IEEE Transactions on Information Theory

Volume 28 Issue 2 • March 1982

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Displaying Results 1 - 25 of 40
  • Editorial

    Publication Year: 1982, Page(s):127 - 128
    Cited by:  Papers (1)
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  • Least squares quantization in PCM

    Publication Year: 1982, Page(s):129 - 137
    Cited by:  Papers (3587)  |  Patents (104)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1227 KB)

    It has long been realized that in pulse-code modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as the number of quanta becomes infinite, the asymptotic fractional density of quanta per unit voltage should vary... View full abstract»

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  • The hexagon theorem

    Publication Year: 1982, Page(s):137 - 139
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (330 KB)

    We wish to<tex>\int_{S}|Z-f(Z)|^{2},S</tex>the unit square, over all choices of<tex>f(Z)</tex>which take just n values. For large n it is shown that<tex>f(Z)</tex>approaches that function which on each face of a "hexagonal mesh" has the value of the centroid of that face. This problem in the design of quantizers for a pulse-code modulation (PCM) system arose in ... View full abstract»

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  • Asymptotic quantization error of continuous signals and the quantization dimension

    Publication Year: 1982, Page(s):139 - 149
    Cited by:  Papers (263)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1504 KB)

    Extensions of the limiting qnanfizafion error formula of Bennet are proved. These are of the form<tex>D_{s,k}(N,F)=N^{-\beta}B</tex>, where<tex>N</tex>is the number of output levels,<tex>D_{s,k}(N,F)</tex>is the<tex>s</tex>th moment of the metric distance between quantizer input and output,<tex>\beta,B&gt;0,k=s/\beta</tex>is the signa... View full abstract»

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  • Minimum entropy quantizers and permutation codes

    Publication Year: 1982, Page(s):149 - 157
    Cited by:  Papers (50)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1442 KB)

    Amplitude quantization and permutation encoding are two approaches to efficient digitization of analog data. It has been proven that they are equivalent in the sense that their optimum rate versus distortion performances are identical. Reviews of the aforementioned results and of work performed in the interim by several investigators are presented. Equations which must be satisfied by the threshol... View full abstract»

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  • On the structure of vector quantizers

    Publication Year: 1982, Page(s):157 - 166
    Cited by:  Papers (218)  |  Patents (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1548 KB)

    Vector quantization is intrinsically superior to predictive coding, transform coding, and other suboptimal and {\em ad hoc} procedures since it achieves optimal rate distortion performance subject only to a constraint on memory or block length of the observable signal segment being encoded. The key limitation of existing techniques is the very large randomly generated code books which must be stor... View full abstract»

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  • On optimal finite-state digital transmission systems

    Publication Year: 1982, Page(s):167 - 186
    Cited by:  Papers (38)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2785 KB)

    The digital transmission of signals by transmitters and receivers that are time-invariant finite-state machines were investigated in general form. An average distortion criterion is used. Some general structure theorems are proved and some examples given that show improvement in performance as the memories of the transmitter and receiver are increased. Many conjectures and unsolved problems are me... View full abstract»

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  • Sufficient conditions for uniqueness of a locally optimal quantizer for a class of convex error weighting functions

    Publication Year: 1982, Page(s):187 - 198
    Cited by:  Papers (73)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1915 KB)

    Sufficient conditions are presented for uniqueness of a locally optimal quantizer being a stationary point of the quantization distortion measure<tex>E[f(x,\eta)]</tex>, the expected value of an error weighting function<tex>f(x,\eta)</tex>, where<tex>x</tex>is a random variable to be quantized, where the probability density function<tex>p(x)</tex>des... View full abstract»

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  • Quantization and the method of<tex>k</tex>-means

    Publication Year: 1982, Page(s):199 - 205
    Cited by:  Papers (73)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1155 KB)

    Asymptotic results from the statistical theory of<tex>k</tex>-means clustering are applied to problems of vector quantization. The behavior of quantizers constructed from long training sequences of data is analyzed by relating it to the consistency problem for<tex>k</tex>-means. View full abstract»

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  • Exponential rate of convergence for Lloyd's method I

    Publication Year: 1982, Page(s):205 - 210
    Cited by:  Papers (28)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (901 KB)

    For a random variable with finite second moment and log-concave density, a unique quantizer exists which produces the minimum expected encoding error, using squared-error distortion. An algorithm given by Lloyd (Lloyd's Method I) yields a sequence of quantizers which converges to the optimum quantizer. Using results of Fleischer, it is shown that the convergence takes place exponentially fast if t... View full abstract»

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  • Voronoi regions of lattices, second moments of polytopes, and quantization

    Publication Year: 1982, Page(s):211 - 226
    Cited by:  Papers (193)  |  Patents (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2071 KB)

    If a point is picked at random inside a regular simplex, octahedron,<tex>600</tex>-cell, or other polytope, what is its average squared distance from the centroid? In<tex>n</tex>-dimensional space, what is the average squared distance of a random point from the closest point of the lattice<tex>A_{n}</tex>(or<tex>D_{n}, E_{n}, A_{n}^{\ast} or D_{n}^{\ast})?... View full abstract»

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  • Fast quantizing and decoding and algorithms for lattice quantizers and codes

    Publication Year: 1982, Page(s):227 - 232
    Cited by:  Papers (271)  |  Patents (29)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (791 KB)

    For each of the lattices<tex>A_{n}(n \geq 1), D_{n}(n \geq 2), E_{6}, E_{7}, E_{8}</tex>, and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point. If these lattices are used for vector quantizing of uniformly distributed data, the algorithm finds the minimum distortion lattice point. If the lattices are used as codes for a Gaussian cha... View full abstract»

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  • The design of two-dimensional quantizers using prequantization

    Publication Year: 1982, Page(s):232 - 239
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (849 KB)

    The theoretical advantages of two-dimensional quantization over univariate quantization have been studied in the literature. However, in many cases there is no known implementation for the two-dimensional quantizer that can operate in real time. A new approach to the design of two-dimensional quantizers is presented. This technique, called prequantization, is used to design two-dimensional quantiz... View full abstract»

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  • Multidimensional asymptotic quantization theory with<tex>r</tex>th power distortion measures

    Publication Year: 1982, Page(s):239 - 247
    Cited by:  Papers (107)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1158 KB)

    Asymptotic properties of the<tex>r</tex>th power distortion measure associated with quantized<tex>k</tex>-dimensional random variables are considered. Subject only to a moment condition, it is shown that the infimum over all<tex>N</tex>level quantizers of the quantity<tex>N^{r/k}</tex>times the<tex>r</tex>th power average distortion conve... View full abstract»

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  • Stochastic stability for feedback quantization schemes

    Publication Year: 1982, Page(s):248 - 254
    Cited by:  Papers (51)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (984 KB)

    Feedback quantization schemes (such as delta modulation. adaptive quantization, differential pulse code modulation (DPCM), and adaptive differential pulse code modulation (ADPCM) encode an information source by quantizing the source letter at each time<tex>i</tex>using a quantizer, which is uniquely determined by examining some function of the past outputs and inputs called the state o... View full abstract»

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  • The complexity of the generalized Lloyd - Max problem (Corresp.)

    Publication Year: 1982, Page(s):255 - 256
    Cited by:  Papers (70)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (350 KB)

    A simple (combinatorial) special case of the generalized Lloyd-Max (or quantization) problem is shown to be nondeterministic polynomial (NP)-complete. {\em A fortiori}, the general problem of communication theory, in its combinatorial forms, has at least that complexity. View full abstract»

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  • Multiple local optima in vector quantizers (Corresp.)

    Publication Year: 1982, Page(s):256 - 261
    Cited by:  Papers (52)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1043 KB)

    Two results are presented on vector quantizers meeting necessary conditions for optimality. First a simple generalization of well-known centroid and moment properties of the squared-error distortion measure to a weighted quadratic distortion measure with an input dependent weighting is presented. The second result is an application of the squared-error special case of the first result to a simulat... View full abstract»

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  • Optimal fixed frame multiplexing in integrated line- and packet-switched communication networks

    Publication Year: 1982, Page(s):263 - 273
    Cited by:  Papers (26)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1602 KB)

    Recently, emphasis has been placed on integrated communication facilities capable of handling both line-switching and packet-switch-ing digital traffic. The problem of dynamically allocating the bandwidth of a trunk to both types of traffic is formulated as a Markovian decision process. Line switching is modeled as a time division multiplexing loss scheme over a varying portion of a fixed time fra... View full abstract»

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  • Equilibria for diffusion models of pairs of communicating computers--Symmetric case

    Publication Year: 1982, Page(s):273 - 284
    Cited by:  Papers (23)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1655 KB)

    The steady-state queueing behavior of interacting computers is basic to computer network theory. Equilibrium properties are determined for the diffusion model for the special case of a symmetrically disposed pair of communicaling computers. In the mathematical model, arrivals to the system can represent the presentation of programming jobs, and each service represents the completion of a stage of ... View full abstract»

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  • Strong universal source coding subject to a rate-distortion constraint

    Publication Year: 1982, Page(s):285 - 295
    Cited by:  Papers (10)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1699 KB)

    The following problem in universal source coding is explored. Some members of a class of sources have various constraints on the maximum rate at which they may be encoded, and thc remainder have various constraints on the maximum distortion that may result from encoding. It is desired to find a universal code that will adapt its performance so that whatever source in the class is encoded, the resu... View full abstract»

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  • Robust memoryless quantization for minimum signal distortion

    Publication Year: 1982, Page(s):296 - 306
    Cited by:  Papers (12)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1461 KB)

    Robust quantizers are designed for situations where there is only an incomplete statistical description of the quantizer input. The goal of the design is to closely approximate quantizer inputs by quantizer outputs without using more than a specified number of quantization levels. The exact probability distribution of the input is unknown, but this distribution is known to belong to some set<te... View full abstract»

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  • A decision procedure for finite decipherability and synchronizability of multivalued encodings

    Publication Year: 1982, Page(s):307 - 318
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2067 KB)

    A multivalued encoding is a variable length coding system in which more than one codeword may correspond to each source symbol. The properties of unique decipherability, decipherability with finite delay, and synchronizability for multivalued encodings are characterized. In particular, the property, of unique decipherability is considered, and a recent conjecture about decipherability with finite ... View full abstract»

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  • Analysis of error-gradient adaptive linear estimators for a class of stationary dependent processes

    Publication Year: 1982, Page(s):318 - 329
    Cited by:  Papers (32)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1498 KB)

    In many applications, the training data to be processed by an adaptive linear estimator can be assumed to have a finite correlation length. An exact analysis for this class of problems that yields the coefficient bias, coefficient correlation matrix, and mean square estimation error is obtained via a stochastic imbedding procedure. A power series expansion in the gain parameter is used to obtain s... View full abstract»

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  • Decoding of erasures and errors for certain RS codes by decreased redundancy

    Publication Year: 1982, Page(s):330 - 336
    Cited by:  Papers (2)  |  Patents (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1138 KB)

    A method is presented for decoding erasures and errors in Reed-Solomon (RS) codes over GF<tex>(q)</tex>. It uses fewer operations when the code is of medium or low rate, when the number of erasures is relatively large, and when<tex>q-1</tex>is prime. This method can be used in conjunction with the customary method of decoding RS codes and can decrease the maximum number of ... View full abstract»

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  • Distortion rate theory and filtering (Corresp.)

    Publication Year: 1982, Page(s):336 - 340
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (658 KB)

    For two samples of the Ornstein-Uhlenbeck process, the constrained distortion rate function is found. The constraint imposed is that the minimization is carried out over realizable processes. The constrained and unconstrained distortion are compared. Applications to filtering theory are discussed. 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.

Full Aims & Scope

Meet Our Editors

Editor-in-Chief
Alexander Barg

Department of Electrical and Computer Engineering and the Institute for Systems Research, University of Maryland

email: abarg-ittrans@ece.umd.edu