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Information Theory, IEEE Transactions on

Issue 4 • Date Jul 1987

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Displaying Results 1 - 15 of 15
  • Trellis-coded modulation with multidimensional constellations

    Page(s): 483 - 501
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2408 KB)  

    Trellis-coded modulation schemes using four-, eight-, or16-dimensional constellations have a number of potential advantages over the usual two-dimensional schemes: a smaller constituent two-dimensional constellation, easier tolerance to phase ambiguities, and a better trade-off between complexity and coding gain. A number of such schemes are presented and evaluated. Starting with a variety of multidimensional lattices, we show how to select multidimensional constellations, how to partition them into subsets, how to construct trellis codes using those subsets, and how to map hits to constellation points. Simplifications of the Viterbi decoding algorithm are presented. We conclude that there are multidimensional trellis-coded modulation schemes that perform better for the same complexity than do two-dimensional schemes. View full abstract»

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  • New results in binary multiple descriptions

    Page(s): 502 - 521
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    An encoder whose input is a binary equiprobable memoryless source produces one output of rateR_{1}and another of rateR_{2}. LetD_{1}, D_{2}, and D_{0}, respectively, denote the average error frequencies with which the source data can be reproduced on the basis of the encoder output of rateR_{l}only, the encoder output of rateR_{2}only, and both encoder outputs. The two-descriptions problem is to determine the regionRof all quintuples(R_{1}, R_{2}, D_{1}, D_{2}, D_{0})that are achievable in thc usual Shannon sense. LetR(D)=1+D log_{2} D+(1-D) log_{2}(1-D)denote the error frequency rate-distortion function of the source. The "no excess rate case" prevails whenR_{1} + R_{2} = R(D_{0}), and the "excess rate case" whenR_{1} + R_{2} > R(D_{0}). Denote the section ofRat(R_{1}, R_{2}, D_{0})byD(R_{1} R_{2}, D_{0}) ={(D_{1},D_{2}): (R_{1}, R_{2}, D_{1},D_{2},D_{0}) in R}. In the no excess rate case we show that a portion of the boundary ofD(R_{1}, R_{2}, D_{0})coincides with the curve(frac{1}{2} + D_{1}-2D_{0})(frac_{1}_{2} + D_{2}-2D_{0})= frac{1}{2}(1-2D_{0})^{2}. This curve is an extension of Witsenhausen's hyperbola bound to the caseD_{0} > 0. It follows that the projection ofRonto the(D_{1}, D_{2})-plane at fixedD_{0}consists of allD_{1} geq D_{0}andD_{2} geq D_{0}that lie on or above this hyperbola. In the excess rate case we show by counterexample that the achievable region of El Gamal and Cover is not tight. View full abstract»

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  • Cutoff points for roll call protocols in multiple access systems

    Page(s): 577 - 581
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    A communication network with multiple users sharing a common broadcast channel is considered. Ak-channel is defined to be a channel that can carry up tok-1successful transmissions simultaneously, but simultaneous transmissions bykor more users cause a collision and no successful transmissions take place. The question arises as to how to organize transmissions to avoid collisions or to resolve them efficiently when they occur. The most conservative approach is to use a roll call scheme, which guarantees that collisions never occur. However, other approaches may sometimes be more efficient. It is supposed that each user has the same probabilitypof wanting to transmit, and for several different models the conditions onpunder which roll call is the most efficient scheme for ak-channel are determined. View full abstract»

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  • A note on the Shannon capacity of run-length-limited codes (Corresp.)

    Page(s): 601 - 605
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    It is proven that 100-percent efficient fixed-rate codes for run-length-limited (RLL)(d,k)and RLL charge-constrained(d, k; c)channels are possible in only two eases, namely(d,k; c)=(0,1;1)and(1,3;3). Specifically, the binary Shannon capacity of RLL(d, k)constrained systems is shown to be irrational for all values of(d, k),0 leq d < k. For RLL charge-constrained systems with parameters(d, k;c), the binary capacity is irrational for all values of(d, k; c),0 leq d < k,2c geq k + 1, except(0,1; 1)and(1,3;3), which both have binary capacity1/2. View full abstract»

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  • On the relationship between the efficiency measures of multicategory information systems

    Page(s): 531 - 538
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    The concepts of efficiency measures of multicategory information systems and similarity measures between two efficiency measures are introduced and developed. The relationship between two efficiency measures is defined by the corresponding setD, and the appropriate marginal functions are introduced. An earlier work of Ben-Bassat's dealing with the ranking of features according to feature selection criteria is generalized and refined. Consequently, a general similarity measure between two efficiency measures is established. It is analyzed in the case of monotonic marginal functions and, especially, when the setDis convex. Some important sufficient conditions forDto be convex are also given. Finally, two other similarity measures are defined and interpreted. View full abstract»

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  • Measures of mutual and causal dependence between two time series (Corresp.)

    Page(s): 598 - 601
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    New measures are proposed for mutual and causal dependence between two time series, based on information theoretical ideas. The measure of mutual dependence is shown to be the sum of the measure of unidirectional causal dependence from the first time series to the second, the measure of unidirectional causal dependence from the second to the first, and the measure of instantaneous causal dependence. The measures are applicable to any kind of time series: continuous, discrete, or categorical. View full abstract»

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  • Robust source coding of weakly compact classes

    Page(s): 522 - 530
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    A fixed-rate block code is said to be strongly robust for a class of sourcesLambdaif its maximum distortion overLambdah is no larger than the maximum of the distortion-rate functions of the sources in the class at the rate of the code. It is shown that such codes exist at all positive rates whenever the class is compact with resect to the topology of weak convergence and satisfies certain additional, but not very strong, constraints on the alphabet and distortion measure. Examples of classes that satisfy these conditions are given. In addition, classes are exhibited for which there are no strongly robust codes. These help to demarcate the boundary between classes for which strongly robust codes do and do not exist. More specifically, they show that strongly robust codes exist more widely than strongly universal codes but !ess widely than weakly universal codes. View full abstract»

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  • On codes with spectral nulls at rational submultiples of the symbol frequency

    Page(s): 557 - 568
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    In digital data transmission (respectively, storage systems), line codes (respectively, recording codes) are used to tailor the spectrum of the encoded sequences to satisfy constraints imposed by the channel transfer characteristics or other system requirements. For instance, pilot tone insertion requires codes with zero mean and zero spectral density at tone frequencies. Embedded tracking/focus servo signals produce similar needs. Codes are studied with spectral nulls at frequenciesf=kf_{s}/n, wheref, is the symbol frequency andk, nare relatively prime integers withk leq n;in other words, nulls at rational submultiples of the symbol frequency. A necessary and sufficient condition is given for a null atfin the form of a finite discrete Fourier transform (DFT) running sum condition. A corollary of the result is the algebraic characterization of spectral nulls which can be simultaneously realized. Specializing to binary sequences, we describe canonical Mealy-type state diagrams (directed graphs with edges labeled by binary symbols) for each set of realizable spectral nulls. Using the canonical diagrams, we obtain a frequency domain characterization of the spectral null systems obtained by the technique of time domain interleaving. View full abstract»

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  • Remarks on codes from Hermitian curves (Corresp.)

    Page(s): 605 - 609
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    Parameters and generator matrices are given for the codes obtained by applying Goppa's algebraic-geometric construction method to Hermitian curves in PG(2,q), whereq = 2^{2s}for somesin {bf N}. Automorphisms of these codes are also discussed, and some results on self-duality and weak self-duality are given. View full abstract»

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  • Some inequalities concerning random subsets of a set (Corresp.)

    Page(s): 596 - 598
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    A class of plausible inequalities between conditional probabilities is considered involving random subsets of a set which arise, for example, in studying the capacity of a multiple access channel. Some of the inequalities are true and can be proved by the Fortuin-Kasteleyn-Ginibre (FKG) inequality. Some others are true but seem to need other methods. Still others are false. The results also apply to studying the conditional probability of the failure of a device designed to achieve reliability by using redundant parts, given side information about the failure of some of its components. View full abstract»

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  • Signal set design for band-limited memoryless multiple-access channels with soft decision demodulation

    Page(s): 539 - 556
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    Signal sets are identified that maximize the cutoff rate region for a multiple-access channel with an additive white Gaussian noise, in which the demodulator output alphabet is allowed to be infinite ("infinitely soft decisions"). The optimizing designs consist of a simplex signal set for each sender, such that each sender's set is orthogonal to those of the other senders. For "second moment" and for "fractional out-of-band-energy" bandwidth constraints on the signals of each sender, conditions are derived under which mutually orthogonal simplex sets are still optimal. For the second moment constraint, simplex sets derived from sinusoidal functions yield an optimal design and, for the out-of-band energy constraint, simplex Sets derived from prolate spheroidal wave functions are optimal. Choices of signal sets that maximize the cutoff rate region for an additive shot-noise limited multiple-access optical channel, subject to average energy and peak amplitude constraints, are also identified. View full abstract»

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  • Comparison of generalized Q- function algorithms (Corresp.)

    Page(s): 591 - 596
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    Several methods have been proposed for calculating the generalizedQ-functionQ_{m}(alpha, beta), but only isolated comparisons of the various techniques have been reported. The accuracy, range, and execution time of prominent methods for computing theQ-function are compared, and limitations of the algorithms are identified. View full abstract»

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  • Asymptotic zero distribution of orthogonal polynomials in sinusoidal frequency estimation

    Page(s): 569 - 576
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    It is shown that the zeros of polynomials orthogonal with respect to certain positive measures on the unit circle have an asymptotic distribution which is uniform on a circle of radius less than or equal to one. These results explain some phenomena observed when various linear prediction methods are used to estimate sinusoidal frequencies. They also describe the asymptotic zero distribution of the prediction error filter polynomials for a class of time series including autoregressive moving average (ARMA) models. View full abstract»

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  • Range and error analysis for a fast Fourier transform computed over Z[{\omega }]

    Page(s): 582 - 590
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    A range and error analysis is developed for a discrete Fourier transform (fast Fourier transform) computed using the ring of cyclotomic integers. Included are derivations of both deterministic and statistical upper bounds for the range of the resulting processor and formulas for the ratio of the mean square error to mean square signal, in terms of the pertinent parameters. Comparisons of theoretical predictions with empirical results are also presented. View full abstract»

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  • The capacity of the Hopfield associative memory

    Page(s): 461 - 482
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    Techniques from coding theory are applied to study rigorously the capacity of the Hopfield associative memory. Such a memory storesn-tuple ofpm 1's. The components change depending on a hard-limited version of linear functions of all other components. With symmetric connections between components, a stable state is ultimately reached. By building up the connection matrix as a sum-of-outer products ofmfundamental memories, one hopes to be able to recover a certain one of themmemories by using an initialn-tuple probe vector less than a Hamming distancen/2away from the fundamental memory. Ifmfundamental memories are chosen at random, the maximum asympotic value ofmin order that most of themoriginal memories are exactly recoverable isn/(2 log n). With the added restriction that every one of themfundamental memories be recoverable exactly,mcan be no more thann/(4 log n)asymptotically asnapproaches infinity. Extensions are also considered, in particular to capacity under quantization of the outer-product connection matrix. This quantized memory capacity problem is closely related to the capacity of the quantized Gaussian channel. 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