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Information Theory, IEEE Transactions on

Issue 2  Part 2 • Date March 1992

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Displaying Results 1 - 25 of 65
  • Some ternary and quaternary codes and associated sphere packings

    Publication Year: 1992 , Page(s): 227 - 246
    Cited by:  Papers (26)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1638 KB)  

    Tables of good ternary and quaternary codes are presented, and they are used in the construction of dense sphere packings. Results include (1) tables of the best ternary and quaternary constacyclic codes (including cyclic codes) up to block length 50; (2) a class of optimal (n, 2) codes over GF(q); (3) the (u+v+w mod 2u+v mod u) construction, a new ternary code construction technique that can be used to construct the ternary Reed-Muller codes (and others); and (4) tables of linear ternary and quaternary codes obtained by modifying and combining various codes here and in the literature. Packings are generated in even dimensions up to 100 using these codes and a sphere-packing construction. In dimensions 36 and 60, new record densities appear to have been achieved.<> View full abstract»

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  • A universal variable-to-fixed length source code based on Lawrence's algorithm

    Publication Year: 1992 , Page(s): 247 - 253
    Cited by:  Papers (8)  |  Patents (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (531 KB)  

    It is shown that the modified Lawrence algorithm is universal over the class of binary memoryless sources and that the rate converges asymptotically optimally fast to the source entropy. It is proven that no codes exist that have a better asymptotic performance. The asymptotic bounds show that universal variable-to-fixed-length codes can have a significantly lower redundancy than universal fixed-to-variable-length codes with the same number of codewords.<> View full abstract»

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  • Multiterminal detection with zero-rate data compression

    Publication Year: 1992 , Page(s): 254 - 267
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1150 KB)  

    The asymptotic performance of a multiterminal detection system comprising a central detector and two remote sensors that have access to discrete, spatially dependent, and temporally memoryless observations is discussed. It is assumed that prior to transmitting information to the central detector, each sensor compresses its observations at a rate which approaches zero as the sample size tends to infinity, and that, on the basis of the compressed data from both sensors, the central detector seeks to determine whether the true distribution of the observations belongs to a null class II or an alternative class Xi . Under the criterion that stipulates minimization of the type-II error rate subject to an upper bound epsilon on the type-I error rate, it is shown that, in the case of simple distribution classes ( mod Pi mod = mod Xi mod =1), the error exponent achievable by such a system has a simple characterization, is independent of the value of epsilon , and is insensitive to changes in compression rate as long as the asymptotic rate on one of the sensors is zero.<> View full abstract»

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  • Chain codes and their linear reconstruction filters

    Publication Year: 1992 , Page(s): 268 - 280
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1182 KB)  

    A differential chain code implementation of the basic eight-directional and N-ring chain code for the encoding of line drawings is considered. Several distortion and rate criteria are considered, and they are evaluated for the special case of encoding infinite straight lines. These results indicate that the differential code outperforms ring codes and the ring delta code. Using a linear decoding filter for reconstructing a smoothed approximation to the original line is also considered. Optimal reconstruction filters for infinite straight lines at various angles are derived. An angle-invariant reconstruction filter that minimizes the expected square distortion taken over all angles is derived. The overall performance using this filter is close to that of the optimum filter. Furthermore, the impulse response of the angle-invariant filter is approximately rectangular, which can lead to simple hardware implementations.<> View full abstract»

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  • Trellis shaping

    Publication Year: 1992 , Page(s): 281 - 300
    Cited by:  Papers (138)  |  Patents (17)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2171 KB)  

    The author discusses trellis shaping, a method of selecting a minimum-weight sequence from an equivalence class of possible transmitted sequences by a search through the trellis diagram of a shaping convolutional code C/sub s/. Shaping gains on the order of 1 dB may be obtained with simple four-state shaping codes and with moderate constellation expansion. The shaping gains obtained with more complicated codes approach the ultimate shaping gain of 1.53 dB. With a feedback-free syndrome-former for C/sub s/, transmitted data can be recovered without catastrophic error propagation. Constellation expansion and peak-to-average energy ratio may be effectively limited by peak constraints. With lattice-theoretic constellations, the shaping operation may be characterized as a decoding of an initial sequence in a channel trellis code by a minimum-distance decoder for a shaping trellis code based on the shaping convolutional code, and the set of possible transmitted sequences is then the set of code sequences in the channel trellis code that lie in the Voronoi region of the trellis shaping code.<> View full abstract»

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  • Trellis precoding: combined coding, precoding and shaping for intersymbol interference channels

    Publication Year: 1992 , Page(s): 301 - 314
    Cited by:  Papers (87)  |  Patents (20)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1503 KB)  

    On a linear Gaussian channel with intersymbol interference (ISI), trellis precoding is a method that achieves the equalization performance of Tomlinson-Harashima (TH) precoding, the coding gain of any known lattice-type coset code, and a considerable shaping gain. Trellis precoding may be viewed as a generalization of trellis shaping to Gaussian ISI channels, or, alternatively, as a generalization of TH precoding, with coded modulation that achieves shaping gain. With trellis precoding channel capacity can be approached essentially as closely on any strictly bandlimited, high signal-to-noise ratio Gaussian channel as on the ideal channel, using the same coding techniques. For first- and second-order FIR and IIR (finite and infinite impulse response) channels, it is shown that shaping gains close to 1 dB can be obtained with a two-dimensional four-state trellis code. Trellis precoding is quite practical whenever channel information is available at the transmitter.<> View full abstract»

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  • Density estimation by stochastic complexity

    Publication Year: 1992 , Page(s): 315 - 323
    Cited by:  Papers (23)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (806 KB)  

    The results by P. Hall and E.J. Hannan (1988) on optimization of histogram density estimators with equal bin widths by minimization of the stochastic complexity are extended and sharpened in two separate ways. As the first contribution, two generalized histogram estimators are constructed. The first has unequal bin widths which, together with the number of the bins, are determined by minimization of the stochastic complexity using dynamic programming. The other estimator consists of a mixture of equal bin width estimators, each of which is defined by the associated stochastic complexity. As the main contribution in the present work, two theorems are proved, which together extend the universal coding theorems to a large class of data generating densities. The first gives an asymptotic upper bound for the code redundancy in the order of magnitude, achieved with a special predictive type of histogram estimator, which sharpens a related bound. The second theorem states that this bound cannot be improved upon by any code whatsoever.<> View full abstract»

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  • Identifiability of hidden Markov information sources and their minimum degrees of freedom

    Publication Year: 1992 , Page(s): 324 - 333
    Cited by:  Papers (17)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (801 KB)  

    If only a function of the state in a finite-state Markov chain is observed, then the stochastic process is no longer Markovian in general. This type of information source is found widely and the basic problem of its identifiability remains open, that is, the problem of showing when two different Markov chains generate the same stochastic process. The identifiability problem is completely solved by linear algebra, where a block structure of a Markov transition matrix plays a fundamental role, and from which the minimum degree of freedom for a source is revealed.<> View full abstract»

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  • Recursive structure of noncausal Gauss-Markov random fields

    Publication Year: 1992 , Page(s): 334 - 354
    Cited by:  Papers (58)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1596 KB)  

    An approach is developed for noncausal Gauss-Markov random fields (GMRFs) that enables the use of recursive procedures while retaining the noncausality of the field. Recursive representations are established that are equivalent to the original field. This is achieved by first presenting a canonical representation for GMRFs that is based on the inverse of the covariance matrix, which is called the potential matrix. It is this matrix rather than the field covariance that reflects in a natural way the MRF structure. From its properties, two equivalent one-sided representations are derived, each of which is obtained as the successive iterates of a Riccati-type equation. For homogeneous fields, these unilateral descriptions are symmetrized versions of each other, the study of only one Riccati equation being required. It is proven that this Riccati equation converges at a geometric rate, therefore the one-sided representations are asymptotically invariant. These unilateral representations make it possible to process the fields with well-known recursive techniques such as Kalman-Bucy filters and two-point smoothers.<> View full abstract»

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  • The suboptimality of randomized tests in distributed and quantized detection systems

    Publication Year: 1992 , Page(s): 355 - 361
    Cited by:  Papers (31)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (579 KB)  

    The design of decentralized (or quantized) detection systems requires simultaneous optimization of quantizer mappings and ultimate fusion rule. It is shown that if the likelihood ratios of the unquantized (or raw) observations are independent and contain no point-masses of probability, the optimal test does not randomize; this is so despite the fact that the data to be fused can be considered discrete. The result is a considerable simplification in the design search.<> View full abstract»

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  • Performance bounds for noncoherent detection under Brownian phase noise

    Publication Year: 1992 , Page(s): 362 - 379
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1668 KB)  

    The performance of noncoherent detection of orthogonal phase-noise impaired signals in the presence of additive white Gaussian noise is considered. The authors present a novel class of upper and lower bounds on the error probability of a binary hypothesis test, comprising quadratic forms of the additive noise and of the filtered noisy-phase signal plus noise. Filtering the noisy-phase signal gives rise to bounded nonlinear functionals of the Brownian motion sample-path, the exact statistics of which are unknown. The classical theory of Chebyshev systems is utilized to solve the limiting values of the required stochastic expectations, based on the availability of the corresponding generalized moments. The resulting multidimensional moment bounds constitute the tightest possible error bounds for the given set of generalized moments, and require only modest computational efforts. The theory is applicable to assess the design and performance of optical heterodyne systems and is most suitable for coded systems employing hard-decisions, for which the obtained bounds are remarkably tight.<> View full abstract»

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  • On the optimal asymptotic performance of universal ordering and of discrimination of individual sequences

    Publication Year: 1992 , Page(s): 380 - 385
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (509 KB)  

    The authors consider the problem of ordering strings of a fixed length over a discrete alphabet according to decreasing probabilities of having been emitted by an unknown finite-state source. Data compression is applied to derive a universal algorithm that solves this problem with an optimal asymptotic performance. This result is employed in the solution of the following problem: discriminate an individual sequence as emitted by an independently identically distributed random source of equally likely symbols or as a signal corrupted by noise. Tight lower and upper bounds on the asymptotic performance of finite-state discriminators are given.<> View full abstract»

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  • A unifying maximum-likelihood view of cumulant and polyspectral measures for non-Gaussian signal classification and estimation

    Publication Year: 1992 , Page(s): 386 - 406
    Cited by:  Papers (59)  |  Patents (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1792 KB)  

    Classification and estimation of non-Gaussian signals observed in additive Gaussian noise of unknown covariance are addressed using cumulants or polyspectra. By integrating ideas from pattern recognition and model identification, asymptotically optimum maximum-likelihood classifiers and ARMA (autoregressive moving average) parameter estimators are derived without knowledge of the data distribution. Identifiability of noncausal and nonminimum phase ARMA models is established using a finite number of cumulant or polyspectral lags of any order greater than two. A unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms. Tentative order determination and model validation tests for non-Gaussian ARMA processes are described briefly. Illustrative simulations are also presented.<> View full abstract»

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  • On the construction of statistically synchronizable codes

    Publication Year: 1992 , Page(s): 407 - 414
    Cited by:  Papers (24)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (807 KB)  

    The problem of constructing statistically synchronizable codes over arbitrary alphabets and for any finite source is considered. It is shown how to efficiently construct a statistically synchronizable code whose average codeword length is within the least likely codeword probability from that of the Huffman code for the same source. Moreover, a method is given for constructing codes having a synchronizing codeword. The method yields synchronous codes that exhibit high synchronizing capability and low redundancy.<> View full abstract»

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  • Entropy-constrained trellis-coded quantization

    Publication Year: 1992 , Page(s): 415 - 426
    Cited by:  Papers (1)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1064 KB)  

    Trellis-coded quantization is generalized to allow noiseless coding of the trellis branch reproduction symbols. An entropy-constrained trellis-coded quantization (ECTCQ) design algorithm is presented, based on the generalized Lloyd algorithm for trellis code design and the entropy-constrained vector quantization design algorithm. ECTCQ systems are designed for memoryless Gaussian and Laplacian sources, and for first- and second-order Gauss-Markov sources. With an 8-state trellis, the mean-squared error ECTCQ encoding performance for memoryless sources with smooth densities is within about 0.5 dB of the rate-distortion function. Small additional improvements are achieved with larger trellises. Similar, though not quite as good, performance is achieved for the Gauss-Markov sources by using the ECTCQ in a predictive coding structure.<> View full abstract»

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  • On the rate-distortion efficiency of subband coding

    Publication Year: 1992 , Page(s): 426 - 428
    Cited by:  Papers (72)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (283 KB)  

    It is shown that for the realizable subband coding of a wide sense stationary Gaussian source, with the implied separate encoding of the subband signals, the encoding performance is generally inferior to the rate-distortion function of the source. It is established that, for small encoding distortion, except for special cases, the subband coding is generally suboptimum.<> View full abstract»

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  • On universal quantization by randomized uniform/lattice quantizers

    Publication Year: 1992 , Page(s): 428 - 436
    Cited by:  Papers (78)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (748 KB)  

    Uniform quantization with dither, or lattice quantization with dither in the vector case, followed by a universal lossless source encoder (entropy coder), is a simple procedure for universal coding with distortion of a source that may take continuously many values. The rate of this universal coding scheme is examined, and a general expression is derived for it. An upper bound for the redundancy of this scheme, defined as the difference between its rate and the minimal possible rate, given by the rate distortion function of the source, is derived. This bound holds for all distortion levels. Furthermore, a composite upper bound on the redundancy as a function of the quantizer resolution that leads to a tighter bound in the high rate (low distortion) case is presented.<> View full abstract»

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  • A note on the competitive optimality of the Huffman code

    Publication Year: 1992 , Page(s): 436 - 439
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (396 KB)  

    A bound on the probability that the length of any source code will be shorter than the self information by gamma bits is easily obtained using a Chebyshev-type argument. From this bound, one can establish the competitive optimality of the self information and of the Shannon-Fano code (up to one bit). In general, however, the Huffman code cannot be examined using this technique. Nevertheless, in the present work, the competitive optimality (up to one bit) of the Huffman code for general sources is also established using a different technique.<> View full abstract»

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  • On the redundancy of optimal codes with limited word length

    Publication Year: 1992 , Page(s): 439 - 445
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (604 KB)  

    Some limitations are given on the redundancy of D-ary codes with maximal codeword length L. An upper bound that improves on a previous result of E.N. Gilbert (1971) is given. It is then shown that the redundancy of these constrained codes is very close to that of the unconstrained Huffman codes when the number of codewords N is such that ND/sup 1-L/ becomes negligible. A tight bound is given on the redundancy when only the most likely probabilities are known. In the binary case, a tight lower bound is given on the redundancy when only the least likely probability is known.<> View full abstract»

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  • Capacity of the L/sub p/ norm-constrained Poisson channel

    Publication Year: 1992 , Page(s): 445 - 450
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (499 KB)  

    The capacity of the Poisson channel is derived with a specified constraint imposed on the L/sub p/ norm // chi t///sub p/ of the encoder intensity chi . Formulae are given for the capacity which establish previously known results for p=1, p=2, and p= infinity to be part of a system of capacity problems with common form and solution. These formulae apply with or without causal feedback and whether or not the encoder intensity is OOK (on/off keying)-constrained.<> View full abstract»

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  • A lower-bound for the error-variance of maximum-likelihood delay estimates of discontinuous pulse waveforms

    Publication Year: 1992 , Page(s): 451 - 457
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (666 KB)  

    A new lower bound is developed for the error variance of maximum-likelihood time-delay estimation when the received signal is a square pulse, corrupted by additive white Gaussian noise. The bound is generated by combining concepts previously developed for a special class of stochastic processes, induced by the signal model. For moderate signal to noise ratios, the new bound is significantly tighter than previously known ones.<> View full abstract»

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  • Tobit maximum-likelihood estimation for stochastic time series affected by receiver saturation

    Publication Year: 1992 , Page(s): 457 - 469
    Cited by:  Papers (1)  |  Patents (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1108 KB)  

    The Tobit (Tobin Probit) model is adapted from the field of econometrics as a maximum likelihood estimator of PDF (probability density function) parameters for data that have been censored and truncated. A general expression for the Tobit estimator is presented. It is shown that when the (standard) maximum likelihood estimator is efficient for the random variable with unlimited dynamic range, the unbiased Tobit estimator is efficient for the censored/truncated random variable. The model is presented in detail for the Rayleigh PDF; its efficiency is confirmed, independent of the degree of truncation/censoring. Results from the application of Tobit estimation to simulated data with Rayleigh, log-normal, Rice-Nakagami, and Nagakami-M PDFs are shown to exhibit very low mean-squared error as well. The limitations and computational complexities of the Tobit estimator are discussed.<> View full abstract»

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  • Steiner system signal sets over the Gaussian channel

    Publication Year: 1992 , Page(s): 469 - 472
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (340 KB)  

    Steiner systems constitute an example of codes that achieve asymptotic error-free transmission for the Gaussian channel. In contrast to simplex and orthogonal codes which also have this property, these codes make more efficient use of the bandwidth by reducing the required dimensionality to generate the M signals. Tight upper bounds for the symbol error probability are derived for coherent and noncoherent detection that include previously reported results as special cases. The relative bandwidth efficiency with respect to orthogonal codes is presented, and a combined performance plot is given that allows a meaningful comparison between the different coding schemes considered.<> View full abstract»

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  • Coding for a degraded memory under a partial modification of records

    Publication Year: 1992 , Page(s): 473 - 477
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (477 KB)  

    The coding problem for the binary degraded memory (DM) or write-once-memory (WOM) under a partial modification of records is considered. For this memory, if '1' is recorded in any cell then the content of this cell cannot be changed during following recordings. Double recording into such a memory with specified constraints is considered. Upper and lower bounds for the capacity of the DM under this kind of recording are derived. The lower bound is derived only for the case where the size of input messages alphabet is going to infinity.<> View full abstract»

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  • On the spectra of the duals of binary BCH codes of designed distance delta =9

    Publication Year: 1992 , Page(s): 478 - 479
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (192 KB)  

    An infinite series of duals of binary BCH codes with designed distance delta =9 and lengths l=2/sup n/ with n odd is found, such that their weights almost satisfy the Carlitz-Uchiyama bound. This solves negatively a problem formulated by F.J. MacWilliams and N.J.A. Sloane (1977).<> 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