:  Papers (1)
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    Large deviation theory makes extensive use of Chernoff exponential bounds to establish exert rates of convergence for certain probabilities. In this article, stronger exponential bounds from martingale theory are utilized to give results on the errors of the maximum-likelihood estimate of the location of a change between two probability measures in terms of the minimum Chernoff entropy (MCE). For example, the probability of estimating the change point exactly is bigger than one minus twice the MCE. These results support the use of the MCE as an appropriate distance measure between probability measures for applications such as the automatic classification of digital modulation signal constellations View full abstract»

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  • CDMA systems in fading channels: admissibility, network capacity, and power control

    Publication Year: 2000 , Page(s): 962 - 981
    Cited by:  Papers (18)
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    We study the admissibility and network capacity of imperfect power-controlled code-division multiple access (CDMA) systems with linear receivers in fading environments. In a CDMA system, a set of users is admissible if their simultaneous transmission does not result in violation of any of their quality-of-service (QoS) requirements; the network capacity is the maximum number of admissible users. We consider a single-cell imperfect power-controlled CDMA system, assuming known received power distributions. We identify the network capacities of single-class systems with matched-filter (MF) receivers for both the deterministic and random signature cases. We also characterize the network capacity of single-class systems with linear minimum-mean-square-error (MMSE) receivers for the deterministic signature case. The network capacities can be expressed uniquely in terms of the users' signal-to-interference ratio (SIR) requirements and received power distributions. For multiple-class systems equipped with MF receivers, we find a necessary and sufficient condition on the admissibility for the random signature case, but only a sufficient condition for the deterministic signature case. We also introduce the notions of effective target SIR and effective bandwidth, which are useful in determining the admissibility and hence network capacity of an imperfect power-controlled system View full abstract»

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  • A minimax robust decoding algorithm

    Publication Year: 2000 , Page(s): 1158 - 1167
    Cited by:  Papers (1)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (328 KB)  

    We study the decoding problem in an uncertain noise environment. If the receiver knows the noise probability density function (PDF) at each time slot or its a priori probability, the standard Viterbi (1967) algorithm (VA) or the a posteriori probability (APP) algorithm can achieve optimal performance. However, if the actual noise distribution differs from the noise model used to design the receiver, there can be significant performance degradation due to the model mismatch. The minimax concept is used to minimize the worst possible error performance over a family of possible channel noise PDFs. We show that the optimal robust scheme is difficult to derive; therefore, alternative, practically feasible, robust decoding schemes are presented and implemented on a VA decoder and two-way APP decoder. The performance analysis and numerical results show our robust decoders have a performance advantage over standard decoders in uncertain noise channels, with no or little computational overhead. Our robust decoding approach can also explain why for turbo decoding overestimating the noise variance gives better results than underestimating it View full abstract»

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  • Asymptotic redundancies for universal quantum coding

    Publication Year: 2000 , Page(s): 801 - 819
    Cited by:  Papers (6)
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    Clarke and Barren (1990, 1994, 1995) have shown that the Jeffreys' invariant prior of Bayesian theory yields the common asymptotic (minimax and maximin) redundancy of universal data compression in a parametric setting. We seek a possible analog of this result for the two-level quantum systems. We restrict our considerations to prior probability distributions belonging to a certain one-parameter family, qu,-∞<u<1. Within this setting, we are able to compute exact redundancy formulas, for which we find the asymptotic limits. We compare our quantum asymptotic redundancy formulas to those derived by naively applying the (nonquantum) counterparts of Clarke and Barren, and find certain common features. Our results are based on formulas we obtain for the eigenvalues and eigenvectors of 2n×2n (Bayesian density) matrices, ζ n(u). These matrices are the weighted averages (with respect to qu) of all possible tensor products of n identical 2×2 density matrices, representing the two-level quantum systems. We propose a form of universal coding for the situation in which the density matrix describing an ensemble of quantum signal states is unknown. A sequence of n signals would be projected onto the dominant eigenspaces of ζn(u) View full abstract»

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  • Grammar-based codes: a new class of universal lossless source codes

    Publication Year: 2000 , Page(s): 737 - 754
    Cited by:  Papers (72)  |  Patents (14)
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    We investigate a type of lossless source code called a grammar-based code, which, in response to any input data string x over a fixed finite alphabet, selects a context-free grammar Gx representing x in the sense that x is the unique string belonging to the language generated by Gx. Lossless compression of x takes place indirectly via compression of the production rules of the grammar Gx. It is shown that, subject to some mild restrictions, a grammar-based code is a universal code with respect to the family of finite-state information sources over the finite alphabet. Redundancy bounds for grammar-based codes are established. Reduction rules for designing grammar-based codes are presented View full abstract»

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  • Rate gains in block-coded modulation systems with interblock memory

    Publication Year: 2000 , Page(s): 851 - 868
    Cited by:  Papers (1)
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    This paper examines the performance gains achievable by adding interblock memory to, and altering the mapping of coded bits to symbols in, block-coded modulation systems. The channel noise considered is additive Gaussian, and the twin design goals are to maximize the asymptotic coding gain and to minimize the number of apparent nearest neighbors. In the case of the additive white Gaussian noise channel, these goals translate into the design of block codes of a given weighted or `normalized' distance whose rate is as high as possible, and whose number of codewords at minimum normalized distance is low. The effect of designing codes for normalized distance rather than Hamming distance is to ease the problem of determining the best codes for given parameters in the cases of greatest interest, and many such best codes are given View full abstract»

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  • Some bounds for the minimum length of binary linear codes of dimension nine

    Publication Year: 2000 , Page(s): 1053 - 1056
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    We prove the nonexistence of binary [69,9,32] codes and construct codes with parameters [76,9,34],[297,9,146], and [300,9,148]. These results show that n(9,32)=70, n(9,34)⩽76,n(9,146)=297, and n(9,148)=300, where n(k,d) denotes the smallest value of n for which there exists an [n,k,d] binary code. We also present some codes of minimum distance 32 and some related codes View full abstract»

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  • On the Hamming distance of linear codes over a finite chain ring

    Publication Year: 2000 , Page(s): 1060 - 1067
    Cited by:  Papers (24)
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    Let R be a finite chain ring (e.g., a Galois ring), K its residue field, and C a linear code over R. We prove that d(C), the Hamming distance of C, is d((¯C¯:¯α¯)¯), where (C:α) is a submodule quotient, α is a certain element of R, and denotes the canonical projection to K. These two codes also have the same set of minimal codeword supports. We explicitly construct a generator matrix/polynomial of (¯C¯:¯α¯)¯ from the generator matrix/polynomials of C. We show that in general d(C)⩽d(C¯) with equality for free codes (i.e., for free R-submodules of Rn) and in particular for Hensel lifts of cyclic codes over K. Most of the codes over rings described in the literature fall into this class. We characterize minimum distance separable (MDS) codes over R and prove several analogs of properties of MDS codes over finite fields. We compute the Hamming weight enumerator of a free MDS code over R View full abstract»

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  • Genetic search for Golomb arrays

    Publication Year: 2000 , Page(s): 1170 - 1173
    Cited by:  Papers (2)
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    Genetic search with a decision level chromosome is used to search efficiently for Golomb (1982) arrays. A Golomb array A is a binary array with three values for its discrete autocorrelation function; M, the number of ones in A for no offset, 1 when there is partial overlap, and 0 otherwise. In one dimension, A is known as a Golomb ruler. The method yields improvement because the genetic search considers only feasible solutions in the most likely portion of the search space. Each chromosome bit represents a decision to place a one in an iterative construction. The representation includes all possible arrays. Since the chromosome bits represent binary decisions in the search space, genetic operations (such as crossover and mutation) always result in feasible descendent chromosomes. Experimental results include comparison to previously known search methods and several new arrays. These results indicate that the proposed search is significantly more efficient than prior methods View full abstract»

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  • An entropy theorem for computing the capacity of weakly (d,k)-constrained sequences

    Publication Year: 2000 , Page(s): 1034 - 1038
    Cited by:  Papers (1)
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    We find an analytic expression for the maximum of the normalized entropy -ΣiεTpiln piiεTipi where the set T is the disjoint union of sets Sn of positive integers that are assigned probabilities Pn, ΣnPn =1. This result is applied to the computation of the capacity of weakly (d,k)-constrained sequences that are allowed to violate the (d,k)-constraint with small probability View full abstract»

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  • New rate pairs in the zero-error capacity region of the binary multiplying channel without feedback

    Publication Year: 2000 , Page(s): 1043 - 1046
    Cited by:  Papers (6)
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    We construct uniquely decodable (UD) code pairs for the binary multiplying channel without feedback, using pairs of binary codes. By taking appropriate cosets of linear codes with many information sets for these binary codes, we obtain new rate pairs in the zero-error capacity region Z of this channel. In particular, the rate pair (log(3/2), log(3/2)) is in Z and yields the largest known sum of the rates of pairs in Z. As this rate pair can be achieved with UD pairs with equal members, we have obtained an asymptotically optimal construction for the combinatorial concept of cancellative families of sets View full abstract»

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  • Constructions of authentication codes from algebraic curves over finite fields

    Publication Year: 2000 , Page(s): 886 - 892
    Cited by:  Papers (3)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (180 KB)  

    We present a new application of algebraic curves over finite fields to the constructions of universal hash families and unconditionally secure codes. We show that the constructions derived from the Garcia-Stichtenoth curves yield new classes of authentication codes and universal hash families which are substantially better than those previously known View full abstract»

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  • Waveform selection in radar target classification

    Publication Year: 2000 , Page(s): 1014 - 1029
    Cited by:  Papers (37)
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    We apply a sequential experiment design procedure to the problem of signal selection for radar target classification. Radar waveforms are designed to discriminate between targets possessing a doubly spread reflectivity function that are observed in clutter. The waveforms minimize decision time by maximizing the discrimination information in the echo signal. Each waveform selected maximizes the Kullback-Leibler (1951) information number that measures the dissimilarity between the observed target and the alternative targets. We discuss in details two scenarios. In the first scenario, the target environment is assumed fixed during illumination. In this case, the optimal waveform selection strategy leads to a fixed library of waveforms. During actual classification, the sequence in which the waveforms are selected from the library is determined from the noise to clutter power in the range-Doppler support of the targets. In the second scenario, the target environment changes between pulse transmissions. In this case, the maximum discrimination information is obtained by a repeated transmission of a single waveform designed from the reflectivity function of the targets. We show that our choice of signals can produce significant gains in detection performance View full abstract»

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  • On the AEP of word-valued sources

    Publication Year: 2000 , Page(s): 1116 - 1120
    Cited by:  Papers (4)
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    We consider a new class of information sources called word-valued sources in order to investigate coding algorithms based upon string parsing. A word-valued source is defined as a pair of an independent and identically distributed (i.i.d.) source with a countable alphabet and a function that maps each symbol into a finite sequence over a finite alphabet. A word-valued source is a nonstationary process and has countable states. If the function of a word-valued source is prefix-free, the entropy rate is characterized with a simple expression and the AEP (asymptotic equipartition property) holds View full abstract»

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  • Quasi-orthogonal sequences for code-division multiple-access systems

    Publication Year: 2000 , Page(s): 982 - 993
    Cited by:  Papers (45)  |  Patents (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (372 KB)  

    The notion of quasi-orthogonal sequence (QOS) as a means of increasing the number of channels in synchronous code-division multiple-access (CDMA) systems that employ Walsh sequences for spreading information signals and separating channels is introduced. It is shown that a QOS sequence may be regarded as a class of Bent (almost Bent) functions possessing, in addition, a certain window property. Such sequences while increasing the system capacity, minimize interference to the existing set of Walsh sequences. The window property gives the system the ability to handle variable data rates. A general procedure of constructing QOSs from well-known families of binary sequences with good correlation, including the Kasami and Gold (1967) sequence families, as well as from the binary Kerdock code is provided. Examples of QOSs are presented for small lengths. Some examples of quaternary QOSs drawn from Family A are also included View full abstract»

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  • Tracing traitors

    Publication Year: 2000 , Page(s): 893 - 910
    Cited by:  Papers (79)  |  Patents (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (356 KB)  

    We give cryptographic schemes that help trace the source of leaks when sensitive or proprietary data is made available to a large set of parties. A very relevant application is in the context of pay television, where only paying customers should be able to view certain programs. In this application, the programs are normally encrypted, and then the sensitive data is the decryption keys that are given to paying customers. If a pirate decoder is found, it is desirable to reveal the source of its decryption keys. We describe fully resilient schemes which can be used against any decoder which decrypts with nonnegligible probability. Since there is typically little demand for decoders which decrypt only a small fraction of the transmissions (even if it is nonnegligible), we further introduce threshold tracing schemes which can only be used against decoders which succeed in decryption with probability greater than some threshold. Threshold schemes are considerably more efficient than fully resilient schemes View full abstract»

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  • On the asymptotic normality of hierarchical mixtures-of-experts for generalized linear models

    Publication Year: 2000 , Page(s): 1005 - 1013
    Cited by:  Papers (7)
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    In the class of hierarchical mixtures-of-experts (HME) models, “experts” in the exponential family with generalized linear mean functions of the form ψ(α+xTβ) are mixed, according to a set of local weights called the “gating functions” depending on the predictor x. Here ψ(·) is the inverse link function. We provide regularity conditions on the experts and on the gating functions under which the maximum-likelihood method in the large sample limit produces a consistent and asymptotically normal estimator of the mean response. The regularity conditions are validated for Poisson, gamma, normal, and binomial experts View full abstract»

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  • Distance-spectrum formulas on the largest minimum distance of block codes

    Publication Year: 2000 , Page(s): 869 - 885
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (576 KB)  

    A general formula for the asymptotic largest minimum distance (in block length) of deterministic block codes under generalized distance functions (not necessarily additive, symmetric, and bounded) is presented. As revealed in the formula, the largest minimum distance can be fully determined by the ultimate statistical characteristics of the normalized distance function evaluated under a properly chosen random-code generating distribution. Interestingly, the new formula has an analogous form to the general information-spectrum expressions of the channel capacity and the optimistic channel capacity, respectively derived by Verdu and Han (1994) and Chen and Alajaji (1998, 1999). As a result, a minor class of distance functions for which the largest minimum distance can be derived is characterized. A general Varshamov-Gilbert lower bound is next addressed. Some discussions on the tightness of the general Varshamov-Gilbert bound are also provided. Finally, lower bounds on the largest minimum distances for several specific block coding schemes are rederived in terms of the new formulas, followed by comparisons with the known results devoted to the same codes 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