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Information Theory, IRE Transactions on

Issue 4 • Date October 1961

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Displaying Results 1 - 21 of 21
  • Optimum linear finite-dimensional estimator of signal waveforms

    Page(s): 206 - 215
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    This paper deals with the linear estimation of noise corrupted signal waveforms, from observation over a specified finite time-interval. Two new features are delineated in this paper: 1) the estimating operator is assumed to be finite-dimensional, because economically realizable operators are finite-dimensional in general, and 2) the cost of observation and estimation is taken into account, and assumed to be dependent upon the dimension of the operator only. As a result, the optimum linear finite-dimensional operator that minimizes the risk (the sum of cost and average loss) is obtained for the case in which a quadratic loss function due to error is adopted. View full abstract»

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  • A method of digital signalling in the presence of additive Gaussian noise

    Page(s): 215 - 223
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    This paper considers the basic problem of transmitting digital information through a noisy channel with minimum probability of error in finite time. The transmitted signals are average-power limited, and the noise is assumed to be additive Gaussian with a power spectrum which may be nonwhite. A theory of so-called efficient codes (minimax, equal separation, and nearly equal separation) is developed. Efficient codes are formed from weighted sums of eigenfunctions generated by an integral equation with its kernel corresponding to the inverse Fourier transform of the Gaussian noise power spectrum. In addition, the theory of equidistant and nearly equidistant codes [1] is extended to the case of nonwhite Gaussian noise. It is shown that efficient codes perform better than equidistant codes if the noise is nonwhite; i.e., properly chosen waveforms are more efficient than binary coding. Performance results are given for several different codes when the interference is white Gaussian noise and when the noise power density increases with increasing frequency. The detection scheme used does not require estimation of the signal or the noise levels at the receiver and is thus independent of fading. View full abstract»

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  • Some results on the problem of discriminating between two Gaussian processes

    Page(s): 224 - 233
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    This paper is concerned with certain aspects of the problem of discriminating between two Gaussian processes. The emphasis is on determining approximate optimum detector structures which avoid some of the mathematical difficulties inherent in the evaluation of the exact optimum detector structure. To this end, an approach termed the "inverse operator" approach is presented which leads to approximate detector structures via the Neumann series expansion of linear operator theory. These approximate detectors are found by using a finite number of terms in an "optimun detector" expansion which results from the use of the above Neumann series expansion. A sufficient condition for the rapid convergence of the optimum detector expansion is found to be that the eigenvalues of a certain operator have magnitudes much less than unity. An upper bound is derived for the error incurred at the detector output by the use of a finite number of terms in the optimum detector expansion. Error probabilities are calculated for the case in which the detector outputs may be assumed approximately normally distributed. From an output "signal-to-noise" ratio point of view, it is shown that the performance of the optimum detector and approximate detectors will differ negligibly if the above eigenvalues have squared magnitudes much less than unity. Some upper bounds are derived for the largest eigenvalue (magnitude). View full abstract»

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  • Error correcting codes and their implementation for data transmission systems

    Page(s): 234 - 244
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    Presented here is a practical automatic error-correcting system that may be applied to many data transmission problems. It is particularly suited to the correction of bursts of errors and so may be applied to the problem of the transmission of data over telephone networks. The attractive feature of the system is its remarkable simplicity from the point of view of implementation. It is so simple that it can readily be incorporated into much existing equipment. In the system, messages are transmitted in blocks and each block is coded separately. The codes used within the blocks are cyclic codes. This means that coders and decoders employ linear feedback shift registers to form check digits and to correct errors. The basic ideas are presented in terms of the hardware components to which the system gives rise and analyzed afterwards in terms of mathematics so that it is easy for the engineer to see, at once, what is involved. The theory usually applies to binary messages in which data is transmitted serially. However, an extension is included which shows how the same ideas may be applied to binary codes in which information is sent in parallel. View full abstract»

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  • On the optimum range resolution of radar signals in noise

    Page(s): 245 - 253
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    Optimum radar resolution is recognized to be a problem in distinguishing between different possible target configurations. Radar reception systems which perform optimum range resolution are then designed using the principles of statistical decision theory. In particular, the design of the optimum resolution system is carried out for a squared-error loss function, modified to provide extra penalties for wrong guesses about the number of targets present. Such a system is capable of simultaneously deciding the number of targets present, their spatial positions (ranges) and their relative amplitudes. The analysis also includes a discussion of an optimum device for the resolution of distributed (clutter-like) targets. View full abstract»

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  • Phase shift pulse codes with good periodic correlation properties

    Page(s): 254 - 257
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    A method of generating phase shift pulse codes of arbitrarily long length with zero periodic correlation except for the peak for zero shift is presented. The codes are of length p^2 where p is any prime number, and p different phase shifts corresponding to the p th roots of unity are necessary to generate them. Since p different phase shifts are required, these codes are not as easy to generate and process as the binary codes, but this does not seem to be a serious limitation to their usefulness. Application of these codes can be made as interpulse phase modulation for range resolution in pulse Doppler radars or for a method of synchronizing a pulse code communication system. View full abstract»

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  • Optimum nonlinear filters for quantized inputs

    Page(s): 257 - 265
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    Optimum least-square filters belonging to Zadeh's nonlinear class mathcal{n}_1 are considered. Attention is restricted to those systems whose present output is influenced only by a portion of the past input. The input signal consists of a message and noise, both of which are stationary random processes. It is assumed that the amplitude of the input time series is bounded and takes on discrete values at all times. This assumption leads to a nonlinear filter which can be realized as a quantizer or amplitude selector followed by a parallel set of linear filters. The system becomes optimum when the impulse responses of the linear filters satisfy a system of integral equations of the Wiener-Hopf type adapted to finite memory filters. By virtue of the assumptions made concerning the joint probabilitY density functions of the message and noise processes, it is found that the Fourier transforms of the kernels of these equations are rational functions. A method is developed for the solution of this set of integral equations. This method is illustrated by an example, and the mean-square error of the nonlinear filter so obtained is compared with the best linear filter. View full abstract»

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  • Comments on a paper by Wax [Corresp.]

    Page(s): 270
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    First Page of the Article
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  • Golay's complementary series (Corresp.)

    Page(s): 273 - 276
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    First Page of the Article
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  • Review of 'Lectures on Communication System Theory' (Baghdady, E. J., Ed.; 1961)

    Page(s): 284 - 285
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    Freely Available from IEEE
  • Review of 'An Introduction to Statistical Communication Theory' (Middleton, D.; 1960)

    Page(s): 285 - 286
    Save to Project icon | Request Permissions | PDF file iconPDF (405 KB)  
    Freely Available from IEEE
  • Review of 'Korrelationselectronik (Correlation Electronics)' (Lange, F. H.; 1959)

    Page(s): 286 - 287
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    Freely Available from IEEE
  • Review of 'Sequential Decoding' (Wozencraft, J. M., and Reiffen, B.; 1961)

    Page(s): 287 - 288
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    Freely Available from IEEE

Aims & Scope

This Transactions ceased production in 1962. The current retitled publication is IEEE Transactions on Information Theory.

Full Aims & Scope