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Information Theory, IEEE Transactions on

Issue 1 • Date Jan 1988

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Displaying Results 1 - 23 of 23
  • Syndrome and transition count are uncorrelated [logic circuit testing]

    Publication Year: 1988 , Page(s): 64 - 69
    Cited by:  Papers (5)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (380 KB)  

    In the testing of logic circuits, two proposed data-compression methods use the number of ones (syndrome) and the number of sequence changes (transition count). An enumeration N(m, k , t) of the number of length-m binary sequences having syndrome value k and transition count t is developed. Examination of this result reveals that the parallel compression of these two methods has small overlap in error masking. An asymptotic expression for N(m, k, t) is developed View full abstract»

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  • Bounds on the entropy series

    Publication Year: 1988 , Page(s): 134 - 138
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (324 KB)  

    Upper bounds on the entropy of a countable integer-valued random variable are furnished in terms of the expectation of the logarithm function. In particular, an upper bound is derived that is sharper than that of P. Elias (ibid., vol.IT-21, no.2, p.194-203, 1975), for all values of Ep(log). Bounds that are better only for large values of Ep than the previous known upper bounds are also provided View full abstract»

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  • On the computation of the performance probabilities for block codes with a bounded-distance decoding rule

    Publication Year: 1988 , Page(s): 70 - 78
    Cited by:  Papers (3)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (636 KB)  

    When a block code is used on a discrete memoryless channel with an incomplete decoding rule that is based on a generalized distance, the probability of decoding failure, the probability of erroneous decoding, and the expected number of symbol decoding errors can be expressed in terms of the generalized weight enumerator polynomials of the code. For the symmetric erasure channel, numerically stable methods to compute these probabilities or expectations are proposed for binary codes whose distance distributions are known, and for linear maximum distance separable (MDS) codes. The method for linear MDS codes saves the computation of the weight distribution and yields upper bounds for the probability of erroneous decoding and for the symbol error rate by the cumulative binomial distribution. Numerical examples include a triple-error-correcting Bose-Chaudhuri-Hocquenghem (BCH) code of length 63 and a Reed-Solomon code of length 1023 and minimum distance 31 View full abstract»

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  • A (16, 9, 6, 5, 4) error-correcting DC free block code

    Publication Year: 1988 , Page(s): 138 - 141
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (348 KB)  

    A (2n, k, l, c, d) DC free binary block code is a code of length 2n, constant weight n, 2k codewords, maximum runlength of a symbol l , maximum accumulated charge c, and minimum distance d . The purpose of this code is to achieve DC freeness and error correction at the same time. The goal is to keep the rate k/2 n and d large and l and c small. Of course, these are conflicting goals. H.C. Ferreira (IEEE Trans. Magn., vol.MAG-20, no.5, p.881-3, 1984) presented a (16, 8, 8, 5, 4) DC free code. Here, a (16, 9, 6, 5, 4) DC free code is presented. Easy encoding and decoding algorithms are also given View full abstract»

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  • On runlength codes

    Publication Year: 1988 , Page(s): 45 - 54
    Cited by:  Papers (66)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (584 KB)  

    Several results on binary (d, k) codes are given. First, a novel derivation for the capacity of these codes based on information-theoretic principles is given. Based on this result the spectrum of a (d, k) code is computed. Finally, the problem of computing the capacity of the binary symmetric channel under the condition that the input sequences satisfy the (d, k ) constraint is considered. Lower bounds on the capacity of such a channel are derived View full abstract»

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  • Nonstationary noise effects in the Abel inversion

    Publication Year: 1988 , Page(s): 158 - 161
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (352 KB)  

    A method for calculating the autocorrelation function of the output noise resulting from the Abel inversion of a wide-sense stationary random process is presented. An internal formula that expresses the autocorrelation in terms of the power spectral density of the input noise and explicitly as a function of radial position is derived. Asymptotic approximations for the variance are found for the case of bandlimited white input noise View full abstract»

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  • Arbitrarily varying channels with constrained inputs and states

    Publication Year: 1988 , Page(s): 27 - 34
    Cited by:  Papers (33)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (672 KB)  

    Random coding theorems are proved for discrete memoryless arbitrarily varying channels (AVCs) with constraints on the transmitted codewords and channel state sequences. Two types of constraints are considered: peak (i.e. required for each n-length sequence almost surely) and average (over the message set or over an ensemble). For peak constraints on the codewords and on the channel state sequences, the AVC is shown to have a (strong) random coding capacity. If the codewords and/or the channel state sequences are constrained in the average sense, the AVCs do not possess (strong) capacities; only ε-capacities are shown to exist View full abstract»

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  • Optimization of linear receivers for data communication signals

    Publication Year: 1988 , Page(s): 79 - 92
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1032 KB)  

    The optimization of receivers constrained to consist of a (linear) filter and level slicer is considered for general data communication signals in additive white Gaussian noise. Special consideration is given to the two limiting cases of arbitrarily low and high signal-to-noise ratios (SNRs). The low-SNR case results in an average matched filter receiver; the high-SNR filter is shown to be the solution to a specific nonlinear mathematical problem with a simple geometric interpretation. An efficient algorithm is developed to solve the problem. The results are illustrated for a duobinary minimum-shift-keyed signal observed over an interval of three-symbol-period duration View full abstract»

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  • Modulatable orthogonal sequences and their application to SSMA systems

    Publication Year: 1988 , Page(s): 93 - 100
    Cited by:  Papers (2)  |  Patents (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (480 KB)  

    A set of N-1 orthogonal sequences of period N 2 is proposed, where N is a natural number. Each orthogonal sequence proposed can be modulated by N complex numbers of absolute value 1, so the modulated sequence is also orthogonal. When N is an odd prime number, the absolute value of the cross-correlation function between any two of the N-1 orthogonal sequences is constant and satisfies the mathematical lower bound. This property of the cross-correlation function is not changed when each of the two orthogonal sequences is modulated by N complex numbers of absolute value 1. Two spread-spectrum multiple-access (SSMA) systems using these sequences are proposed. One system is an asynchronous SSMA system, using the proposed sequences unmodulated. The cochannel interference peak between any two channels in this system realizes the mathematical lower bound for an asynchronous SSMA system using a set of orthogonal sequences. The other system is a synchronous SSMA system without cochannel interference which uses the modulated form of the proposed sequences View full abstract»

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  • Coset correlation of m-sequences

    Publication Year: 1988 , Page(s): 141 - 143
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (204 KB)  

    It is well-known that there exists a unique shift l of the m-sequence S(k) such that the value of S0(k)=S(k+l) is only determined by the cyclotomic coset to which k belongs. A measure called the `coset correlation' is introduced. It is proven that the shift l can be determined by the coset correlation View full abstract»

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  • Determination of the merit factor of Legendre sequences

    Publication Year: 1988 , Page(s): 161 - 164
    Cited by:  Papers (16)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (240 KB)  

    M.J.E. Golay (ibid., vol.IT-23, no.1, p.43-51, 1977) has used the ergodicity postulate to calculate that the merit factor F of a Legendre sequence offset by a fraction f of its length has an asymptotic value given by 1/F=(2/3)-4|f|+8f 2, |f|⩽1/2, which gives F=6 for |f |=1/4. Here this is proved without using the ergodicity postulate View full abstract»

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  • Estimating random integrals from noisy observations: sampling designs and their performance

    Publication Year: 1988 , Page(s): 111 - 127
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1012 KB)  

    The problem of estimating a weighted average of a random process from noisy observations at a finite number of sampling points is considered. The performance of sampling designs with optimal or suboptimal, but easily computable, estimator coefficients is studied. Several examples and special cases are studied, including additive independent noise, nonlinear distortion with noise, and quantization noise View full abstract»

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  • Frequency-hopping code sequence designs having large linear span

    Publication Year: 1988 , Page(s): 146 - 151
    Cited by:  Papers (43)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (524 KB)  

    In frequency-hopping spread-spectrum multiple-access communication systems, it is desirable to use sets of hopping patterns that, in addition to having good Hamming correlation properties and large period, are also derived from sequences having large linear span. Here, two such frequency hopping code sequence designs that are based on generalized bent functions and generalized bent sequences are presented. The Hamming correlation properties of the designs are optimal in the first case and close to optimal in the second. In terms of the alphabet size p (required to be prime in both cases), the period and family size of the two designs are given by (p2, p) and (p n, pn/2+1) (n an even integer), respectively. The finite field sequences underlying the patterns in the first design have linear span exceeding p, whereas still larger linear spans (when compared to the sequence period) can be obtained using the second design method View full abstract»

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  • Representations for multivariate reciprocal Gaussian processes

    Publication Year: 1988 , Page(s): 155 - 157
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (308 KB)  

    Multivariate reciprocal Gaussian processes are represented as a sum of two independent processes: a piecewise Markov process, which is also represented in terms of a Wiener-type process, and a time-dependent linear transformation of a normally distributed random vector. This result is then applied to the first-passage time problem View full abstract»

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  • An upper bound on the cutoff rate of sequential decoding

    Publication Year: 1988 , Page(s): 55 - 63
    Cited by:  Papers (14)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (644 KB)  

    An upper bound is given on the cutoff rate of discrete memoryless channels. This upper bound, which coincides with a known lower bound, determines the cutoff rate, and settles a long-standing open problem View full abstract»

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  • Some characterizations of the directed divergence using cyclic symmetry

    Publication Year: 1988 , Page(s): 130 - 134
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (404 KB)  

    An axiomatic characterization of the directed divergence based on a weak condition of cyclic symmetry is given View full abstract»

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  • Sliding-block coding for input-restricted channels

    Publication Year: 1988 , Page(s): 2 - 26
    Cited by:  Papers (32)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1900 KB)  

    Work on coding arbitrary sequences into a constrained system of sequences (called a sofic system) is presented. Such systems model the input constraints for input-restricted channels (e.g., run-length limits and spectral constraints for the magnetic recording channel). In this context it is important that the code be noncatastrophic to ensure that the decoder has limited error propagation. A constructive proof is given of the existence of finite-state invertible noncatastrophic codes from arbitrary n-ary sequences to a sofic system S at constant rate p:q provided only that Shannon's condition (p/q)⩽(h/log n) is satisfied, where h is the entropy of the system S. If strict inequality holds or if equality holds and S satisfies a natural condition called `almost of finite type' (which includes the systems used in practice), a stronger result is obtained, namely, the decoders can be made `state-independent' sliding-block. This generalizes previous results. An example is also given to show that the stronger result does not hold for general sofic systems View full abstract»

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  • Conflict multiplicity estimation and batch resolution algorithms

    Publication Year: 1988 , Page(s): 101 - 110
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (780 KB)  

    The standard model of a multiple-access channel with ternary feedback is considered. When packets of a batch of k nodes initially collide, it is assumed that no a priori statistical information about k is available. An algorithm is presented and analyzed that enables the nodes to compute a statistical estimate of k. Combining the estimation procedure with tree algorithms leads to batch-resolution algorithms that resolve conflicts more efficiently than any other reported to date. Both complete-resolution and partial-resolution algorithms are presented View full abstract»

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  • N-shift cross-orthogonal sequences

    Publication Year: 1988 , Page(s): 143 - 146
    Cited by:  Papers (141)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (304 KB)  

    N-shift cross-orthogonal sequences and a complete complementary code derived from them are defined and discussed. A general method for generating this code is also discussed. A synchronous multiple-user spread-spectrum multiple system is proposed that uses N-shift cross-orthogonal sequences View full abstract»

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  • Bounds for the size of radar arrays

    Publication Year: 1988 , Page(s): 164 - 167
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (240 KB)  

    Improved upper and lower bounds for the size of radar arrays are presented View full abstract»

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  • Number of degrees of freedom, correlation times, and equivalent bandwidths of a random process

    Publication Year: 1988 , Page(s): 151 - 155
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (388 KB)  

    New definitions for the number of degrees of freedom (NDF) of a stationary process are proposed and their general form derived for Gaussian processes. Correlation times and equivalent bandwidths, which have been important in random processes and some fields in physics, are deduced from the first-order and second-order NDF and studied View full abstract»

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  • Balancing sets of vectors

    Publication Year: 1988 , Page(s): 128 - 130
    Cited by:  Papers (26)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (292 KB)  

    For n>0, d⩾0, nd (mod 2), let K(n, d) denote the minimal cardinality of a family V of ±1 vectors of dimension n, such that for any ±1 vector w of dimension n there is a vV such that |v- w|⩽d, where v-w is the usual scalar product of v and w. A generalization of a simple construction due to D.E. Knuth (1986) shows that K(n , d)⩽[n/(d+1)]. A linear algebra proof is given here that this construction is optimal, so that K(n, d)-[n/(d+1)] for all nd (mod 2). This construction and its extensions have applications to communication theory, especially to the construction of signal sets for optical data links View full abstract»

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  • Totally asynchronous Slepian-Wolf data compression

    Publication Year: 1988 , Page(s): 35 - 44
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (668 KB)  

    It is proved that the Slepian-Wolf data compression theorem still holds when both encoders are operating totally asynchronously. In addition it is shown that in this case the Wyner-Ahlswede-Korner source-coding theorem holds 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