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Information Theory, IEEE Transactions on

Issue 2 • Date March 1968

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Displaying Results 1 - 25 of 27
  • Nonbinary BCH decoding (Abstr.)

    Publication Year: 1968 , Page(s): 242
    Cited by:  Papers (17)
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    The decoding of BCH codes readily reduces to the solution of a certain key equation. An iterative algorithm is presented for solving this equation over any field. Following a heuristic derivation of the algorithm, a complete statement of the algorithm and proofs of its principal properties are given. The relationship of this algorithm to the classical matrix methods and the simplification which the algorithm takes in the special case of binary codes is then discussed. The generalization of the algorithm to BCH codes with a slightly different definition, the generalization of the algorithm to decode erasures as well as errors, and the extension of the algorithm to decode more than t errors in certain eases are also presented. View full abstract»

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  • Review of 'Computation: Finite and Infinite Machines' (Minsky, Marvin; 1967)

    Publication Year: 1968 , Page(s): 354 - 355
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    Freely Available from IEEE
  • Rapid acquisition sequences

    Publication Year: 1968 , Page(s): 221 - 225
    Cited by:  Papers (5)  |  Patents (2)
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    A recurring communications systems problem involves the determination, with relatively high precision, of the phase of a periodic, noise-corrupted signal. Perhaps the most commonly proposed signals for such purposes are pseudorandom sequences. Indeed, such signals are known to be optimum, at least when the noise is white and Gaussian, in the sense of minimizing the time needed to find the correct phase with a specified reliability. Equipment limitations, however, often preclude the efficient use of these sequences. In particular, suppose the received signal is known to be of the form y(t) = x(t - \nu \Delta T) + n(t) , with x(t) a signal periodic with period T , and n(t) additive white Gaussian noise. The problem is to determine as reliably and rapidly as possible the "phase" \nu of the received signal. The optimum detector involves the formation of the N = \Delta T/T correlations I_{\nu} = \int y(t)x(t - \nu \Delta T) dt and the selection of the largest of these. Frequently, however, equipment constraints force these correlations to be made serially. In this event, the required search time can be as much as N times as great as that needed in the absence of such constraints. Even the most sophisticated sequential search algorithms require search times directly proportional to N , the number of contending phases. In this paper a class of binary sequences is demonstrated which require a search time on the order of only (log2 N)2, a substantial improvement when N is large. These sequences are shown to be essentially optimum under the conditions outlined. View full abstract»

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  • A 'best' mismatched filter response for radar clutter discrimination

    Publication Year: 1968 , Page(s): 280 - 287
    Cited by:  Papers (39)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (896 KB)  

    The response of a mismatched filter which will reduce the effects of radar clutter energy on signal detection is considered in this paper. Clutter is assumed to result from scatterers having a range-velocity distribution different from that of a desired target. A tradeoff between signal-to-clutter ratio (SCR) and signal-to-noise ratio (SNR) is made. The mathematical treatment involves controlling the distribution of the volume of the squared magnitude t/f cross-correlation function associated with a given transmitted waveform and the response of the mismatched receiving filter. A measure of this volume is minimized for variations in mismatched filter response under suitable constraints on the output signal and noise powers. The essential result is contained in a linear integral equation. A method of solution is illustrated which enables one to choose a "best" tradeoff between SCR and SNR. View full abstract»

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  • The uncorrelated output components of a nonlinearity

    Publication Year: 1968 , Page(s): 250 - 255
    Cited by:  Papers (20)
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    Using his characteristic-function approach, Rice (1945) obtained a double series for the autocorrelation function of a sinusoidal signal and Gaussian noise after passage through a memoryless nonlinearity. It is shown here that the output of the nonlinearity can be expressed as the sum of uncorrelated terms whose auto-correlation functions are the terms of Rice's double series. Such a decomposition of the output is shown to be generally possible if and only if the bivariate probability density functions of the input signal and the input noise can both be expressed in the diagonal form studied by Barrett and Lampard (1955), though not necessarily involving polynomials, as they can in the sinusoidal and Gaussian cases. In addition, a more direct and meaningful equation is found for the coefficients in Rice's double series. View full abstract»

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  • Optimum thresholds for binary integration (Corresp.)

    Publication Year: 1968 , Page(s): 349 - 353
    Cited by:  Papers (22)
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    First Page of the Article
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  • A summary, by illustrations, of least-squares filters with constraints

    Publication Year: 1968 , Page(s): 269 - 272
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (440 KB)  

    Several methods of combining a number of time series into a single series are discussed. They are all individual filtering followed by summation and are somewhat like Wiener filtering in that a least-squares criterion is used to design the filter coefficients. They differ from Wiener filtering in that signal information is given in the form of various constraints on the filter coefficients rather than being given as a signal correlation function. The equations are worked out explicitly for the case of two time series and three filter points and presented in such a way as to make generalization clear. View full abstract»

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  • New generalizations of the Reed-Muller codes--II: Nonprimitive codes

    Publication Year: 1968 , Page(s): 199 - 205
    Cited by:  Papers (19)
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    In this paper a class of nonprimitive cyclic codes quite similar in structure to the original Reed-Muller codes is presented. These codes, referred to herein as nonprimitive Reed-Muller codes, are shown to possess many of the properties of the primitive codes. Specifically, two major results are presented. First the code length, number of information symbols, and minimum distance are shown to be related by means of a parameter known as the order of the code. These relationships show that for given values of code length and rate the codes have relatively large minimum distances. It is also shown that the codes are subcodes of the BCH codes of the same length and guaranteed minimum distance; thus in general the codes are not as powerful as the BCH codes. However, for most interesting values of code length and rate the difference between the two types of codes is slight. The second result is the observation that the codes can be decoded with a variation of the original algorithm proposed by Reed for the Reed-Muller codes. In other words, they are L -step orthogonalizable. Because of their large minimum distances and the simplicity of their decoders, nonprimitive Reed-Muller codes seem attractive for use in error-control systems requiring multiple random-error correction. View full abstract»

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  • The resolution of closely spaced signals

    Publication Year: 1968 , Page(s): 288 - 293
    Cited by:  Papers (19)
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    This paper presents a method for resolving signals closely spaced in parameter space in the sense that the parameters of the signals being measured (i.e., time of arrival, frequency, etc.) are close together. A maximum-likelihood method is used to resolve M signals in K -dimensional space, where M may be unknown. The resulting procedure first generates a K -dimensional cross-ambiguity function and then passes this function through a K -dimensional linear filter. The procedure effectively reduces the problem from its original form of optimally searching for a maximum in the (M \times K) -dimensional space to searching for M maxima in the K -dimensional parameter space. The method is obviously sub-optimal; its advantage lies in the relatively simple form of the detection scheme. View full abstract»

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  • The response of a particular nonlinear system with feedback to each of two random processes

    Publication Year: 1968 , Page(s): 255 - 264
    Cited by:  Papers (20)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1416 KB)  

    A discrete time, nonlinear system composed of an integrator preceded by a binary quantizer with integrated negative feedback, which can model a tracking loop or a single integrating delta modulation communication system, is discussed with regard to the input-output statistics for two types of input processes: independent inputs and independent increments inputs. A recursion on time for the joint distribution of input and output is obtained for the independent inputs process and explicitly solved for the time asymptotic distribution, when it exists. The solution is examined in greater detail for the special case of IID normal inputs. When the system is excited by a process of independent increments, the asymptotic behavior of the input and output (they diverge) is of less interest than that of the difference between input and output, the tracking error. A recursion in time for the characteristic function of the error is developed and the time asymptotic solution found, The tracking error is interpreted by decomposition into static and dynamic parts, and an exponential bound to its distribution is provided. The particular case of normal increments input is discussed in additional detail. View full abstract»

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  • An upper bound on average estimation error in nonlinear systems

    Publication Year: 1968 , Page(s): 243 - 250
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1104 KB)  

    An upper bound is obtained on the probability density of the estimate of the parameter m when a nonlinear function s(t, m) is transmitted over a channel that adds Gaussian noise, and maximum likelihood or maximum a posteriori estimation is used. If this bound is integrated with a loss function, an upper bound on the average error is obtained. Nonlinear (below threshold) effects are included. The problem is viewed in a Euclidean space. Evaluation of the probability density can be reduced to integrating the probability density of the observation over part of a hyperplane. By bounding the integrand, and using a larger part of the hyperplane, an upper bound is obtained. The resulting bound on mean-square error is quite close for the cases calculated. View full abstract»

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  • Exponential error bounds for erasure, list, and decision feedback schemes

    Publication Year: 1968 , Page(s): 206 - 220
    Cited by:  Papers (133)
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    By an extension of Gallager's bounding methods, exponential error bounds applicable to coding schemes involving erasures, variable-size lists, and decision feedback are obtained. The bounds are everywhere the tightest known. View full abstract»

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  • New generalizations of the Reed-Muller codes--I: Primitive codes

    Publication Year: 1968 , Page(s): 189 - 199
    Cited by:  Papers (35)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1152 KB)  

    First it is shown that all binary Reed-Muller codes with one digit dropped can be made cyclic by rearranging the digits. Then a natural generalization to the nonbinary case is presented, which also includes the Reed-Muller codes and Reed-Solomon codes as special cases. The generator polynomial is characterized and the minimum weight is established. Finally, some results on weight distribution are given. View full abstract»

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  • Design of binary bandlimited signals imbedded in colored Gaussian noise and intersymbol interference

    Publication Year: 1968 , Page(s): 312 - 320
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    This paper considers the design of binary bandlimited receiver signals as well as the design of the receiver filter for signal immunity to intersymbol interference and additive colored Gaussian noise. The design problem is treated in the frequency domain. The maximum probability of error is minimized by choosing signals with zero intersymbol interference. When transmission is below the Nyquist rate, bandlimited signals with gradual cutoff are designed. Other waveforms, with intersymbol interference but possessing no sequences of unbounded amplitude, are also investigated. Examples are given demonstrating the application of the theory. View full abstract»

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  • The performance of an adaptive image data compression system in the presence of noise

    Publication Year: 1968 , Page(s): 273 - 279
    Cited by:  Papers (2)
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    In the present paper the problem of image data compression is considered, and the evaluation of system performance with quantitative figures of merit as well as qualitative results is attempted. Three adaptive prediction techniques proposed by Balakrishnan are described and applied to video data for the removal of so-called redundant samples. Typical prediction efficiencies of several predictors are cited and compared. Encoding of "compressed" data for transmission in a noiseless channel is next considered. The efficiencies of several practical encoding procedures are compared with the efficiency of the ideal noiseless code. The most important results describe the performance of an image data compression system in a noisy channel. Davisson has related the sample error rate of the data reconstructed at the receiver to the channel error rate for a special case. This result is used as a quantitative basis for evaluating the effects of channel errors on the performance of a specific compression system. In addition, sample television pictures which depict the qualitative effects of channel errors are exhibited. Finally, an experimental laboratory facility is briefly described, and its use in this and future work is outlined. View full abstract»

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  • Sequential detection without a feedback channel (Corresp.)

    Publication Year: 1968 , Page(s): 353 - 354
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    First Page of the Article
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  • A method for the recognition of Japanese hiragana characters

    Publication Year: 1968 , Page(s): 226 - 233
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (664 KB)  

    A method for the recognition of Japanese hiragana characters is described. To recognize Japanese hiragana characters having complicated outlines, rotation indices are introduced. Sequences of the rotation indices contain information of the figure of the character. Smoothings and irregularity processing operations are performed for an economy of memory. The method developed will be applicable to recognition of other characters. The experimental results were obtained by simulation on a FACOM 231 computer. View full abstract»

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  • Sensor-array data processing for multiple-signal sources

    Publication Year: 1968 , Page(s): 294 - 305
    Cited by:  Papers (61)
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    Techniques are considered for processing the outputs of a sensor array that is observing J distinct signal sources. Three types of wideband signals are discussed: unknown, stochastic, and parameterized. Narrowband signals are a special case. Four types of random errors are discussed: additive sensor noise, sensor gain errors, sensor time-delay errors, and "beam-pointing' errors. It is concluded that the so-called decoupled-beam data processor is a very promising technique, which can be implemented by passing the output of J individual "beams" through a J -input, J -output linear system. When sensor gain-delay and beam-pointing errors are not present, the decoupled-beam data processor provides "infinite sidelobe rejection." View full abstract»

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  • On a class of majority-logic decodable cyclic codes

    Publication Year: 1968 , Page(s): 182 - 188
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (936 KB)  

    A new infinite class of cyclic codes is studied. Codes of this class can be decoded in a step-by-step manner, using` majority logic. Some previously known codes fall in this class, and thus admit simpler decoding procedures. As random error-correcting codes, the codes are nearly as powerful as the Bose-Chaudhuri codes. View full abstract»

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  • Optimal algorithmic encoding schemes for information sources

    Publication Year: 1968 , Page(s): 340 - 348
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    Sequences of integers which represent the output of a time sampled and quantized information source are considered. If the sequences are known to have first differences less than a given positive integer s or if they are known to be monotonic (either increasing or decreasing) and have first differences satisfying the above property, optimal encoding schemes are presented, in terms of s , the number of samples m , and the number of quantization levels q . The encoding schemes are presented as simple algorithms which may be implemented in a special purpose computer on board scientific spacecraft. View full abstract»

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  • The effect of weak fading on the output spectrum of an FM system

    Publication Year: 1968 , Page(s): 265 - 268
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    The error spectrum at the output of an ideal FM discriminator is derived for the case where the source of the error is a weak scatter component, which perturbs a strong specular component in the transmission medium. Illustrative examples are given. View full abstract»

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  • A contribution to the signal-design problem for incoherent-phase communication systems

    Publication Year: 1968 , Page(s): 306 - 311
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    In a previous study, a general expression for the detection probability was given for the transmission of an arbitrary M -ary signaling alphabet through the incoherent-phase channel which adds white Gaussian noise. Necessary and sufficient conditions were obtained demonstrating that with no dimensionality or bandwidth restrictions, the incoherent orthogonal signal structure locally minimizes the error probability for all signal-to-noise ratios. The previous expression is improved herein, from which it is verified that, when the signal dimensionality and bandwidth are restricted to be less than that necessary for the previous optimum, necessary conditions to locally extremize the probability of error are satisfied by the signal-waveform inner product matrix whose dimensionality is as large as possible. The form of the solution obtained is a 2 \times 2 block diagonal matrix with each block the regular simplex inner-product matrix. View full abstract»

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  • Center-of-gravity information feedback

    Publication Year: 1968 , Page(s): 324 - 331
    Cited by:  Papers (17)
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    We consider M signals in a D -dimensional signal space. These M signals are used to communicate over an additive Gaussian white noise channel. It is shown that if a noiseless feedback channel is available one could use this feedback channel to inform the transmitter of the location of the center of gravity of the signal structure and thus obtain a very efficient signaling scheme. Each signal point is assigned a mass proportional to its posterior probability at the particular instant. The center of gravity is used by the transmitter as a new origin for the signal space. It is shown that some previously considered coding schemes for channels with feedback are particular cases of center-of-gravity feedback. The probability of error decreases as a double exponential function of the coding delay as opposed to an exponential decrease for one-way systems. The effect of noise in the feedback path is briefly considered. View full abstract»

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  • The minimum variance of estimates in quantum signal detection

    Publication Year: 1968 , Page(s): 234 - 242
    Cited by:  Papers (10)
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    A quantum-mechanical form of the Cramér-Rao inequality is derived, setting a lower bound to the variance of an unbiased estimate of a parameter of a density operator. It is applied to the estimates of parameters such as amplitude, arrival time, and carrier frequency of a coherent signal as picked up by an ideal receiver in the presence of thermal noise. The estimation of parameters of a noise-like signal is also treated. View full abstract»

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  • Optimal signal design for sequential signaling over a channel with feedback

    Publication Year: 1968 , Page(s): 331 - 340
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1424 KB)  

    Turin [1] has studied the problem of optimal sequential detection over a channel with feedback when the signals used are subject to peak and average power constraints. With special additional constraints on the signals he was able to obtain a series solution for the first passage probability density and hence find optimal signals when the ratio of peak power to average power was infinity or one. Horstein,[2] concurrently with this study, was able to find optimal signals for arbitrary ratios of peak to average power when the signals were subject to the same special constraints. This paper presents a simpler and more direct approach for obtaining optimal signals which minimize the expected time to decision for arbitrary peak power constraints and various average power constraints. Explicit closed form solutions are derived for the expected energies and times to decision without having to first obtain the probability distribution of the first passage time. No special constraints are required on the signals. For communication with white noise in the feedback link, optimal stationary signals are found for peak and average power constraints. It is shown that communication rates up to but strictly less than channel capacity are possible with noisy feedback. However, it is also noted that for the schemes considered here, the stationary signals and white noise in the feedback link imply infinite feedback power. 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