Showing papers in "IEEE Transactions on Information Theory in 1988"
TL;DR: The family of Barnes-Wall lattices and their principal sublattices, which are useful in constructing coset codes, are generated by iteration of a simple construction called the squaring construction, and are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum-likelihood decoding algorithms.
Abstract: For pt.I see ibid., vol.34, no.5, p.1123-51 (1988). The family of Barnes-Wall lattices (including D/sub 4/ and E/sub 8/) of lengths N=2/sup n/ and their principal sublattices, which are useful in constructing coset codes, are generated by iteration of a simple construction called the squaring construction. The closely related Reed-Muller codes are generated by the same construction. The principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions, which also exhibit the interrelationships between codes and lattices of different lengths. An extension called the cubing construction generates good codes and lattices of lengths N=3*2/sup n/, including the Golay code and Leech lattice, with the use of special bases for 8-space. Another related construction generates the Nordstrom-Robinson code and an analogous 16-dimensional nonlattice packing. These constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum-likelihood decoding algorithms. >
685 citations
TL;DR: The known types of coset codes, as well as a number of new classes that systematize and generalize known codes, are classified and compared in terms of these parameters.
Abstract: Practically all known good constructive coding techniques for bandlimited channels, including lattice codes and various trellis-coded modulation schemes, can be characterized as coset codes. A coset code is defined by a lattice partition Lambda / Lambda ' and by a binary encoder C that selects a sequence of cosets of the lattice Lambda '. The fundamental coding gain of a coset code, as well as other important parameters such as the error coefficient, the decoding complexity, and the constellation expansion factor, are purely geometric parameters determined by C Lambda / Lambda '. The known types of coset codes, as well as a number of new classes that systematize and generalize known codes, are classified and compared in terms of these parameters. >
676 citations
TL;DR: The author defines a set of operators which localize in both time and frequency, similar to but different from the low-pass time-limiting operator, the singular functions of which are the prolate spheroidal wave functions.
Abstract: The author defines a set of operators which localize in both time and frequency. These operators are similar to but different from the low-pass time-limiting operator, the singular functions of which are the prolate spheroidal wave functions. The author's construction differs from the usual approach in that she treats the time-frequency plane as one geometric whole (phase space) rather than as two separate spaces. For disk-shaped or ellipse-shaped domains in time-frequency plane, the associated localization operators are remarkably simple. Their eigenfunctions are Hermite functions, and the corresponding eigenvalues are given by simple explicit formulas involving the incomplete gamma functions. >
657 citations
TL;DR: Two polynomial-time algorithms are given for scheduling conversations in a spread spectrum radio network that jointly meet a prespecified end-to-end demand and has the smallest possible length.
Abstract: Two polynomial-time algorithms are given for scheduling conversations in a spread spectrum radio network. The constraint on conversations is that each station can converse with only one other station at a time. The first algorithm is strongly polynomial and finds a schedule of minimum length that allows each pair of neighboring stations to converse directly for a prescribed length of time. The second algorithm is designed for the situation in which messages must be relayed multiple hops. The algorithm produces, in polynomial time, a routing vector and compatible link schedule that jointly meet a prespecified end-to-end demand, so that the schedule has the smallest possible length. >
602 citations
TL;DR: In this article, it was shown that any continuous-phase-modulation (CPM) system can be decomposed into a continuous phase encoder and a memoryless modulator in such a way that the former is a linear (modulo some integer P) time-invariant sequential circuit and the latter is also time invariant.
Abstract: It is shown that any continuous-phase-modulation (CPM) system can be decomposed into a continuous-phase encoder and a memoryless modulator in such a way that the former is a linear (modulo some integer P) time-invariant sequential circuit and the latter is also time invariant. This decomposition is exploited to obtain alternative realizations of the continuous-phase encoder (and hence of CPM) and also to obtain alternative forms of the optimum decoding algorithm. When P is a prime p so that the encoder is linear over the finite field GF(p), it is shown that cascading it with an outside convolutional encoder is equivalent to a single convolutional encoder. It is pointed out that the cascade of the modulator, the waveform channel (which it is assumed is characterized by additive white Gaussian noise), and the demodulator that operates over one symbol interval yield a discrete memoryless channel that can be studied without the distractions introduced by continuous-phase encoding. >
515 citations
TL;DR: It is shown that the stability region for the case of two terminals can be obtained in a simple way and lower (inner) bounds are obtained for the Stability region of the system with an arbitrary finite number of terminals that are tighter than the ones already known.
Abstract: The standard discrete-time slotted ALOHA system with a finite number of buffered terminals is considered. The stability (ergodicity) region for this system is known only for the case of two terminals and for the case of any number of symmetric terminals. The stability of the system is studied by means of a simple concept of dominance. It is shown that the stability region for the case of two terminals can be obtained in a simple way. Lower (inner) bounds are obtained for the stability region of the system with an arbitrary finite number of terminals that are tighter than the ones already known. A similarity between these stability results and the achievable region of the no-feedback collision channel is pointed out that suggests a connection between the two problems. >
442 citations
TL;DR: It is shown that a Boolean combining function f(x) of n variables is mth-order correlation-immune if and only if its Walsh transform F( omega ) vanishes for all omega with Hamming weight between 1 and m, inclusive.
Abstract: It is shown that a Boolean combining function f(x) of n variables is mth-order correlation-immune if and only if its Walsh transform F( omega ) vanishes for all omega with Hamming weight between 1 and m, inclusive. This result is used to extend slightly Siegenthaler's (IEEE Trans. Comput., vol. C-34, pp. 81-85, Jan. 1985) characterization of the algebraic normal form of correlation-immune combining functions. >
423 citations
TL;DR: The capacity of the AVC is determined with constraints on the transmitted codewords as well as on the channel state sequences, and it is demonstrated that it may be positive but less than the corresponding random code capacity.
Abstract: A well-known result of R. Ahlswede (1970) asserts that the deterministic code capacity of an arbitrarily varying channel (AVC), under the average-error-probability criterion, either equals its random code capacity or else is zero. A necessary and sufficient condition is identified for deciding between these alternative, namely, the capacity is zero if and only if the AVC is symmetrizable. The capacity of the AVC is determined with constraints on the transmitted codewords as well as on the channel state sequences, and it is demonstrated that it may be positive but less than the corresponding random code capacity. A special case of the results resolves a weakened version of a fundamental problem of coding theory. >
364 citations
TL;DR: A synchronous multiple-user spread-spectrum multiple system is proposed that uses N-shift cross-orthogonal sequences and a complete complementary code derived from them are defined and discussed.
Abstract: N-shift cross-orthogonal sequences and a complete complementary code derived from them are defined and discussed. A general method for generating this code is also discussed. A synchronous multiple-user spread-spectrum multiple system is proposed that uses N-shift cross-orthogonal sequences. >
343 citations
TL;DR: The probabilistic method is used to find minimum weights of all extended quadratic residue codes of length 440 or less, and can be generalized to codes over GF(q) with q>2.
Abstract: An algorithm is developed that can be used to find, with a very low probability of error (10/sup -100/ or less in many cases), the minimum weights of codes far too large to be treated by any known exact algorithm. The probabilistic method is used to find minimum weights of all extended quadratic residue codes of length 440 or less. The probabilistic algorithm is presented for binary codes, but it can be generalized to codes over GF(q) with q>2. >
268 citations
TL;DR: It is proved that, in the limit of increasing block length N, the capacity of the discrete-time Gaussian channel (DTGC) with ISI using a per block average-energy input constraint (N-block DTGC) is indeed also the capacity when using the per symbol average- energy constraint.
Abstract: The discrete-time Gaussian channel with intersymbol interference (ISI) where the inputs are subject to a per symbol average-energy constraint is considered. The capacity of this channel is derived by means of a hypothetical channel model called the N-circular Gaussian channel (NCGC), whose capacity is readily derived using the theory of the discrete Fourier transform. The results obtained for the NCGC are used further to prove that, in the limit of increasing block length N, the capacity of the discrete-time Gaussian channel (DTGC) with ISI using a per block average-energy input constraint (N-block DTGC) is indeed also the capacity when using the per symbol average-energy constraint. >
TL;DR: In this article, the capacity and error exponent of the direct detection optical channel are discussed and an upper bound is obtained on the error exponent which coincides with the lower bound, thus, this channel is the only channel for which error exponent can be known exactly.
Abstract: For pt.I see ibid., vol.34, no.6, p.1449-61 (1980). The discussion of the capacity and error exponent of the direct detection optical channel is continued. The channel input in a T-second interval is a waveform satisfying certain peak and average power constraints for the optical signals. The channel output is a Poisson process with an intensity parameter that accounts for the dark-current component. An upper bound is obtained on the error exponent which coincides with the lower bound. Thus, this channel is one for which the error exponent can be known exactly. >
TL;DR: It is shown that minimal proper trellises exists for all block codes and bounds are shown to be exact for maximum distance separable codes and nearly so for perfect codes.
Abstract: Basic concepts in the study of trellises of block codes are defined. It is shown that minimal proper trellises exists for all block codes. Bounds on the size of such trellises are established. These bounds are shown to be exact for maximum distance separable codes and nearly so for perfect codes. >
TL;DR: A general class of Bayesian lower bounds on moments of the error in parameter estimation is formulated, and it is shown that the Cramer-Rao, the Bhattacharyya, the Bobrovsky-Zakai, and the Weiss-Weinstein lower bounds are special cases in the class.
Abstract: A general class of Bayesian lower bounds on moments of the error in parameter estimation is formulated, and it is shown that the Cramer-Rao, the Bhattacharyya, the Bobrovsky-Zakai, and the Weiss-Weinstein lower bounds are special cases in the class. The bounds can be applied to the estimation of vector parameters and any given function of the parameters. The extension of these bounds to multiple parameter is discussed. >
TL;DR: The authors show, for example, how to generate probability density functions of the magnitude of a filtered laser tone and how to analytically represent the characteristic function of the PDF in closed form in the small-phase-noise realm.
Abstract: The phase noise associated with single-mode semiconductor lasers must be accounted for in performance studies of lightwave communication systems. The standard phase noise model is a Brownian-motion stochastic process. Although many analyses of lightwave communication systems have been published, none, to the authors knowledge, has fully adhered to the standard model. The reason is that a proper characterization of filtered lightwave signal had not been achieved. Such a characterization, along with theoretical approaches to obtaining it, is detailed. The authors show, for example, how to generate probability density functions (PDFs) of the magnitude of a filtered laser tone (with special attention to the tail region) and how to analytically represent the characteristic function of the PDF in closed form in the small-phase-noise realm. With the characterization in place, the stage is now set for determining the bit-error rate performance of advanced detection techniques which seek to mitigate the phase noise impairment. >
TL;DR: In this paper, a deterministic constructions of (L, d)-universal test sets are presented, and lower and upper bounds on the optimal sizes of such sets are proven.
Abstract: (L, d)-universal sets are useful for exhaustively testing logic circuits with a large number of functional components, designed so that every functional component depends on at most d inputs. Randomized and deterministic constructions of (L, d)-universal test sets are presented, and lower and upper bounds on the optimal sizes of such sets are proven. It is also proven that the design of an optimal exhaustive test set for an arbitrary logic circuit is an NP-complete problem. >
TL;DR: Properties of codes defined by Goppa's algebraic-geometric method using Hermitian curves are discussed and results concerning the minimum distance and the weight distribution of the codes are provided.
Abstract: Properties of codes defined by Goppa's algebraic-geometric method using Hermitian curves are discussed. Generator and parity check matrices for such codes are derived explicitly. Results concerning the minimum distance and the weight distribution of the codes are provided. >
TL;DR: The authors reconsider the problem of determining the minimum distance between output sequences of an ideal band-limiting channel that are generated by uncoded binary sequences transmitted at a rate exceeding the Nyquist rate and find the best L/sup 2/ Fourier approximation to the constant 1 on the interval.
Abstract: The authors reconsider the problem of determining the minimum distance between output sequences of an ideal band-limiting channel that are generated by uncoded binary sequences transmitted at a rate exceeding the Nyquist rate. For signaling rates up to about 25% faster than the Nyquist rate, it is shown that the minimum distance does not drop below the value which it would have in the ideal case wherein there is not intersymbol interference. Mathematically, the problem is to decide if the best L/sup 2/ Fourier approximation to the constant 1 on the interval (- sigma pi , sigma pi ), 0 0, with coefficients restricted to be =1 or =0, occurs when all coefficients are zero. This is shown to be optimal for 0.802... >
TL;DR: It is demonstrated that the normalized least mean square (NLMS) algorithm can be viewed as a modification of the widely used LMS algorithm and is shown to have an important advantage over the LMS, which is that its convergence is independent of environmental changes.
Abstract: It is demonstrated that the normalized least mean square (NLMS) algorithm can be viewed as a modification of the widely used LMS algorithm. The NLMS is shown to have an important advantage over the LMS, which is that its convergence is independent of environmental changes. In addition, the authors present a comprehensive study of the first and second-order behavior in the NLMS algorithm. They show that the NLMS algorithm exhibits significant improvement over the LMS algorithm in convergence rate, while its steady-state performance is considerably worse. >
TL;DR: It is shown that for large signal-to-noise ratio, the asymptotic distribution of the phase is of the Tikhonov type and this framework is then used for the synthesis of differentially coherent receiver structures, one for M-ary phase-shift keying (MPSK) and the other for minimum-shiftkeying (MSK).
Abstract: Some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by Gaussian noise. It is shown that for large signal-to-noise ratio, the asymptotic distribution of the phase is of the Tikhonov type. This framework is then used for the synthesis of differentially coherent receiver structures, one for M-ary phase-shift keying (MPSK) and the other for minimum-shift keying (MSK). The first structure bridges the performance gap between coherent and differentially coherent demodulation of MPSK. The MSK receiver uses matched filtering with differential demodulation. >
TL;DR: It is demonstrated that if one of the probability measure of the two classes is not known, it is still possible to define a universal discrimination function which performs as the optimal (likelihood ratio) discriminant function (which can be evaluated only if the probability measures of theTwo classes are available).
Abstract: Classification with empirically observed statistics is studied for finite alphabet sources. Efficient universal discriminant functions are described and shown to be related to universal data compression. It is demonstrated that if one of the probability measure of the two classes is not known, it is still possible to define a universal discrimination function which performs as the optimal (likelihood ratio) discriminant function (which can be evaluated only if the probability measures of the two classes are available). If both of the probability measures are not available but training vectors from at least one of the two classes are available, it is demonstrated that no discriminant function can perform efficiency of the length of the training vectors does not grow at least linearly with the length of the classified vector. A universal discriminant function is introduced and shown to perform efficiently when the length of the training vectors grows linearly with the length of the classified sequence, in the sense that it yields an error exponent that is arbitrarily close to that of the optimal discriminant function. >
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TL;DR: Several results on binary (d, k) codes are given, including a novel derivation for the capacity of these codes based on information-theoretic principles and lower bounds on thecapacity of such a channel are derived.
Abstract: Several results on binary (d, k) codes are given. First, a novel derivation for the capacity of these codes based on information-theoretic principles is given. Based on this result the spectrum of a (d, k) code is computed. Finally, the problem of computing the capacity of the binary symmetric channel under the condition that the input sequences satisfy the (d, k) constraint is considered. Lower bounds on the capacity of such a channel are derived. >
TL;DR: Several results related to the reproducing kernel Hilbert space of fractional Brownian motion are presented to facilitate the study of signal detection in additive fractional Gaussian noise.
Abstract: Several results related to the reproducing kernel Hilbert space of fractional Brownian motion are presented to facilitate the study of signal detection in additive fractional Gaussian noise. This Hilbert space is completely characterized, and an alternative characterization for the restriction of this class of functions to a compact interval (0.T) is given. Infinite- and finite-interval whitening filters for fractional Brownian motion are also developed. The application of these results to the signal detection problem yields necessary and sufficient conditions for a deterministic or stochastic signal to produce a nonsingular shift when embedded in additive fractional Gaussian noise. A formula for the likelihood ratio corresponding to any deterministic nonsingular shift is developed. >
TL;DR: It is shown that this can be done with O(ln(lnN) bits of communication from each node, which is equivalent to communicating all the node states to one node with only marginally more communication.
Abstract: A broadcast network of N+1 nodes is considered in which each binary digit transmitted by each node is received by every other node via a binary symmetric channel of given transition probability. The errors on these channels are independent over transmitters, receivers and time. Each node has a binary state, and the problem is to construct a distributed algorithm to find the parity of the set of states with some given reliability. It is shown that this can be done with O(ln(lnN)) bits of communication from each node. Communicating all the node states to one node can be accomplished with only marginally more communication. >
TL;DR: A neural network model is presented in which each neuron performs a threshold logic function that always converges to a stable state when operating in a serial mode and to a cycle of length at most 2 whenoperating in a fully parallel mode.
Abstract: A neural network model is presented in which each neuron performs a threshold logic function. The model always converges to a stable state when operating in a serial mode and to a cycle of length at most 2 when operating in a fully parallel mode. This property is the basis for the potential applications of the model, such as associative memory devices and combinatorial optimization. The two convergence theorems (for serial and fully parallel modes of operation) are reviewed, and a general convergence theorem is presented that unifies the two known cases. New relations between the neural network model and the problem of finding a minimum cut in a graph are obtained. >
TL;DR: The cochannel interference peak between any two channels in this system realizes the mathematical lower bound for an asynchronous SSMA system using a set of orthogonal sequences.
Abstract: A set of N-1 orthogonal sequences of period N/sup 2/ is proposed, where N is a natural number. Each orthogonal sequence proposed can be modulated by N complex numbers of absolute value 1, so the modulated sequence is also orthogonal. When N is an odd prime number, the absolute value of the cross-correlation function between any two of the N-1 orthogonal sequences is constant and satisfies the mathematical lower bound. This property of the cross-correlation function is not changed when each of the two orthogonal sequences is modulated by N complex numbers of absolute value 1. Two spread-spectrum multiple-access (SSMA) systems using these sequences are proposed. One system is an asynchronous SSMA system, using the proposed sequences unmodulated. The cochannel interference peak between any two channels in this system realizes the mathematical lower bound for an asynchronous SSMA system using a set of orthogonal sequences. The other system is a synchronous SSMA system without cochannel interference which uses the modulated form of the proposed sequences. >
TL;DR: A construction of perfect maps, i.e. periodic r*v binary arrays in which each n*m binary matrix appears exactly once, is given.
Abstract: A construction of perfect maps, i.e. periodic r*v binary arrays in which each n*m binary matrix appears exactly once, is given. A similar construction leads to arrays in which only the zero n*m matrix does not appear and to a construction in which only a few n*m binary matrices do not appear. A generalization to the nonbinary case is given. The constructions involve an interesting problem in shift-register theory. The solution is given for almost all the case of this problem. >
TL;DR: Random coding theorems are proved for discrete memoryless arbitrarily varying channels (AVCs) with constraints on the transmitted codewords and channel state sequences and the AVC is shown to have a (strong) random coding capacity.
Abstract: Random coding theorems are proved for discrete memoryless arbitrarily varying channels (AVCs) with constraints on the transmitted codewords and channel state sequences. Two types of constraints are considered: peak (i.e. required for each n-length sequence almost surely) and average (over the message set or over an ensemble). For peak constraints on the codewords and on the channel state sequences, the AVC is shown to have a (strong) random coding capacity. If the codewords and/or the channel state sequences are constrained in the average sense, the AVCs do not possess (strong) capacities; only epsilon -capacities are shown to exist. >
TL;DR: In frequency-hopping spread-spectrum multiple-access communication systems, it is desirable to use sets of hopping patterns that, in addition to having good Hamming correlation properties and large period, are also derived from sequences having large linear span.
Abstract: In frequency-hopping spread-spectrum multiple-access communication systems, it is desirable to use sets of hopping patterns that, in addition to having good Hamming correlation properties and large period, are also derived from sequences having large linear span. Here, two such frequency hopping code sequence designs that are based on generalized bent functions and generalized bent sequences are presented. The Hamming correlation properties of the designs are optimal in the first case and close to optimal in the second. In terms of the alphabet size p (required to be prime in both cases), the period and family size of the two designs are given by (p/sup 2/, p) and (p/sup n/, p/sup n/2/+1) (n an even integer), respectively. The finite field sequences underlying the patterns in the first design have linear span exceeding p, whereas still larger linear spans (when compared to the sequence period) can be obtained using the second design method. >
IBM1
TL;DR: It is shown that if formulas are used to compute Boolean functions in the presence of randomly occurring failures then: there is a limit strictly less than 1/2 to the failure probability per gate that can be tolerated, and formulas that tolerate failures must be deeper than those that do not.
Abstract: It is shown that if formulas are used to compute Boolean functions in the presence of randomly occurring failures then: (1) there is a limit strictly less than 1/2 to the failure probability per gate that can be tolerated, and (2) formulas that tolerate failures must be deeper (and, therefore, compute more slowly) than those that do not. The heart of the proof is an information-theoretic argument that deals with computation and errors in very general terms. The strength of this argument is that it applies with equal ease no matter what types of gate are available. Its weaknesses is that it does not seem to predict quantitatively the limiting value of the failure probability or the ratio by which computation proceeds more slowly in the presence of failures. >