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Information Theory, IEEE Transactions on

Issue 3 • Date May 1987

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Displaying Results 1 - 25 of 25
  • Binary transmission codes with higher order spectral zeros at zero frequency (Corresp.)

    Publication Year: 1987 , Page(s): 452 - 454
    Cited by:  Papers (26)  |  Patents (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (512 KB)  

    A method is presented for designing binary channel codes in such a way that both the power spectral density function and its low-order derivatives vanish at zero frequency. The performance of the new codes is compared with that of channel codes designed with a constraint on the unbalance Of the number of transmitted positive and negative pulses. Some remarks are made on the error-correcting capabilities of these codes. View full abstract»

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  • Confidence intervals based on one or more observations

    Publication Year: 1987 , Page(s): 373 - 382
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1632 KB)  

    On the basis of n\geq 2 observations, confidence limits of the form \overline{X} \pm tS/ \sqrt {n} are constructed for the location (e.g., the median) of any distribution of known form with unknown location and dispersion (scale), where \overline{X} and S are the sample mean and "unbiased" standard deviation. Particular attention is given to the values of t needed for the Cauchy and uniform distributions. The latter t suffices for any (unknown) symmetric unimodal distribution if t \geq n - 1 . A table compares these values of t for n=2,3,4 , and 5 with those for the normal case, which are derived here very simply and are identical with those found by "Student." We are also able to include the case of a single observation (n=1) , where confidence intervals of various forms are made just wide enough for the least favorable dispersion. They, therefore, include the true location with at least but, in general, not exactly the desired probability; these intervals involve a predetermined value that plays a role reminiscent of but quite different from that of the prior distribution that would enter into a Bayesian analysis. In addition, upper confidence limits for the dispersion are constructed for n \geq 1 . View full abstract»

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  • Sequences achieving the boundary of the entropy region for a two-source are virtually memoryless (Corresp.)

    Publication Year: 1987 , Page(s): 443 - 448
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (856 KB)  

    For a joint distribution {\rm dist}(X,Y) , the function T(t)=\min { H(Y|U): I(U \wedge Y|X)=O, H(X|U)\geq t} is an important characteristic. It equals the asymptotic minimum of (1/n)H(Y^{n}) for random pairs of sequences (X^{n}, Y^{n}) , where frac{1}{n} \sum ^{n}_{i=1}{\rm dist} X_{i} \sim {\rm dist} X, {\rm dist} Y^{n}|X^{n} = ({\rm dist} Y|X)^{n}, frac{1}{n}H(X^{n})\geq t. We show that if, for (X^{n}, Y^{n}) as given, the rate pair [(1/n)H(X^{n}) , (1/n)H(Y^{n})] approaches the nonlinear part of the curve (t,T(t)) , then the sequence X^{n} is virtually memoryless. Using this, we determine some extremal sections of the rate region of entropy characterization problems and find a nontrivial invariant for weak asymptotic isomorphy of discrete memoryless correlated sources. View full abstract»

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  • The rate-distortion function of a binary symmetric source when side information may be absent (Corresp.)

    Publication Year: 1987 , Page(s): 448 - 452
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (720 KB)  

    A binary symmetric source with binary side information is given. An encoder codes the source for data compression with no knowledge of the side information. It is then decoded, perhaps with and perhaps without the presence of side information. The rate-distortion function of this scheme is a function of two variables: D_{1} is the distortion when side information is present at the decoder, and D2 is the distortion when side information is absent at the decoder. The rate-distortion function is shown to reduce to previously solved problems in much of the (D_{1}, D_{2}) -plane. Tight upper and lower bounds are found for the rate-distortion function in the rest of the (D_{1}, D_{2}) -plane. View full abstract»

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  • Analysis of adaptive differential PCM of a stationary Gauss - Markov input

    Publication Year: 1987 , Page(s): 350 - 359
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1520 KB)  

    An adaptive matched differential pulse-code modulator (AMDPCM) is analyzed. The adaptation of the symmetric uniform quantizer parameter \Delta _{n} is performed by fixed multipliers assigned to the quantizer output levels. The input is stationary first-order Gauss-Markov. The correlation of the samples is used as the leakage parameter in the matched integrator, with the predictive reconstruction similarly matched. For a 4 -level quantizer and multipliers (\gamma ^{-1}, \gamma ) the limiting joint distribution of the prediction error and \Delta _{n} is derived and the asymptotic sample-point and time-averaged mean-square error (rose) and mean and variance of \Delta _{n} as functions of \gamma \in (1,2] are computed and plotted. It is found that the asymptotic performance of AMDPCM does not depend on the choice of \Delta _{0} , that the increase in mse incurred by using A(M)DPCM instead of (M)DPCM with \Delta _{opt} is small, with mse(A(M)DPCM) \downarrow \min_{\Delta } mse ((M)DPCM) as \gamma \downarrow 1 , and that the signal-to-noise ratio of AMDPCM does not depend on the input power. View full abstract»

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  • Optimal coding strategies for certain permuting channels

    Publication Year: 1987 , Page(s): 310 - 314
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (664 KB)  

    We give optimal coding strategies for nonprobabilistic permuting (especially, "trapdoor") channels and also for a permuting relay channel. Our results open the door to a coding theory for nonprobabilistic (or deterministic) channels with memory. View full abstract»

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  • On the equivalence between Berlekamp's and Euclid's algorithms (Corresp.)

    Publication Year: 1987 , Page(s): 428 - 431
    Cited by:  Papers (17)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (632 KB)  

    It is shown that Berlekamp's iterative algorithm can be derived from a normalized version of Euclid's extended algorithm. Simple proofs of the results given recently by Cheng are also presented. View full abstract»

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  • Identification of linear stochastic systems via second- and fourth-order cumulant matching

    Publication Year: 1987 , Page(s): 393 - 407
    Cited by:  Papers (129)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2120 KB)  

    The identification problem for time-invariant single-input single-output linear stochastic systems driven by non-Gaussian white noise is considered. The system is not restricted to be minimum phase, and it is allowed to contain all-pass components. A least-squares criterion that involves matching the second- and the fourth-order cumulant functions of the noisy observations is proposed. Knowledge of the probability distribution of the driving noise is not required. An order determination criterion that is a modification of the Akaike information criterion is also proposed. Strong consistency of the proposed estimator is proved under certain sufficient conditions. Simulation results are presented to illustrate the method. View full abstract»

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  • Linear prediction from samples of a function and its derivatives

    Publication Year: 1987 , Page(s): 360 - 366
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1040 KB)  

    Some formulas for the prediction of the values of a band-limited function based on its samples from the past are generalized by including past samples of its first derivative. The new sums, developed by an approach based on Newton series, make it possible to double the distance between the sample points. The resulting formulas are shown to apply to the prediction problem for a large class of entire functions of exponential type. In addition, a related prediction formula which uses past samples of successively higher derivatives is shown to behave similarly to the Taylor series approximation, again for a class of functions that includes the band-limited functions. View full abstract»

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  • Performance boundaries for prioritized multiplexing systems

    Publication Year: 1987 , Page(s): 329 - 340
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1920 KB)  

    Systems in which many data sources are multiplexed over a single communication channel are considered. Data from all the sources are generated in fixed-length packets and are stored in a common buffer with finite capacity. Packets that overflowed or were removed from the buffer prior to transmission are lost. The system performance measure is the set of packet loss probabilities associated with the sources. Queueing disciplines vary depending on the stringency of prioritization and the utilization of the system resources. The set of all possible performances is characterized as we span the set of all queueing disciplines. Whether a given performance is possible can be deduced. Strategies that achieve the minimum overall loss probability are identified. The extreme disciplines are specified, and their performances are calculable by means of a given algorithm. View full abstract»

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  • Packet delay under the golden ratio weighted TDM policy in a multiple-access channel

    Publication Year: 1987 , Page(s): 341 - 349
    Cited by:  Papers (22)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1328 KB)  

    Consider n transmission stations sharing a single communication channel. Packets arrive at the stations according to n independent renewal processes, possibly with different rates. The transmitters are assumed to be able to store an unlimited number of packets in their buffers. The stations transmit packets during time slots allocated to them according to a given {em conflict-free distributed protocol.} The cost criterion according to which protocols are evaluated is the long-run weighted average buffer occupancies. (The average waiting time is a special case of such a weighting.) A lower bound to the cost criterion under time division multiplexing (TDM) protocols is given, and the costs of two protocols are analyzed. The first protocol is the {em random-control} policy, and the second is the {em golden ratio} policy which is shown to achieve a cost close to the lower bound for realistic parameters. View full abstract»

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  • Corrections and additions to 'Error recovery for variable length codes' by J.C. Maxted and J.P. Robinson

    Publication Year: 1987 , Page(s): 454 - 456
    Cited by:  Papers (9)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB)  

    An error in the subject article is corrected. Additionally, a method of calculating the standard deviation of the expected span of errors is presented. For four example codes, the standard deviation of the subject article's reduced model is compared to the standard deviation of the subject article's complete model. View full abstract»

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  • First and second passage times of Rayleigh processes (Corresp.)

    Publication Year: 1987 , Page(s): 419 - 425
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (960 KB)  

    The first and second passage times of a stationary Rayleigh process R(t,a) are discussed. R(t,a) represents the envelope of a stationary random process consisting of a sinusoidal signal of amplitude and frequency f_{0} plus stationary Gaussian noise of unit variance having a narrow-band power spectral density which is symmetrical about f_{0} . Approximate integral equations are developed whose solutions yield approximate probability densities concerning the first and second passage times of R(t,a) . The resulting probability functions are presented in graphs for the case when the power spectral density of the noise is Gaussian. Related results concerning the approximate distribution function of the absolute minimum or absolute maximum of R(t,a) in the closed interval [0,\tau ] are also presented. The exact probability densities are expressed in the form of an infinite series of multiple integrals. View full abstract»

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  • A heuristic algorithm for the construction of a code with limited word length (Corresp.)

    Publication Year: 1987 , Page(s): 438 - 443
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (784 KB)  

    A depth-first algorithm is presented for the construction of a binary minimum-redundancy variable length code with limited word length. In this algorithm, heuristic information on the mean word length is used for efficient searching. The extension to Q -ary codes is also discussed. View full abstract»

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  • Approximations for the probability in the tails of the binomial distribution (Corresp.)

    Publication Year: 1987 , Page(s): 426 - 428
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (416 KB)  

    Upper and lower bounds for the probability in the tails of a binomial distribution are investigated. New bounds are obtained which are computationally simple and, in the case of the lower bound, significantly better than previously known bounds. View full abstract»

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  • A new distributed algorithm to find breadth first search trees

    Publication Year: 1987 , Page(s): 315 - 322
    Cited by:  Papers (26)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1288 KB)  

    A new distributed algorithm is presented for constructing breadth first search (BFS) trees. A BFS tree is a tree of shortest paths from a given root node to all other nodes of a network under the assumption of unit edge weights; such trees provide useful building blocks for a number of routing and control functions in communication networks. The order of communication complexity for the new algorithm is O(V^{1.6} + E) where V is the number of nodes and E the number of edges. For dense networks with E \geq V^{1.6} this order of complexity is optimum. View full abstract»

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  • Asymptotically convergent modified recursive least-squares with data-dependent updating and forgetting factor for systems with bounded noise

    Publication Year: 1987 , Page(s): 383 - 392
    Cited by:  Papers (93)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1280 KB)  

    Continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances. An algorithm which eliminates these difficulties is investigated. Based on a set theoretic assumption, the algorithm yields modified least-squares estimates with a forgetting factor. It updates the estimates selectively depending on whether the observed data contain sufficient information. The information evaluation required at each step involves very simple computations. In addition, the parameter estimates are shown to converge asymptotically, at an exponential rate, to a region around the true parameter. View full abstract»

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  • Network control by Bayesian broadcast

    Publication Year: 1987 , Page(s): 323 - 328
    Cited by:  Papers (83)  |  Patents (27)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (904 KB)  

    A transmission control strategy is described for slotted-ALOHA-type broadcast channels with ternary feedback. At each time slot, each station estimates the probability that n stations are ready to transmit a packet for each n , using Bayes' rule and the observed history of collisions, successful transmissions, and holes (empty slots). A station transmits a packet in a probabilistic manner based on these estimates. This strategy is called Bayesian broadcast. An elegant and very practical strategy--pseudo-Bayesian broadcast--is then derived by approximating the probability estimates with a Poisson distribution with mean \nu and further simplifying. Each station keeps a copy of \nu , transmits a packet with probability 1/\nu , and then updates \nu in two steps: For collisions, increment \nu by (e-2)^{-l}=1.39221 \cdots . For successes and holes, decrement \nu by 1 . Set \nu to \max (\nu + \hat{\lambda }, 1) , where \hat{\lambda } is an estimate of the arrival rate \lambda of new packets into the system. Simulation results are presented showing that pseudo-Bayesian broadcast performs well in practice, and methods that can be used to prove that certain versions of pseudo-Bayesian broadcast are stable for \lambda < e^{-1} are discussed. View full abstract»

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  • Generalized Reed - Solomon codes from algebraic geometry

    Publication Year: 1987 , Page(s): 305 - 309
    Cited by:  Papers (23)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (696 KB)  

    A few years ago Tsfasman {em et al.,} using results from algebraic geometry, showed that there is a sequence of codes which are generalizations of Goppa codes and which exceed the Gilbert-Varshamov bound. We show that a similar sequence of codes (in fact, the duals of the previous codes) can be found by generalizing the construction of Reed-Solomon codes. Our approach has the advantage that it uses less complicated concepts from algebraic geometry. View full abstract»

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  • New upper bounds on the size of codes correcting asymmetric errors (Corresp.)

    Publication Year: 1987 , Page(s): 434 - 437
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (488 KB)  

    New upper bounds on the size of codes correcting asymmetric errors are derived by sharpening some of the constraints in the integer programming problem of Delsarte and Piret. It is shown that their code for length 9 and asymmetric distance 2 is optimal. View full abstract»

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  • On the robust discrimination of Poisson random counting measures (Corresp.)

    Publication Year: 1987 , Page(s): 415 - 419
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1016 KB)  

    Statistical decisions are considered between two hypotheses which consist of classes of Poisson distributions for random counting measures. Each Poisson distribution is generated by an intensity measure on a general observation space. The classes are specified by Choquet capacity bounds on the intensity measures. This problem was first posed and studied by Geraniotis and Poor. A minimax Neyman-Pearson result for error probability performance is the main contribution. Recursive computation of the minimax test statistic is also investigated. View full abstract»

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  • Nonparametric sequential estimation of zeros and extrema of regression functions

    Publication Year: 1987 , Page(s): 367 - 372
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (792 KB)  

    Let (X,Y), (X_{l}, Y_{l}), (X_{2}, Y_{2}), \cdots be independent identically distributed pairs of random variables, and let m(x)=E(Y|X = x) be the regression curve of Y on X . The estimation of zeros and extrema of the regression curve via stochastic approximation methods is considered. Consistency results of some sequential procedures are presented and termination rules are defined providing fixed width confidence intervals for the parameters to be estimated. View full abstract»

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  • Duadic codes (Corresp.)

    Publication Year: 1987 , Page(s): 432 - 433
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (360 KB)  

    The notion of duadic codes over GF (2) is generalized to arbitrary fields. Duadic codes of composite length are constructed. An upper bound is given for the minimum distance of duadic codes of length a prime power. View full abstract»

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  • Stability of linear predictors and numerical range of a linear operator (Corresp.)

    Publication Year: 1987 , Page(s): 412 - 415
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (728 KB)  

    The zeros of a predictor polynomial are shown to belong to the numerical range of a linear operator associated with the particular prediction problem considered. Application of this result to the autocorrelation and postwindowed cases shows that the predictor polynomials enjoy a well-defined stability margin which depends in particular on the length of the data sequence. The generalization of these results to the multichannel case is also discussed. View full abstract»

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  • Necessary and sufficient conditions for Bayes risk consistency of a recursive kernel classification rule (Corresp.)

    Publication Year: 1987 , Page(s): 408 - 412
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (648 KB)  

    It is shown that, for a nonparametric recursive kernel classification rule, \sum ^{n}_{i=1}h^{d}(i)I_{ {h(i) > \epsilon } } / \sum ^{n}_{j=1} h^{d} (j) \rightarrow 0 {\rm as} n \rightarrow \infty , all \epsilon > 0 and \sum ^{\infty }_{i=1}h^{d}(i)= \infty constitute a set of conditions which are not only sufficient but also necessary for weak and strong Bayes risk consistency of the rule. In this way, weak and strong consistencies are shown to be equivalent. 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