Showing papers in "IEEE Transactions on Information Theory in 1983"
TL;DR: Several models are formulated in which the security of protocols can be discussed precisely, and algorithms and characterizations that can be used to determine protocol security in these models are given.
Abstract: Recently the use of public key encryption to provide secure network communication has received considerable attention. Such public key systems are usually effective against passive eavesdroppers, who merely tap the lines and try to decipher the message. It has been pointed out, however, that an improperly designed protocol could be vulnerable to an active saboteur, one who may impersonate another user or alter the message being transmitted. Several models are formulated in which the security of protocols can be discussed precisely. Algorithms and characterizations that can be used to determine protocol security in these models are given.
5,145 citations
TL;DR: It is shown that the optimal transmitter adapts its signal to the state S rather than attempting to cancel it, which is also the capacity of a standard Gaussian channel with signal-to-noise power ratio P/N.
Abstract: A channel with output Y = X + S + Z is examined, The state S \sim N(0, QI) and the noise Z \sim N(0, NI) are multivariate Gaussian random variables ( I is the identity matrix.). The input X \in R^{n} satisfies the power constraint (l/n) \sum_{i=1}^{n}X_{i}^{2} \leq P . If S is unknown to both transmitter and receiver then the capacity is \frac{1}{2} \ln (1 + P/( N + Q)) nats per channel use. However, if the state S is known to the encoder, the capacity is shown to be C^{\ast} =\frac{1}{2} \ln (1 + P/N) , independent of Q . This is also the capacity of a standard Gaussian channel with signal-to-noise power ratio P/N . Therefore, the state S does not affect the capacity of the channel, even though S is unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the state S rather than attempting to cancel it.
4,130 citations
TL;DR: A generalization of the convex hull of a finite set of points in the plane leads to a family of straight-line graphs, "alpha -shapes," which seem to capture the intuitive notions of "fine shape" and "crude shape" of point sets.
Abstract: A generalization of the convex hull of a finite set of points in the plane is introduced and analyzed. This generalization leads to a family of straight-line graphs, " \alpha -shapes," which seem to capture the intuitive notions of "fine shape" and "crude shape" of point sets. It is shown that a-shapes are subgraphs of the closest point or furthest point Delaunay triangulation. Relying on this result an optimal O(n \log n) algorithm that constructs \alpha -shapes is developed.
1,648 citations
TL;DR: A class of nonlinear estimation algorithms is described to estimate the unknown phase of a carrier which is fully modulated by m -ary PSK modulation, and the effect of quantization and finite read-only-memory implementation of the nonlinearity are determined by computer simulation.
Abstract: Burst transmission of digital data and voice has become commonplace, particularly in satellite communication systems employing time-division multiple-access (TI)MA) and packet demand-assignment multiple-access (DAMA) techniques. In TDMA systems particularly, phase estimation on each successive burst is a requirement, while bit timing and carrier frequency can be accurately tracked between bursts. A class of nonlinear estimation algorithms is described to estimate the unknown phase of a carrier which is fully modulated by m -ary PSK modulation. Performance of the method is determined in closed form and compared to the Cramer-Rao lower bound for the variance of the estimation error in the phase of an unmodulated carrier. Results are also obtained when the carrier frequency is imprecisely known. Finally, the effect of quantization and finite read-only-memory (ROM) implementation of the nonlinearity are determined by computer simulation.
1,116 citations
IBM1
TL;DR: A universal data compression algorithm is described which is capable of compressing long strings generated by a "finitely generated" source, with a near optimum per symbol length without prior knowledge of the source.
Abstract: A universal data compression algorithm is described which is capable of compressing long strings generated by a "finitely generated" source, with a near optimum per symbol length without prior knowledge of the source. This class of sources may be viewed as a generalization of Markov sources to random fields. Moreover, the algorithm does not require a working storage much larger than that needed to describe the source generating parameters.
708 citations
TL;DR: A linear coding scheme for secret sharing is exhibited which subsumes the polynomial interpolation method proposed by Shamir and can also be viewed as a deterministic version of Blakley's probabilistic method.
Abstract: A "secret sharing system" permits a secret to be shared among n trustees in such a way that any k of them can recover the secret, but any k-1 have complete uncertainty about it. A linear coding scheme for secret sharing is exhibited which subsumes the polynomial interpolation method proposed by Shamir and can also be viewed as a deterministic version of Blakley's probabilistic method. Bounds on the maximum value of n for a given k and secret size are derived for any system, linear or nonlinear. The proposed scheme achieves the lower bound which, for practical purposes, differs insignificantly from the upper bound. The scheme may be extended to protect several secrets. Methods to protect against deliberate tampering by any of the trustees are also presented.
695 citations
TL;DR: A method is proposed for a key safeguarding scheme in which the shadows are congruence classes of a number associated with the original key that provides efficient error detection and exposes deliberate tampering.
Abstract: A method is proposed for a key safeguarding scheme (threshold scheme) in which the shadows are congruence classes of a number associated with the original key. A variation of this scheme provides efficient error detection and even exposes deliberate tampering. Certain underlying similarities of this scheme with Shamir's interpolation method make it possible to incorporate these protective features in that method as well.
616 citations
TL;DR: A series of known and new protocols for connectivity test, shortest path, and path updating are described and validated and extended to networks with changing topology.
Abstract: A unified approach to the formal description and validation of several distributed protocols is presented. After introducing two basic protocols, a series of known and new protocols for connectivity test, shortest path, and path updating are described and validated. All protocols are extended to networks with changing topology.
471 citations
TL;DR: Some aspects of statistical inference for a class of spatial-interaction models for finite images are presented: primarily the simultaneous autoregressive (SAR) models and conditional Markov (CM) models.
Abstract: Some aspects of statistical inference for a class of spatial-interaction models for finite images are presented: primarily the simultaneous autoregressive (SAR) models and conditional Markov (CM) models. Each of these models is characterized by a set of neighbors, a set of coefficients, and a noise sequence of specified characteristics. We are concerned with two problems: the estimation of the unknown parameters in both SAR and CM models and the choice of an appropriate model from a class of such competing models. Assuming Gaussian-distributed variables, we discuss maximum likelihood (ML) estimation methods. In general, the ML scheme leads to nonlinear optimization problems. To avoid excessive computation, an iterative scheme is given for SAR models, which gives approximate ML estimates in the Gaussian case and reasonably good estimates in some non-Gaussian situations as well. Likewise, for CM models, an easily computable consistent estimate is given. The asymptotic mean-squared error (mse) of this estimate for a four-neighbor CM model is shown tn be substantially less than the mse of the popular coding estimate. Asymptotically consistent decision rules are given for choosing an appropriate SAR or CM model. The usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns. Synthetic patterns obeying known SAR and CM models are generated, and the models corresponding to true and several competing neighbor sets are fitted. The estimation scheme yields estimates close to the parameters of the true models, and the decision rule for the choice of neighbors picks up the true model from the class of competing models.
465 citations
TL;DR: A computer memory with defects is modeled as a discrete memoryless channel with states that are statistically determined, and Arimoto-Blahut type algorithms are used to compute the storage capacity.
Abstract: A computer memory with defects is modeled as a discrete memoryless channel with states that are statistically determined. The storage capacity is found when complete defect information is given to the encoder or to the decoder, and when the defect information is given completely to the decoder but only partially to the encoder. Achievable storage rates are established when partial defect information is provided at varying rates to both the encoder and the decoder. Arimoto-Blahut type algorithms are used to compute the storage capacity.
430 citations
TL;DR: A solution to the inverse problem for the same lattices, namely, given an integer k, to find the kth code vector, and to the closely related problem of finding the index k of a given code vector.
Abstract: In an earlier paper the authors described a very fast method which, for the root lattices A_{n}, D_{n}, E_{n} , their duals and certain other lattices, finds the closest lattice point to an arbitrary point of the underlying space. If the lattices are used as codes for a Gaussian channel, the algorithm provides a fast decoding procedure, or if they are used as vector quantizers the algorithm performs the analog-to-digital conversion efficiently. The present paper offers a solution to the inverse problem for the same lattices (the encoding problem for channel codes or the digital-to-analog part of quantizing), namely, given an integer k , to find the kth code vector, and to the closely related problem of finding the index k of a given code vector.
TL;DR: It turns out that the optimal conference is very simple: by proving a converse and giving an achievability proof, the capacity region of the multiple access channel with partially cooperating encoders is established.
Abstract: We introduce the communication situation in which the encoders of a multiple access channel are partially cooperating. These encoders are connected by communication links with finite capacities, which permit both encoders to communicate with each other. First we give a general definition of such a communication process (conference). Then, by proving a converse and giving an achievability proof, we establish the capacity region of the multiple access channel with partially cooperating encoders. It turns out that the optimal conference is very simple.
IBM1
TL;DR: This work proves an extension of a coding theorem of Marcus and traces a line of mathematics from abstract topological dynamics to concrete logic network diagrams.
Abstract: Ideas which have origins in Shannon's work in information theory have arisen independently in a mathematical discipline called symbolic dynamics. These ideas have been refined and developed in recent years to a point where they yield general algorithms for constructing practical coding schemes with engineering applications. In this work we prove an extension of a coding theorem of Marcus and trace a line of mathematics from abstract topological dynamics to concrete logic network diagrams.
TL;DR: In this paper, it is shown that the decision problem regarding the membership of a given point in the capacity region of a packet radio network (PRN) is NP-complete.
Abstract: : It is shown that the decision problem regarding the membership of a given point in the capacity region of a packet radio network (PRN) is NP- complete. The capacity region is the set of all feasible sets of average origin- to-destination traffic rates, where the feasibility is defined as the existence of any set of rules (deterministic or non-deterministic) for moving the data through the network so that the desired rates are satisfied. The analysis includes a linear programming formulation of TDMA (time-division-multi-access) schemes for PRNs and NP-completeness results for some other related problems. Implicit in the analysis is the optimality of TDMA schemes in terms of achieving a given set of link traffic rates.
TL;DR: The problem of transmitting a sequence of identically distributed independent Gaussian random variables through a Gaussian memoryless channel with a given input power constraint, in the presence of an intelligent jammer, is considered and the optimal policy of the transmitter is to amplify the input sequence to the given power level by a linear transformation, and the receiver is to use a Bayes estimator.
Abstract: The problem of transmitting a sequence of identically distributed independent Gaussian random variables through a Gaussian memoryless channel with a given input power constraint, in the presence of an intelligent jammer, is considered. The jammer taps the channel and feeds back a signal, at a given energy level, for the purpose of jamming the transmitting sequence. Under a square-difference distortion measure which is to be maximized by the jammer and to be minimized by the transmitter and the receiver, this correspondence obtains the complete set of optimal (saddle-point) policies. The solution is essentially unique, and it is structurally different in three different regions in the parameter space, which are determined by the signal-to-noise ratios and relative magnitudes of the noise variances. The best (maximin) policy of the jammer is either to choose a linear function of the measurement he receives through channel-tapping, or to choose, in addition (and additively), an independent Gaussian noise sequence, depending on the region where the parameters lie. The optimal (minimax) policy of the transmitter is to amplify the input sequence to the given power level by a linear transformation, and that of the receiver is to use a Bayes estimator.
TL;DR: Three polygon decomposition problems are shown to be NP-hard and thus unlikely to admit efficient algorithms, and the polygonal region is permitted to contain holes.
Abstract: The inherent computational complexity of polygon decomposition problems is of theoretical interest to researchers in the field of computational geometry and of practical interest to those working in syntactic pattern recognition. Three polygon decomposition problems are shown to be NP-hard and thus unlikely to admit efficient algorithms. The problems are to find minimum decompositions of a polygonal region into (perhaps overlapping) convex, star-shaped, or spiral subsets. We permit the polygonal region to contain holes. The proofs are by transformation from Boolean three-satisfiability, a known NP-complete problem. Several open problems are discussed.
TL;DR: Two interesting cosets of the first-order Reed-Muller code of block length 2^{15} are described, which provide counterexamples to a conjecture on the covering radius.
Abstract: Two interesting cosets of the first-order Reed-Muller code of block length 2^{15} are described. They provide counterexamples to a conjecture on the covering radius.
TL;DR: It is shown that encoding is useless for a class of symmetric channels and channel feedback information is shown to be useful in general.
Abstract: The symbols produced by a finite Markov source are causally encoded so as to be transmitted through a noisy memoryless channel. The encoder is assumed to have channel feedback information and the decoder to be causal. The feedback information is shown to be useful in general. Separation results are derived and used to prove that encoding is useless for a class of symmetric channels.
TL;DR: A coding theorem is introduced and established for another type of source-channel matching problem, i.e., a system of source coding with side information via a MAC, which can be regarded as an extension of the Ahlswede-Korner-Wyner type noiseless coding system.
Abstract: A simple proof of the coding theorem for the multiple-access channel (MAC) with arbitrarily correlated sources (DMCS) of Cover-El Carnal-Salehi, which includes the results of Ahlswede for the MAC and of Slepian-Wolf for the DMCS and the MAC as special cases, is first given. A coding theorem is introduced and established for another type of source-channel matching problem, i.e., a system of source coding with side information via a MAC, which can be regarded as an extension of the Ahlswede-Korner-Wyner type noiseless coding system. This result is extended to a more general system with several principal sources and several side information sources subject to cross observation at the encoders in the sense of Han. The regions are shown to be optimal in special situations. Dueck's example shows that this is in general not the case for the result of Cover-El Gamal-Salehi and the present work. In another direction, the achievable rate region for the module-two sum source network found by Korner-Marton is improved. Finally, some ideas about a new approach to the source-channel matching problem in multi-user communication theory are presented. The basic concept is that of a correlated channel code. The approach leads to several new coding problems.
TL;DR: A new source coding problem is considered for a one-way communication system with correlated source outputs where one of the source outputs must be transmitted to the receiver within a prescribed distortion tolerance as in ordinary source coding.
Abstract: A new source coding problem is considered for a one-way communication system with correlated source outputs \{XY\} . One of the source outputs, i.e., \{X\} , must be transmitted to the receiver within a prescribed distortion tolerance as in ordinary source coding. On the other hand, the other source output, i.e., \{Y\} , has to be kept as secret as possible from the receiver or wiretappers. For this case the equivocation-distortion function \Gamma \ast(d) and the rate-distortion-equivocation function R\ast (d,e) are defined and evaluated. The former is the maximum achievable equivocation of \{Y\} under the distortion tolerance d for \{X\} , and the latter is the minimum rate necessary to attain both the equivocation tolerance e for \{Y\} and the distortion tolerance d for \{X\} . Some examples are included.
TL;DR: In this paper, a quantum mechanical compound state of an input state and its output state generated through a communication channel is constructed, and the mutual information of quantum communication theory is defined by using the compound state, and its fundamental properties are studied.
Abstract: A quantum mechanical compound state of an input state and its output state generated through a communication channel is constructed. The mutual information of quantum communication theory is defined by using the compound state, and its fundamental properties are studied.
TL;DR: The complexity of a periodic sequence is defined to be the least number of stages in a linear feedback shift register that generates periodic sequences.
Abstract: The complexity of a periodic sequence (s) is defined to be the least number of stages in a linear feedback shift register that generates (s)
TL;DR: The consistency and asymptotic expressions for the bias and covariance of discrete-time estimates f_{n}(x) for the marginal probability density function f(X) of continuous-time processes X(t) are established.
Abstract: For broad classes of deterministic and random sampling schemes \{t_{k}\} we establish the consistency and asymptotic expressions for the bias and covariance of discrete-time estimates f_{n}(x) for the marginal probability density function f(x) of continuous-time processes X(t) . The effect of the sampling scheme and the sampling rate on the performance of the estimates is studied. The results are established for continuous-time processes X(t) satisfying various asymptotic independence-uncorrelatedness conditions.
TL;DR: In this paper, the problem of sequential detection of abrupt changes in the spectral behavior of a digital signal is addressed, for example, in the sequential segmentation of nonstationary digital signals such as speech, EEG, ECG, and geophysical signals.
Abstract: The problem of sequential detection of abrupt changes in the spectral behavior of a digital signal is addressed. This problem arises, for example, in the sequential segmentation of nonstationary digital signals such as speech, (EEG) electroencepholograms, (ECG) electrocardiogram, and geophysical signals. The limitations of a classical test will be emphasized, and some new algorithms will be presented and compared via a simulation study and from a theoretical point of view.
TL;DR: New outer bounds are demonstrated for the capacity regions of discrete memoryless interference channels and Gaussian interference channels, which improves previous knowledge when the interference is of medium strength.
Abstract: New outer bounds are demonstrated for the capacity regions of discrete memoryless interference channels and Gaussian interference channels. The bound for discrete channels coincides with the capacity region in special cases. The bound for Gaussian channels improves previous knowledge when the interference is of medium strength.
TL;DR: The principle of minimum cross-entropy is shown to follow from the adoption of an additional axiom: if new information is consistent with a prior estimate of a probability distribution, then the posterior estimate equals the prior.
Abstract: An error in the subject paper is pointed out: when the axioms given there are restricted to the discrete case, they do not imply the discrete case of the principle of minimum cross-entropy. The principle is shown to follow, however, from the adoption of an additional axiom: if new information is consistent with a prior estimate of a probability distribution, then the posterior estimate equals the prior. Minor other improvements and corrections to the arguments in the paper are made.
Journal Article•
TL;DR: A quantum mechanical compound state of an input state and its output state generated through a communication channel is constructed and its fundamental properties are studied.
IBM1
TL;DR: The symbolwise equivalent of the Ziv-Lempel algorithm is extended to incomplete parse trees and requires the proper handling of the comma when one phrase is the prefix of another phrase.
Abstract: The Ziv-Lempel compression algorithm is a string matching and parsing approach to data compression. The symbolwise equivalent for parsing models has been defined by Rissanen and Langdon and gives the same ideal codelength at the same cost in coding parameters. By describing the context and coding parameter for each symbol an insight is provided into how the Ziv-Lempel method achieves compression. This treatment does not employ a probabilistic source for the data string. The Ziv-Lempel method effectively counts symbol instances within parsed phrases. The coding parameter for each symbolwise context is determined by cumulative count ratios. The code string length increase for a symbol y following substring s , under the symbolwise equivalent, is the log of the ratio of node counts in subtrees s and s\cdot y of the Ziv-Lempel parsing tree. To demonstrate the symbolwise equivalent of the Ziv-Lempel algorithm, we extend the work of Rissanen and Langdon to incomplete parse trees. The result requires the proper handling of the comma when one phrase is the prefix of another phrase.
TL;DR: A new lower bound for the minimum distance of a linear code is derived and when applied to cyclic codes both the Bose-Chaudhuri-Hocquenghem (BCH) bound and the Hartmann-Tzeng (HT) bound are obtained as corollaries.
Abstract: A new lower bound for the minimum distance of a linear code is derived. When applied to cyclic codes both the Bose-Chaudhuri-Hocquenghem (BCH) bound and the Hartmann-Tzeng (HT) bound are obtained as corollaries. Examples for which the new bound is superior to these two bounds, as well as to the Carlitz-Uchiyama bound, are given.
TL;DR: A majority decoding method for certain classes of cyclic binary UEP codes is treated and bounds on the length of a LUEP code that ensures a given unequal error protection are derived.
Abstract: It is possible for a linear block code to provide more protection for selected positions in the input message words than is guaranteed by the minimum distance of the code. Linear codes having this property are called linear unequal error protection (LUEP) codes. Bounds on the length of a LUEP code that ensures a given unequal error protection are derived. A majority decoding method for certain classes of cyclic binary UEP codes is treated. A list of short (i.e., of length less than 16) binary LUEP codes of optimal (i.e., minimal) length and a list of all cyclic binary UEP codes of length less than 40 are included.