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Information Theory, IEEE Transactions on

Issue 5 • Date September 1970

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Displaying Results 1 - 25 of 31
  • On exponential smoothing of discrete time series (Corresp.)

    Publication Year: 1970 , Page(s): 630
    Cited by:  Papers (1)
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    The k th-order exponential filter is analyzed using a two-dimensional z transform. The weighting functions for both the data and the initial conditions are derived. View full abstract»

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  • Comments on "Polynomial codes" by Kasami, T., Lin, S., and Peterson, W.W.

    Publication Year: 1970 , Page(s): 635 - 638
    Cited by:  Papers (1)
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  • On permutation decoding of binary cyclic double-error-correcting codes of certain lengths (Corresp.)

    Publication Year: 1970 , Page(s): 641 - 643
    Cited by:  Papers (4)
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  • Comments on "A note on the nonbinary BCH code" by Ong, A.

    Publication Year: 1970 , Page(s): 648 - 649
    Cited by:  Patents (1)
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  • Review of 'Theory of Automata' (Salomaa, A.; 1969)

    Publication Year: 1970 , Page(s): 652 - 653
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    Freely Available from IEEE
  • Correction to A Lower Bound for Discrimination Information in Terms of Variation

    Publication Year: 1970 , Page(s): 652
    Cited by:  Papers (5)
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  • Review of Statistical Theory of Signal Detection, 2nd edn.(Helstrom, C. W.; 1968)

    Publication Year: 1970 , Page(s): 653 - 654
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    Freely Available from IEEE
  • Design of signals for analog communication

    Publication Year: 1970 , Page(s): 581 - 587
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (960 KB)  

    A method for the design of time-limited and effectively band-limited waveforms for analog communication systems is developed. The design problem is first formulated in the L_2 (0, T) space. Nonlinear modulation threshold effects are incorporated directly into the design by introducing constraints in the form of minimum distance between points on the locus. It is shown that all pertinent information can be expressed in terms of the inner product function generated by the locus and its cross derivative. The design is then transformed into a constrained minimization problem in a space of inner product functions. The cases of stationary locus and N -dimensional locus are further investigated. View full abstract»

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  • On Gaussian noise envelopes

    Publication Year: 1970 , Page(s): 522 - 528
    Cited by:  Papers (5)
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    The first-passage time problem for a continuous one-dimensional Markov process is reviewed, and upper bounds are obtained for both the probability of failure (or passage and the moments of the time to failure, in terms of the mean time to failure. In addition, stationary Gaussian variables arising from systems with N degrees of freedom that have autocorrelation functions of the form begin{equation} R(r) = e^{-b mid tau mid} sum_{k=1}^{N} d_k^2 cos omega_k tau end{equation} are shown to be derivable from a 2N -dimensional (or 2N - 1, if one of the \omega _k is zero) Markov process that possesses a "pseudoenvelope," which is itself the result of a one-dimensional Markov process. This pseudo-envelope can be used as a bound on the magnitude of the Gaussian variable, and its first-passage time problem can be solved explicitly or utilized to obtain convenient bounds for the probability of failure of the Gaussian process. View full abstract»

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  • Dynamical representation of Markov processes of the separable class

    Publication Year: 1970 , Page(s): 529 - 534
    Cited by:  Papers (2)
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    The mean-squared continuous Markov process of the separable class is represented by a nonlinear stochastic differential equation. The representation for the strictly stationary case implies that the process is determined by its autocorrelation function and first-order probability density function. A class of stationary Markov separable processes may be obtained by a zero-memory nonlinear (ZNL) transformation of a wider class of stationary Markov processes. A special case of the multidimensional process is shown to result in a separable process of degree N . Several examples are considered to illustrate the representation. View full abstract»

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  • Concatenation schemes for the Gaussian channel with feedback (Corresp.)

    Publication Year: 1970 , Page(s): 632 - 635
    Cited by:  Papers (1)
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    The use of feedback with concatenation is proposed as a technique for achieving the desired performance with less system complexity. Feedback can be used with the inner code, outer code, or both. The concatenation error exponents for several feedback schemes employing the Gaussian channel are determined analytically and found to be significantly better than those of the channel with no feedback. View full abstract»

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  • On Rudolph's majority-logic decoding algorithm (Corresp.)

    Publication Year: 1970 , Page(s): 651 - 652
    Cited by:  Papers (7)
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    In this correspondence, a modification of Rudolph's one-step majority-logic decoding algorithm is introduced. Using this modification, it is proved that all single-error-correcting codes can be one-step majority decoded. View full abstract»

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  • Image detection through bipolar correlation

    Publication Year: 1970 , Page(s): 534 - 541
    Cited by:  Papers (11)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1168 KB)  

    The purpose of this paper is to describe the bipolar reference concept. A bipolar reference is simply a reference that can take on a continuous range of both positive and negative numerical values. It will be shown that for map matching via the convolution operation, references that yield maximum signal-to-noise ratios, in general, will be bipolar references. Algorithms for generating bipolar references and digital simulation results are given. View full abstract»

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  • On decoding iterated codes

    Publication Year: 1970 , Page(s): 624 - 627
    Cited by:  Papers (20)  |  Patents (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (616 KB)  

    Algorithms to decode iterated codes when at least one of the "component codes" is majority decodable are given. The decoding algorithms allow the use of the decoders of the component codes and still make it possible to correct all error patterns guaranteed to be correctable by the minimum distance of the iterated code. View full abstract»

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  • A note on the free distance of a convolutional code (Corresp.)

    Publication Year: 1970 , Page(s): 646 - 648
    Cited by:  Papers (2)
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    A counterexample to a conjecture on the number of constraint lengths required to achieve the free distance of a rate 1/n systematic convolutional code is presented. View full abstract»

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  • The equivalence of rank permutation codes to a new class of binary codes (Corresp.)

    Publication Year: 1970 , Page(s): 640 - 641
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (336 KB)  

    An equivalence between the rank permutation codes and a new class of binary codes has been observed. A binary code may be generated by direct transformation of a permutation code. The binary codes are usually nonlinear and may be decoded by the inverse transformation and rank correlation of the equivalent permutation. View full abstract»

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  • Sequential decoding of systematic and nonsystematic convolutional codes with arbitrary decoder bias

    Publication Year: 1970 , Page(s): 611 - 624
    Cited by:  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1632 KB)  

    This paper presents several results involving Fano's sequential decoding algorithm for convolutional codes. An upper bound to the a th moment of decoder computation is obtained for arbitrary decoder bias B and a \leq 1 . An upper bound on error probability with sequential decoding is derived for both systematic and nonsystematic convolutional codes. This error bound involves the exact value of the decoder bias B . It is shown that there is a trade-off between sequential decoder computation and error probability as the bias B is varied. It is also shown that for many values of B , sequential decoding of systematic convolutional codes gives an exponentially larger error probability than sequential decoding of nonsystematic convolutional codes when both codes are designed with exponentially equal optimum decoder error probabilities. View full abstract»

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  • A class of continuous signal-design problems in burst noise

    Publication Year: 1970 , Page(s): 570 - 581
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1688 KB)  

    In this paper, signal design in a burst-noise environment is considered. Two distinct approaches are presented, each resulting in a class of signals for which the trade-off between signal bandwidth and immunity to large-amplitude bursts is shown. In the first approach the design is treated as an optimization problem subject to energy and endpoint constraints in a fixed time interval, and a uniform probability distribution of the location of the burst within the interval. The second approach considers signal design as a two-player differential game, where design flexibliity is obtained through the second player's choice of an initial value in the resulting differential equation. Performance curves for signals designed by using both methods are compared. It is shown how the first design procedure is easily extended to M -ary alphabets, thus obtaining the full advantage of the proposed technique. View full abstract»

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  • The probability density function for the output of an analog crosscorrelator with bandpass inputs (Corresp.)

    Publication Year: 1970 , Page(s): 627 - 629
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (464 KB)  

    A general solution is obtained for the probability density function of the low-pass output of a crosscorrelator with bandpass inputs. The input signals are sinusoidal with arbitrary amplitudes and phases, and the noise inputs are Gaussian and uncorrelated. An approximation to simplify the necessary calculations is developed and examined. View full abstract»

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  • Sequential structure and parameter-adaptive pattern recognition--I: Supervised learning

    Publication Year: 1970 , Page(s): 548 - 556
    Cited by:  Papers (11)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1440 KB)  

    Bayes optimal sequential structure and parameter-adaptive pattern-recognition systems for continuous data are derived. Both off-line (or prior to actual operation) and on-line (while in operation) supervised learning is considered. The concept of structure adaptation is introduced and both structure as well as parameter-adaptive optimal pattern-recognition systems are obtained. Specifically, for the class of supervised-learning pattern-recognition problems with Gaussian process models and linear dynamics, the adaptive pattern-recognition systems are shown to be decomposable ("partition theorem") into a linear nonadaptive part consisting of recursive matched Kalman filters, a nonlinear part--a set of probability computers--that incorporates the adaptive nature of the system, and finally a part of the correlator-estimator (Kailath) form. Extensions of the above results to the M -ary hypotheses case where M \geq 2 are given. View full abstract»

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  • A distribution-free discrimination procedure based on clustering

    Publication Year: 1970 , Page(s): 541 - 548
    Cited by:  Papers (6)
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    A method is presented for constructing distribution-free tolerance regions for one distribution based on the clusters of the sample from a second distribution. The tolerance regions are constructed so as to minimize the probability of reserve judgment in a two-class discrimination procedure that allows the conditional error probabilities to be controlled within prescribed upper bounds. The method results in discrimination functions that are easily implemented on a computer. Although the method is not, in general, consistent with optimal procedures, it is appealing for high-dimensional problems with multimodal distributions. View full abstract»

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  • Systematic construction of self-orthogonal diffuse codes

    Publication Year: 1970 , Page(s): 594 - 604
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1528 KB)  

    A systematic procedure for constructing binary self-orthogonal diffuse codes is presented. These codes correct both random and burst errors. A lower bound on actual constraint length for this class of codes is found. The given construction procedure generally yields codes that approach the lower bound for large burst error correction and are, therefore, asymptotically optimal. View full abstract»

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  • On unsupervised estimation algorithms

    Publication Year: 1970 , Page(s): 556 - 569
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1528 KB)  

    There are several approaches to unsupervised estimation that have application to problems of communications, control, and pattern recognition. This paper presents properties of several different digitally implemented algorithms suitable for unsupervised estimation. One result is the rate of convergence in mean square of the Bayes solution for a discretized parameter space. A regression function that is the expected value of the natural logarithm of the mixture probability density function naturally arises from the Bayes approach. This regression function can be used to devise unsupervised estimation algorithms of the stochastic approximation form. Also, the asymptotic solution and rates of convergence in mean square of a class of minimum-integral-square-difference algorithms are determined. Two other estimators that use a "net" on the parameter space are also presented. View full abstract»

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  • Best Fire codes with length up to 1200 bits (Corresp.)

    Publication Year: 1970 , Page(s): 649 - 650
    Cited by:  Papers (1)  |  Patents (1)
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    This correspondence presents 11 tables of best unshortened Fire codes of length up to 1200 bits, classified into groups according to their relative redundancy. View full abstract»

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  • The behavior of analog communication systems

    Publication Year: 1970 , Page(s): 587 - 594
    Cited by:  Papers (21)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1024 KB)  

    We consider the problem of transmission of analog data over a noisy channel. It is assumed that the channel input is of the form \surd S f(t, X) , where X is an n -dimensional source vector, and S is the allowable transmitted power. The performance of any given modulation scheme f(t, \cdot ) as a function of the transmitted power S is studied. Lower bounds on the average distortion produced by noise for a class of distortion functions are derived. These bounds relate the "smoothness" of modulation techniques to the minimum error that can be achieved with them. It is shown that when the analog source emits a sequence of mutually independent real random variables at a rate of R per second, the mean-square error that is associated with any practical modulation scheme f(t, \cdot) decays no faster than S^{-2} as the signal power S \rightarrow \infty . It follows that in the case of a band-limited additive white Gaussian channel no single modulation scheme f(t, \cdot ) can achieve the ideal rate-distortion bound on the mean-square error for all values of S , if the channel bandwidth is larger than the source rate R . 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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Meet Our Editors

Editor-in-Chief
Frank R. Kschischang

Department of Electrical and Computer Engineering