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Information Theory, IEEE Transactions on

Issue 2 • Date March 1993

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Displaying Results 1 - 25 of 45
  • Trellis coding with multidimensional QAM signal sets

    Page(s): 325 - 336
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    Trellis coding using multidimensional quadrature amplitude modulation (QAM) signal sets is investigated. Finite-size 2D signal sets are presented that have minimum average energy, are 90 degrees rotationally symmetric, and have from 16 to 1024 points. The best trellis codes using the finite 16-QAM signal set with two, four, six, and eight dimensions are found by computer search (the multidimensional (multi-D) signal set is constructed from the 2-D signal set). The best moderate complexity trellis codes for infinite lattices with two, four six, and eight dimensions are also found. The minimum free squared Euclidean distance and number of nearest neighbors for these codes were used as the selection criteria. Many of the multi-D codes are fully rotationally invariant and give asymptotic coding gains up to 6.0 dB. From the infinite lattice codes, the best codes for transmitting J, J+1/4, J+1/3, J+1/2, J+2/3, and J+3/4 b/sym (J an integer) are presented.<> View full abstract»

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  • A new model of numerical computer data and its application for construction of minimum-redundancy codes

    Page(s): 389 - 397
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    Numerical computer data in many applications contain numerous leading and trailing zeros, and this data feature has been neglected in common source models and related data compression methods. A new approach to source modeling, consisting of the description of this data feature by probabilities pij of data values with i leading and j trailing zeros, is proposed. The entropy of this source model is proved to be less than the entropy of the common ones. Based on this model a few codes of different computational complexity are proposed. Experiments on typical computer files show that the coding algorithms based on the new source and data model considerably outperform existing data compression algorithms View full abstract»

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  • Deterministic prediction in progressive coding

    Page(s): 398 - 408
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    Deterministic prediction in progressive coding of images is investigated. Progressive coding first creates a sequence of resolution layers by beginning with an original image and reducing its resolution several times by factors of some natural number M. The resultant layers are losslessly encoded, beginning with the lowest-resolution layer and, then encoding each higher resolution image incrementally upon the previous one. Coding efficiency may be improved if knowledge of the rules which produced the lower-resolution image of each pair is used to deterministically predict pixels of the higher, so they need not be encoded. Given reduction rules expressing each low-resolution pixel as a function of nearby high-resolution pixels and previously generated low-resolution pixels, it is shown that finding a complete set of rules, each of which deterministically predicts the value of a high-resolution pixel when certain values are found in nearby low-resolution pixels and previously coded high-resolution pixels, is NP-complete. A recursive algorithm for solving the problem in optimal time as a depth-first tree search is proposed, and the characteristics of the resultant prediction process are studied View full abstract»

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  • On the minimum distance of ternary cyclic codes

    Page(s): 409 - 422
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    There are many ways to find lower bounds for the minimum distance of a cyclic code, based on investigation of the defining set. Some new theorems are derived. These and earlier techniques are applied to find lower bounds for the minimum distance of ternary cyclic codes. Furthermore, the exact minimum distance of ternary cyclic codes of length less than 40 is computed numerically. A table is given containing all ternary cyclic codes of length less than 40 and having a minimum distance exceeding the BCH bound. It seems that almost all lower bounds are equal to the minimum distance. Especially shifting, which is also done by computer, seems to be very powerful. For length 40⩽n⩽50, only lower bounds are computed. In many cases (derived theoretically), however, these lower bounds are equal to the minimum distance View full abstract»

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  • Perfect (d,k)-codes capable of correcting single peak-shifts

    Page(s): 656 - 662
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    Codes for the multibit peak-shift recording channel, called (d ,k)-codes of reduced length N, are considered. Arbitrary (d,k)- and perfect (d,k)-codes capable of correcting single peak-shifts of given size t are defined. For the construction of perfect codes, a general combinatorial method connected with finding `good' weight sequences in Abelian groups is used, and the concept of perfect t-shift N-designs is introduced. Explicit constructions of such designs for t=1, t=2, and t =(p-1)/2 are given, where p is a prime. This construction is universal in that it does not depend on the (d,k)-constraints. It also allows automatic correction of those peak-shifts that violate (d,k)-constraints. The construction is extended to (d,k)-codes of fixed binary length and allows the beginning of the next codeword to be determined. The question whether the designed codes can be represented as systematic codes with minimal redundancy is considered as well View full abstract»

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  • A new Reed-Solomon code decoding algorithm based on Newton's interpolation

    Page(s): 358 - 365
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    A Reed-Solomon code decoding algorithm based on Newton's interpolation is presented. This algorithm has as main application fast generalized-minimum-distance decoding of Reed-Solomon codes. It uses a modified Berlekamp-Massey algorithm to perform all necessary generalized-minimum-distance decoding steps in only one run. With a time-domain form of the new decoder the overall asymptotic generalized-minimum-distance decoding complexity becomes O(dn), with n the length and d the distance of the code (including the calculation of all error locations and values). This asymptotic complexity is optimal. Other applications are the possibility of fast decoding of Reed-Solomon codes with adaptive redundancy and a general parallel decoding algorithm with zero delay View full abstract»

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  • Coding for skew-tolerant parallel asynchronous communications

    Page(s): 379 - 388
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    A communication channel consisting of several subchannels transmitting simultaneously and asynchronously is considered, an example being a board with several chips, where the subchannels are wires connecting the chips and differences in the lengths of the wires can result in asynchronous reception. A scheme that allows transmission without an acknowledgment of the message, therefore permitting pipelined communication and providing a higher bandwidth, is described. The scheme allows a certain number of transitions from a second message to arrive before reception of the current message has been completed, a condition called skew. Necessary and sufficient conditions for codes that can detect skew as well as for codes that are skew-tolerant, i.e. can correct the skew and allow continuous operation, are derived. Codes that satisfy the necessary and sufficient conditions are constructed, their optimality is studied, and efficient decoding algorithms are devised. Potential applications of the scheme are in on-chip, on-board, and board to board communications, enabling much higher communication bandwidth View full abstract»

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  • Universal redundancy rates do not exist

    Page(s): 520 - 524
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    The expected redundancy per symbol of an n-block prefix code Cn on a source μ measures how far the code is from being optimal for that source. The existence of sequences of codes with expected redundancy per symbol of O((log n)/n) for `nice' classes of sources, such as Markov sources of a given order, is well known. It is shown that some restriction on the class of processes is necessary in order to obtain such redundancy bounds, for there is no universal redundancy rate for any sequence of prefix codes on the class of all ergodic sources View full abstract»

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  • Super-exponential methods for blind deconvolution

    Page(s): 504 - 519
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    A class of iterative methods for solving the blind deconvolution problem, i.e. for recovering the input of an unknown possibly nonminimum-phase linear system by observation of its output, is presented. These methods are universal do not require prior knowledge of the input distribution, are computationally efficient and statistically stable, and converge to the desired solution regardless of initialization at a very fast rate. The effects of finite length of the data, finite length of the equalizer, and additive noise in the system on the attainable performance (intersymbol interference) are analyzed. It is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems. Recursive and sequential algorithms are also developed, which allow real-time implementation and adaptive equalization of time-varying systems View full abstract»

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  • The input-output map of a monotone discrete-time quasireversible node [queueing theory]

    Page(s): 543 - 552
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    A class of discrete-time quasi-reversible nodes called monotone, which includes discrete-time analogs of the ./M/∞ and ./M/1 nodes, is considered. For stationary ergodic nonnegative integer valued arrival processes, the existence and uniqueness of stationary regimes are proven when a natural rate condition is met. Coupling is used to prove the contractiveness of the input-output map relative to a natural distance on the space of stationary arrival processes that is analogous to Ornstein's d¯ distance. A consequence is that the only stationary ergodic fixed points of the input-output map are the processes of independent and identically distributed Poisson random variables meeting the rate condition View full abstract»

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  • The cutoff rate of time correlated fading channels

    Page(s): 612 - 617
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    The cutoff rate of Rician and Rayleigh channels characterized by time correlated fading is derived for M-ary phase shift keying (MPSK) modulation. It is useful for situations where perfect interleaving cannot be achieved. It indicates the practical achievable information rate of the channel when coding is employed. It is used to determine the potential coding gains of coded modulation over the correlated fading channel View full abstract»

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  • Some results on the covering radii of Reed-Muller codes

    Page(s): 366 - 378
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    Let R(r,m) be the rth-order Reed-Muller code of length 2m and let ρ(r,m ) be its covering radius. R(2,7), R(2,8), R (3,7), and R(4,8) are among those smallest Reed-Muller codes whose covering radii are not known. New bounds for the covering radii of these four codes are obtained. The results are ρ(2,7)⩾40, ρ(2,8)⩾84, 20⩽ρ(3,7)⩽23, and ρ(4,8)⩾22. Noncomputer proofs for the known results that ρ(2,6)=18 and that R(1,5) is normal are given View full abstract»

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  • Analysis of identified 2-D noncausal models

    Page(s): 525 - 534
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    There are two approaches to the identification of noncausal autoregressive systems in two dimensions differing in the assumed noise model. For both approaches, the maximum likelihood estimator formulated in the frequency domain is presented. The Fisher information matrix is evaluated and found to be the sum of a block-Toeplitz and a block-Hankel matrix. The variance of the parameters, however, cannot be used for comparison of the two approaches, so the variance in the frequency domain is evaluated, assuming that the true system in each case can be described by a model of that type, possibly high-order. In particular, the variance of the spectrum estimate is derived. If the number of parameters tends to infinity, it is shown that the two approaches give the same spectrum estimate variance. The question of which set of true spectra can be described by the respective approaches is discussed View full abstract»

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  • On the asymptotic efficiency of importance sampling techniques

    Page(s): 710 - 715
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    The asymptotic efficiency of importance sampling (IS) techniques for the simulation of rare events in a multidimensional nonlinear setting was studied by J.S. Sadowsky and J.A. Bucklew (see ibid., vol.36, p.579-88, 1990). Fundamental results on the asymptotic efficiency of the mean-value modification (MM) technique were derived. Additionally, a statement was made that other IS techniques cannot be asymptotically efficient. It is shown that for the simulation of digital communication systems with Gaussian input, a broad class of asymptotically efficient IS techniques exists. Necessary and sufficient conditions are provided for the asymptotic efficiency of five different IS techniques (including MM) for one-dimensional linear systems. Multidimensional generalizations of these IS techniques are proposed. A sufficient condition for the asymptotic efficiency of these techniques applied to multidimensional nonlinear systems is provided View full abstract»

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  • Difference bases and sparse sensor arrays

    Page(s): 716 - 721
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    Difference bases are discussed and their relevance to sensor arrays is described. Several new analytical difference base structures that result in near optimal low-redundancy sensor arrays are introduced. Algorithms are also presented for efficiently obtaining sparse sensor arrays and/or difference bases. New bounds, related to arrays that have both redundancies and holes in their coarray, are presented. Some extensions to the idea of difference bases that may yield useful results for sensor array design are discussed View full abstract»

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  • An updated table of minimum-distance bounds for binary linear codes

    Page(s): 662 - 677
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    Tables with lower and upper bounds for dmax ( n,k), the maximum possible minimum distance of a binary linear code with word length n and dimension k, are shown View full abstract»

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  • Algebraic decoding using special divisors

    Page(s): 694 - 698
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    The basic algorithm for decoding of algebraic-geometric codes corrects up to (dc-1)2-g/2 errors, where d c denotes the designed minimum distance of a code and g denotes the genus of a curve. The modified algorithm improves on this, but applies to a restricted class of codes. An extended modified algorithm that applies to all codes is formulated. It will correct up to (dc-1)/2-s errors, s is called the Clifford defect of a curve. For curves with g⩾1, this defect satisfies 0⩽s⩽(g-1)/2. The success of the algorithm depends highly on the curve that is used and the result is in the first place a theoretical result. To support the practical importance, two special cases are considered. All codes from hyperelliptic curves can be decoded up to the designed minimum distance. For plane curves that contain at least one rational point, it is shown that s⩽(g+1)/4 View full abstract»

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  • Uniform switching system by families of switching sets

    Page(s): 479 - 490
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    A new mathematical method in coding theory that is applicable to various practical problems in communication systems is introduced. The uniform switching system based on k-sets is defined, and its cardinalities, an index system, and error correctabilities are studied. The cardinalities of a uniform switching system based on general families of switching sets are discussed. The asymptotic cardinality is obtained for the Reed-Muller codes of general order View full abstract»

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  • On limiting characterizations of memoryless multiuser capacity regions

    Page(s): 609 - 612
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    The restriction to Gaussian inputs in the limiting expression for the capacity regions of memoryless Gaussian interference and multiple-access channels is shown to fall short of achieving capacity even if the inputs are allowed to be dependent and nonstationary. In addition, the equality between the limiting and the single-letter characterizations of memoryless multiple-access channel capacity is established directly, without recourse to independent coding theorems View full abstract»

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  • Decentralized sequential detection with a fusion center performing the sequential test

    Page(s): 433 - 442
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    A decentralized sequential detection problem is considered in which each one of a set of sensors receives a sequence of observations about the hypothesis. Each sensor sends a sequence of summary messages to the fusion center where a sequential test is carried out to determine the true hypothesis. A Bayesian framework for this problem is introduced, and for the case when the information structure in the system is quasi-classical, it is shown that the problem is tractable. A detailed analysis of this case is presented, along with some numerical results View full abstract»

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  • On the number of correctable errors for some AG-codes

    Page(s): 681 - 684
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    An algorithm that, for codes from a regular plane curve, corrects up to (d*/2)-(m2/8)+(m/4)-(9/8) errors, where d* is the designed distance and m is the degree of the curve, was presented in an earlier work (see ibid., vol.35, p.811-21, 1989). It is now shown that this bound is the best possible for the algorithm considered View full abstract»

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  • Minimum support weights of binary codes

    Page(s): 648 - 654
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    Some relations between the minimum support weights are discussed. In particular, the possible weight hierarchies of codes of dimension 4 are determined View full abstract»

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  • Dynamic server allocation to parallel queues with randomly varying connectivity

    Page(s): 466 - 478
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    Consider N parallel queues competing for the attention of a single server. At each time slot each queue may be connected to the server or not depending on the value of a binary random variable, the connectivity variable. Allocation at each slot; is based on the connectivity information and on the lengths of the connected queues only. At the end of each slot, service may be completed with a given fixed probability. Such a queueing model is appropriate for some communication networks with changing topology. In the case of infinite buffers, necessary and sufficient conditions are obtained for stabilizability of the system in terms of the different system parameters. The allocation policy that serves the longest connected queue stabilizes the system when the stabilizability conditions hold. The same policy minimizes the delay for the special case of symmetric queues. In a system with a single buffer per queue, an allocation policy is obtained that maximizes the throughput and minimizes the delay when the arrival and service statistics of different queues are identical View full abstract»

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  • On the converse theorem in statistical hypothesis testing

    Page(s): 623 - 628
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    Simple statistical hypothesis testing is investigated by making use of the divergence geometric method. The asymptotic behavior of the minimum value of the error probability of the second kind under the constraint that the error probability of the first kind is bounded above by exp(-rn) is looked for, where r is a given positive number. If r is greater than the divergence of the two probability measures, the so-called converse theorem holds. It is shown that the condition under which the converse theorem holds can be divided into two separate cases by analyzing the geodesic connecting the two probability measures, and, as a result, an explanation is given for the Han-Kobayashi linear function fT(X˜) View full abstract»

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  • Vector quantizers with direct sum codebooks

    Page(s): 565 - 580
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    The use of direct sum codebooks to minimize the memory requirements of vector quantizers is investigated. Assuming arbitrary fixed partitions, necessary conditions for minimum distortion codebooks are derived, first for scalar codebooks, assuming mean-squared error distortion, and then for vector codebooks and a broader class of distortion measures. An iterative procedure is described for designing locally optimal direct sum codebooks. Both optimal and computationally efficient suboptimal encoding schemes are considered. It is shown that although an optimal encoding can be implemented by a sequential encoder, the complexity of implementing optimal stagewise partitions generally exceeds the complexity of an exhaustive search of the direct sum codebook. It is also shown that sequential nearest-neighbor encoders can be extremely inefficient. The M-search method is explored as one method of improving the effectiveness of suboptimal sequential encoders. Representative results for simulated direct sum quantizers are presented 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