Showing papers in "IEEE Transactions on Information Theory in 2000"
TL;DR: When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput /spl lambda/(n) obtainable by each node for a randomly chosen destination is /spl Theta/(W//spl radic/(nlogn)) bits persecond under a noninterference protocol.
Abstract: When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput /spl lambda/(n) obtainable by each node for a randomly chosen destination is /spl Theta/(W//spl radic/(nlogn)) bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is /spl Theta/(W/spl radic/An) bit-meters per second. Thus even under optimal circumstances, the throughput is only /spl Theta/(W//spl radic/n) bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance.
9,008 citations
TL;DR: This work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated, and by employing coding at the nodes, which the work refers to as network coding, bandwidth can in general be saved.
Abstract: We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a point-to-point communication network on which a number of information sources are to be multicast to certain sets of destinations. We assume that the information sources are mutually independent. The problem is to characterize the admissible coding rate region. This model subsumes all previously studied models along the same line. We study the problem with one information source, and we have obtained a simple characterization of the admissible coding rate region. Our result can be regarded as the max-flow min-cut theorem for network information flow. Contrary to one's intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated. Rather, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This finding may have significant impact on future design of switching systems.
8,533 citations
TL;DR: This work designs some multiple-antenna signal constellations and simulates their effectiveness as measured by bit-error probability with maximum-likelihood decoding and demonstrates that two antennas have a 6-dB diversity gain over one antenna at 15-dB SNR.
Abstract: Motivated by information-theoretic considerations, we propose a signaling scheme, unitary space-time modulation, for multiple-antenna communication links. This modulation is ideally suited for Rayleigh fast-fading environments, since it does not require the receiver to know or learn the propagation coefficients. Unitary space-time modulation uses constellations of T/spl times/M space-time signals (/spl Phi//sub i/, l=1, ..., L), where T represents the coherence interval during which the fading is approximately constant, and M
1,116 citations
TL;DR: A model for time-varying communication single-access and multiple-access channels without feedback is presented and the rate of time variation of the channel is related to the loss in mutual information due to imperfect knowledge of the measured channel.
Abstract: We present a model for time-varying communication single-access and multiple-access channels without feedback. We consider the difference between mutual information when the receiver knows the channel perfectly and mutual information when the receiver only has an estimate of the channel. We relate the variance of the channel measurement error at the receiver to upper and lower bounds for this difference in mutual information. We illustrate the use of our bounds on a channel modeled by a Gauss-Markov process, measured by a pilot tone. We relate the rate of time variation of the channel to the loss in mutual information due to imperfect knowledge of the measured channel.
1,038 citations
TL;DR: This work proposes a general approach to differential modulation for multiple transmit antennas based on group codes, which can be applied to any number of transmit and receive antennas, and any signal constellation, and can be demodulated with or without channel estimates.
Abstract: Space-time coding and modulation exploit the presence of multiple transmit antennas to improve the performance on multipath radio channels Thus far, most work on space-time coding has assumed that perfect channel estimates are available at the receiver In certain situations, however, it may be difficult or costly to estimate the channel accurately, in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver We propose a general approach to differential modulation for multiple transmit antennas based on group codes This approach ran be applied to any number of transmit and receive antennas, and any signal constellation We also derive low-complexity differential receivers, error bounds, and modulator design criteria, which we use to construct optimal differential modulation schemes for two transmit antennas These schemes can be demodulated with or without channel estimates This permits the receiver to exploit channel estimates when they are available The performance degrades by approximately 3 dB when estimates are not available
944 citations
Journal Article•
TL;DR: Although this algorithm is guaranteed to give exact answers only in certain cases (the "junction tree" condition), unfortunately not including the cases of GTW with cycles or turbo decoding, there is much experimental evidence, and a few theorems, suggesting that it often works approximately even when it is not supposed to.
Abstract: We discuss a general message passing algorithm, which we call the generalized distributive law (GDL). The GDL is a synthesis of the work of many authors in information theory, digital communications, signal processing, statistics, and artificial intelligence. It includes as special cases the Baum-Welch algorithm, the fast Fourier transform (FFT) on any finite Abelian group, the Gallager-Tanner-Wiberg decoding algorithm, Viterbi's algorithm, the BCJR algorithm, Pearl's "belief propagation" algorithm, the Shafer-Shenoy probability propagation algorithm, and the turbo decoding algorithm. Although this algorithm is guaranteed to give exact answers only in certain cases (the "junction tree" condition), unfortunately not including the cases of GTW with cycles or turbo decoding, there is much experimental evidence, and a few theorems, suggesting that it often works approximately even when it is not supposed to.
811 citations
TL;DR: This paper proposes a systematic method for creating constellations of unitary space-time signals for multiple-antenna communication links and systematically produces the remaining signals by successively rotating this signal in a high-dimensional complex space.
Abstract: We propose a systematic method for creating constellations of unitary space-time signals for multiple-antenna communication links. Unitary space-time signals, which are orthonormal in time across the antennas, have been shown to be well-tailored to a Rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients. The signals can achieve low probability of error by exploiting multiple-antenna diversity. Because the fading coefficients are not known, the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum-Euclidean-distance norm. Our construction begins with the first signal in the constellation-an oblong complex-valued matrix whose columns are orthonormal-and systematically produces the remaining signals by successively rotating this signal in a high-dimensional complex space. This construction easily produces large constellations of high-dimensional signals. We demonstrate its efficacy through examples involving one, two, and three transmitter antennas.
761 citations
TL;DR: The experimental results demonstrate that the new hyperspectral measure, the spectral information measure (SIM), can characterize spectral variability more effectively than the commonly used spectral angle mapper (SAM).
Abstract: A hyperspectral image can be considered as an image cube where the third dimension is the spectral domain represented by hundreds of spectral wavelengths. As a result, a hyperspectral image pixel is actually a column vector with dimension equal to the number of spectral bands and contains valuable spectral information that can be used to account for pixel variability, similarity and discrimination. We present a new hyperspectral measure, the spectral information measure (SIM), to describe spectral variability and two criteria, spectral information divergence and spectral discriminatory probability for spectral similarity and discrimination, respectively. The spectral information measure is an information-theoretic measure which treats each pixel as a random variable using its spectral signature histogram as the desired probability distribution. Spectral information divergence (SID) compares the similarity between two pixels by measuring the probabilistic discrepancy between two corresponding spectral signatures. The spectral discriminatory probability calculates spectral probabilities of a spectral database (library) relative to a pixel to be identified so as to achieve material identification. In order to compare the discriminatory power of one spectral measure relative to another, a criterion is also introduced for performance evaluation, which is based on the power of discriminating one pixel from another relative to a reference pixel. The experimental results demonstrate that the new hyperspectral measure can characterize spectral variability more effectively than the commonly used spectral angle mapper (SAM).
505 citations
TL;DR: It is shown that high diversity can be achieved using relatively simple codes as long as very high spectral efficiency is not required and in some cases, performances approaching the information-theoretic bounds.
Abstract: This work considers the achievable performance for coded systems adapted to a multipath block-fading channel model. This is a particularly useful model for analyzing mobile-radio systems which employ techniques such as slow frequency-hopping under stringent time-delay or bandwidth constraints for slowly time-varying channels. In such systems, coded information is transmitted over a small number of fading channels in order to achieve diversity. Bounds on the achievable performance due to coding are derived using information-theoretic techniques. It is shown that high diversity can be achieved using relatively simple codes as long as very high spectral efficiency is not required. Examples of simple block codes and carefully chosen trellis codes are given which yield, in some cases, performances approaching the information-theoretic bounds.
460 citations
TL;DR: It is shown that, subject to some mild restrictions, a grammar-based code is a universal code with respect to the family of finite-state information sources over the finite alphabet.
Abstract: We investigate a type of lossless source code called a grammar-based code, which, in response to any input data string x over a fixed finite alphabet, selects a context-free grammar G/sub x/ representing x in the sense that x is the unique string belonging to the language generated by G/sub x/. Lossless compression of x takes place indirectly via compression of the production rules of the grammar G/sub x/. It is shown that, subject to some mild restrictions, a grammar-based code is a universal code with respect to the family of finite-state information sources over the finite alphabet. Redundancy bounds for grammar-based codes are established. Reduction rules for designing grammar-based codes are presented.
437 citations
TL;DR: This work shows that if the private exponent d used in the RSA (Rivest-Shamir-Adleman (1978) public-key cryptosystem is less than N/sup 0.292/ then the system is insecure.
Abstract: We show that if the private exponent d used in the RSA (Rivest-Shamir-Adleman (1978)) public-key cryptosystem is less than N/sup 0.292/ then the system is insecure. This is the first improvement over an old result of Wiener (1990) showing that when d is less than N/sup 0.25/ the RSA system is insecure. We hope our approach can be used to eventually improve the bound to d less than N/sup 0.5/.
TL;DR: New fundamental code constructions for both quasi-static and time-varying channels are developed, perhaps the first general constructions-other than delay diversity schemes-that guarantee full spatial diversity for an arbitrary number of transmit antennas.
Abstract: The design of space-time codes to achieve full spatial diversity over fading channels has largely been addressed by handcrafting example codes using computer search methods and only for small numbers of antennas. The lack of more general designs is in part due to the fact that the diversity advantage of a code is the minimum rank among the complex baseband differences between modulated codewords, which is difficult to relate to traditional code designs over finite fields and rings. We present general binary design criteria for PSK-modulated space-time codes. For linear BPSK/QPSK codes, the rank of (binary projections of) the unmodulated codewords, as binary matrices over the binary field, is a sufficient design criterion: full binary rank guarantees full spatial diversity. This criterion accounts for much of what is currently known about PSK-modulated space-time codes. We develop new fundamental code constructions for both quasi-static and time-varying channels. These are perhaps the first general constructions-other than delay diversity schemes-that guarantee full spatial diversity for an arbitrary number of transmit antennas.
TL;DR: A new inequality is shown between the errors of the first kind and the second kind, which complements the result of Hiai and Petz (1991) to establish the quantum version of Stein's lemma and yields the strong converse in quantum hypothesis testing.
Abstract: The hypothesis testing problem for two quantum states is treated. We show a new inequality between the errors of the first kind and the second kind, which complements the result of Hiai and Petz (1991) to establish the quantum version of Stein's lemma. The inequality is also used to show a bound on the probability of errors of the first kind when the power exponent for the probability of errors of the second kind exceeds the quantum relative entropy, which yields the strong converse in quantum hypothesis testing. Finally, we discuss the relation between the bound and the power exponent derived by Han and Kobayashi (1989) in classical hypothesis testing.
TL;DR: The main results involve asymptotic expressions for the signal-to-interference ratio of linear multiuser receivers in the limit of large processing gain, with the number of users divided by the processing gain held constant.
Abstract: A linear multiuser receiver for a particular user in a code-division multiple-access (CDMA) network gains potential benefits from knowledge of the channels of all users in the system. In fast multipath fading environments we cannot assume that the channel estimates are perfect and the inevitable channel estimation errors will limit this potential gain. We study the impact of channel estimation errors on the performance of linear multiuser receivers, as well as the channel estimation problem itself. Of particular interest are the scalability properties of the channel and data estimation algorithms: what happens to the performance as the system bandwidth and the number of users (and hence channels to estimate) grows? Our main results involve asymptotic expressions for the signal-to-interference ratio of linear multiuser receivers in the limit of large processing gain, with the number of users divided by the processing gain held constant. We employ a random model for the spreading sequences and the limiting signal-to-interference ratio expressions are independent of the actual signature sequences, depending only on the system loading and the channel statistics: background noise power, energy profile of resolvable multipaths, and channel coherence time. The effect of channel uncertainty on the performance of multiuser receivers is succinctly captured by the notion of effective interference.
TL;DR: This study depends on two measures of discrimination, called capacitory discrimination and triangular discrimination, and obtains certain improvements of the well-known Pinsker inequality.
Abstract: Inequalities which connect information divergence with other measures of discrimination or distance between probability distributions are used in information theory and its applications to mathematical statistics, ergodic theory, and other scientific fields. We suggest new inequalities of this type, often based on underlying identities. As a consequence, we obtain certain improvements of the well-known Pinsker inequality. Our study depends on two measures of discrimination, called capacitory discrimination and triangular discrimination. The discussion contains references to related research and comparison with other measures of discrimination, e.g., Ali-Silvey-Csiszar (1996, 1966) divergences and, in particular, the Hellinger distance.
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TL;DR: In this article, the authors describe fully resilient schemes which can be used against any decoder which decrypts with non-negligible probability, while threshold tracing schemes are only used against decoders which succeed in decryption with probability greater than some threshold.
Abstract: We give cryptographic schemes that help trace the source of leaks when sensitive or proprietary data is made available to a large set of parties. A very relevant application is in the context of pay television, where only paying customers should be able to view certain programs. In this application, the programs are normally encrypted, and then the sensitive data is the decryption keys that are given to paying customers. If a pirate decoder is found, it is desirable to reveal the source of its decryption keys. We describe fully resilient schemes which can be used against any decoder which decrypts with nonnegligible probability. Since there is typically little demand for decoders which decrypt only a small fraction of the transmissions (even if it is nonnegligible), we further introduce threshold tracing schemes which can only be used against decoders which succeed in decryption with probability greater than some threshold. Threshold schemes are considerably more efficient than fully resilient schemes.
TL;DR: Analytical results relating to first- and second-moment characterization of direction dispersion and spatial selectivity in the radio channel as well as to the duality between these two effects are presented.
Abstract: We present analytical results relating to first- and second-moment characterization of direction dispersion and spatial selectivity in the radio channel as well as to the duality between these two effects. Dispersion in direction can be characterized either by the direction power spectrum or by a family of spatial Doppler power spectra at the reception site. Two measures called the direction spread and the maximum spatial Doppler spread are introduced which describe the extent of channel dispersion in direction and in spatial Doppler frequency, respectively. Both measures are analogous to the delay and Doppler spreads, which are commonly employed to describe the extent of dispersion in delay and Doppler frequency, respectively. The relationships between the two approaches for characterizing spatial dispersion and especially between the direction and maximum spatial Doppler spreads are analytically established. The coherence distance at a certain level summarizes certain features of space selectivity in the radio channel which impact on the performance of communication systems. Two uncertainty relations between the direction spread and the coherence distance as well as between the maximum spatial Doppler spread and the coherence distance express the duality between direction dispersion and space selectivity. These relations are analogous to those established previously between the delay spread and the coherence bandwidth and between the Doppler spread and the coherence time. Examples relevant to mobile communications in the case where the waves propagate only horizontally illustrate the theoretical results. An application of these results to the design of uniform linear antenna arrays is also discussed.
TL;DR: The wide-band limit, and, in particular, the mismatch capacity per unit cost, and the achievable rates on an additive-noise spread-spectrum system with single-letter decoding and binary signaling are studied.
Abstract: The mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given (possibly suboptimal) decoding rule. This quantity has been studied extensively for single-letter decoding rules over discrete memoryless channels (DMCs). Here we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non-single-letter decoding rules. We also study the wide-band limit, and, in particular, the mismatch capacity per unit cost, and the achievable rates on an additive-noise spread-spectrum system with single-letter decoding and binary signaling.
TL;DR: The problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples is examined and an explicit reconstruction formula is derived.
Abstract: We examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. This sampling scheme, which has been studied previously, has an interesting optimality property that uniform sampling lacks: one can sample and reconstruct the class /spl Bscr/(/spl Fscr/) of multiband signals with spectral support /spl Fscr/, at rates arbitrarily close to the Landau (1969) minimum rate equal to the Lebesgue measure of /spl Fscr/, even when /spl Fscr/ does not tile R under translation. Using the conditions for exact reconstruction, we derive an explicit reconstruction formula. We compute bounds on the peak value and the energy of the aliasing error in the event that the input signal is band-limited to the "span of /spl Fscr/" (the smallest interval containing /spl Fscr/) which is a bigger class than the valid signals /spl Bscr/(/spl Fscr/), band-limited to /spl Fscr/. We also examine the performance of the reconstruction system when the input contains additive sample noise.
TL;DR: It is shown that the sphere bound can be approached by a large class ofcoset codes or multilevel coset codes with multistage decoding, including certain binary lattices, andExponential error bounds for coset code bounds are developed, generalizing Poltyrev's (1994) bounds for lattices.
Abstract: A simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array L and its error probability on an additive white Gaussian noise (AWGN) channel. It is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding, including certain binary lattices. These codes have structure of the kind that has been found to be useful in practice. Capacity curves and design guidance for practical codes are given. Exponential error bounds for coset codes are developed, generalizing Poltyrev's (1994) bounds for lattices. These results are based on the channel coding theorems of information theory, rather than the Minkowski-Hlawka theorem of lattice theory.
TL;DR: In general, it is shown that data compression is almost always the best strategy, both in model selection and prediction.
Abstract: The relationship between the Bayesian approach and the minimum description length approach is established. We sharpen and clarify the general modeling principles minimum description length (MDL) and minimum message length (MML), abstracted as the ideal MDL principle and defined from Bayes's rule by means of Kolmogorov complexity. The basic condition under which the ideal principle should be applied is encapsulated as the fundamental inequality, which in broad terms states that the principle is valid when the data are random, relative to every contemplated hypothesis and also these hypotheses are random relative to the (universal) prior. The ideal principle states that the prior probability associated with the hypothesis should be given by the algorithmic universal probability, and the sum of the log universal probability of the model plus the log of the probability of the data given the model should be minimized. If we restrict the model class to finite sets then application of the ideal principle turns into Kolmogorov's minimal sufficient statistic. In general, we show that data compression is almost always the best strategy, both in model selection and prediction.
TL;DR: An effective numerical procedure is constructed for the determination of optimal pairs (f,h) that appears to converge satisfactorily for most values of input SINR.
Abstract: Optimal detection of a target return contaminated by signal-dependent interference, as well as additive channel noise, requires the design of a transmit pulse f(t) and a receiver impulse response h(t) jointly maximizing the output signal to interference plus noise ratio (SINR). Despite the highly nonlinear nature of this problem, it has been possible to show that f(t) may always be chosen minimum-phase. A full analysis concludes with the construction of an effective numerical procedure for the determination of optimal pairs (f,h) that appears to converge satisfactorily for most values of input SINR. Extensive simulation reveals that the shape of f(t) can be a critical factor. In particular, the performance of a chirp-like pulse is often unacceptable, especially when clutter and channel noise are low-pass dominant and comparable.
TL;DR: It is shown that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel, and that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity.
Abstract: For the discrete memoryless quantum channel, we show the equivalence of two different notions of quantum channel capacity: that which uses the entanglement fidelity as its criterion for success in transmission, and that which uses the minimum fidelity of pure states in a subspace of the input Hilbert space as its criterion. As a corollary, any source with entropy rate less than the capacity may be transmitted with high entanglement fidelity. We also show that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel. This enables us to simplify a known upper bound for the channel capacity. It also enables us to show that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity.
TL;DR: An algorithm able to compute a fully discriminant signature for most linear codes by determining a set of properties invariant by permutation, one for each coordinate, called a signature is presented.
Abstract: Two linear codes are permutation-equivalent if they are equal up to a fixed permutation on the codeword coordinates. We present here an algorithm able to compute this permutation. It operates by determining a set of properties invariant by permutation, one for each coordinate, called a signature. If this signature is fully discriminant-i.e., different for all coordinates-the support of the code splits into singletons, and the same signature computed for any permutation-equivalent code will allow the reconstruction of the permutation. A procedure is described to obtain a fully discriminant signature for most linear codes. The total complexity of the support splitting algorithm is polynomial in the length of the code and exponential in the dimension of its hull, i.e., the intersection of the code with its dual.
TL;DR: Bounds to this rate are found for the intracell TDMA protocol by incorporating information-theoretic inequalities and the Chebyshev-Markov moment theory as applied to the limiting distribution of the eigenvalues of a quadratic form of tridiagonal random matrices.
Abstract: Shannon-theoretic limits on the achievable throughput for a simple infinite cellular multiple-access channel (MAC) model (Wyner 1994) in the presence of fading are presented. In this model, which is modified to account for flat fading, the received signal, at a given cell-site's antenna, is the sum of the faded signals transmitted from all users within that cell plus an attenuation factor /spl alpha//spl isin/[0,1] times the sum of the faded signals received from the adjacent cells, accompanied by Gaussian additive noise. This model serves as a tractable model providing considerable insight into complex and analytically intractable real-world cellular communications. Both linear and planar cellular arrays are considered with exactly K active users in each cell. We assume a hyper-receiver, jointly decoding all of the users, incorporating the received signals from all of the active cell-sites. The hyper-receiver is assumed to be aware of the codebooks and realizations of the fading processes of all the users in the system. In this work we consider the intracell time-division multiple-access (TDMA) and the wideband (WB) protocols. We focus on the maximum reliably transmitted equal rate. Bounds to this rate are found for the intracell TDMA protocol by incorporating information-theoretic inequalities and the Chebyshev-Markov moment theory as applied to the limiting distribution of the eigenvalues of a quadratic form of tridiagonal random matrices. We demonstrate our results for the special case where the amplitudes of the fading coefficients are drawn from a Rayleigh distribution, i.e., Rayleigh fading. For this special case, we observe the rather surprising result that fading may increase the maximum equal rate, for a certain range of /spl alpha/ as compared to the nonfaded case. In this setting, the WB strategy, which achieves the maximum reliable equal rate of the model, is proved to be superior to the TDMA scheme. An upper bound to the maximum equal rate of the WB scheme is also obtained. This bound is asymptotically tight when the number of users is large (K/spl Gt/1). The asymptotic bound shows that the maximum equal rate of the WB scheme in the presence of fading is higher than the rate which corresponds to the nonfaded case for any intercell interference factor /spl alpha//spl isin/[0,1] signal-to-noise ratio (SNR) values. This result is found to be independent of the statistics of the fading coefficients.
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IBM1
TL;DR: The so-called denoising problem, relative to normal models for noise, is formalized such that "noise" is defined as the incompressible part in the data while the compressible part defines the meaningful information-bearing signal.
Abstract: 'The so-called denoising problem, relative to normal models for noise, is formalized such that "noise" is defined as the incompressible part in the data while the compressible part defines the meaningful information-bearing signal. Such a decomposition is effected by minimization of the ideal code length, called for by the minimum description length (MDL) principle, and obtained by an application of the normalized maximum-likelihood technique to the primary parameters, their range, and their number. For any orthonormal regression matrix, such as defined by wavelet transforms, the minimization can be done with a threshold for the squared coefficients resulting from the expansion of the data sequence in the basis vectors defined by the matrix.
TL;DR: By interpreting message authentication as a hypothesis testing problem, this paper provides a generalized treatment of information-theoretic lower bounds on an opponent's probability of cheating in one-way message authentication.
Abstract: By interpreting message authentication as a hypothesis testing problem, this paper provides a generalized treatment of information-theoretic lower bounds on an opponent's probability of cheating in one-way message authentication. We consider the authentication of an arbitrary sequence of messages, using the same secret key shared between sender and receiver. The adversary tries to deceive the receiver by forging one of the messages in the sequence. The classical two types of cheating are considered, impersonation and substitution attacks, and lower bounds on the cheating probability for any authentication system are derived for three types of goals the adversary might wish to achieve. These goals are: (1) that the fraudulent message should be accepted by the receiver, or, in addition, (2) that the adversary wishes to know or (3) wants to even choose the value of the plaintext message obtained by the legitimate receiver after decoding with the secret key.
TL;DR: A universal method to establish constraints that augment the Delsarte inequalities for constant-weight codes, used in the linear programming bound is developed and produces a bound on A(n,d,w) that is tighter than the Johnson bound.
Abstract: Let A(n,d,w) denote the maximum possible number of codewords in an (n,d,w) constant-weight binary code. We improve upon the best known upper bounds on A(n,d,w) in numerous instances for n/spl les/24 and d/spl les/12, which is the parameter range of existing tables. Most improvements occur for d=8, 10, where we reduce the upper bounds in more than half of the unresolved cases. We also extend the existing tables up to n/spl les/28 and d/spl les/14. To obtain these results, we develop new techniques and introduce new classes of codes. We derive a number of general bounds on A(n,d,w) by means of mapping constant-weight codes into Euclidean space. This approach produces, among other results, a bound on A(n,d,w) that is tighter than the Johnson bound. A similar improvement over the best known bounds for doubly-constant-weight codes, studied by Johnson and Levenshtein, is obtained in the same way. Furthermore, we introduce the concept of doubly-bounded-weight codes, which may be thought of as a generalization of the doubly-constant-weight codes. Subsequently, a class of Euclidean-space codes, called zonal codes, is introduced, and a bound on the size of such codes is established. This is used to derive bounds for doubly-bounded-weight codes, which are in turn used to derive bounds on A(n,d,w). We also develop a universal method to establish constraints that augment the Delsarte inequalities for constant-weight codes, used in the linear programming bound. In addition, we present a detailed survey of known upper bounds for constant-weight codes, and sharpen these bounds in several cases. All these bounds, along with all known dependencies among them, are then combined in a coherent framework that is amenable to analysis by computer. This improves the bounds on A(n,d,w) even further for a large number of instances of n, d, and w.
TL;DR: This work designs sequence detectors for channels with intersymbol interference (ISI) and correlated (and/or signal-dependent) noise and derives the optimal maximum-likelihood sequence detector (MLSD) and the optimalmaximum a posteriori (MAP) sequence detector extending to the correlated noise case the Viterbi algorithm.
Abstract: This work designs sequence detectors for channels with intersymbol interference (ISI) and correlated (and/or signal-dependent) noise. We describe three major contributions. (i) First, by modeling the noise as a finite-order Markov process, we derive the optimal maximum-likelihood sequence detector (MLSD) and the optimal maximum a posteriori (MAP) sequence detector extending to the correlated noise case the Viterbi algorithm. We show that, when the signal-dependent noise is conditionally Gauss-Markov, the branch metrics in the MLSD are computed from the conditional second-order noise statistics. We evaluate the branch metrics using a bank of finite impulse response (FIR) filters. (ii) Second, we characterize the error performance of the MLSD and MAP sequence detector. The error analysis of these detectors is complicated by the correlation asymmetry of the channel noise. We derive upper and lower bounds and computationally efficient approximations to these bounds based on the banded structure of the inverses of Gauss-Markov covariance matrices. An experimental study shows the tightness of these bounds. (iii) Finally, we derive several classes of suboptimal sequence detectors, and demonstrate how these and others available in the literature relate to the MLSD. We compare their error rate performance and their relative computational complexity, and show how the structure of the MLSD and the performance evaluation guide us in choosing a best compromise between several types of suboptimal sequence detectors.
TL;DR: Several new constructions for optimal optical orthogonal codes with weight k/spl ges/4 and correlation constraints /spl lambda//sub a/=/spl Lambda//sub c/=1 are described by means of optimal cyclic packings.
Abstract: A (v, k, /spl lambda//sub a/, /spl lambda//sub c/) optical orthogonal code (OOC) C is a family of (0, 1)-sequences of length v and weight k satisfying the following two correlation properties: (1) /spl Sigma//sub 0/spl les/t/spl les/v-1/x/sub t/x/sub t+i//spl les//spl lambda//sub a/ for any x=(x/sub 0/,x/sub 1/,/spl middot//spl middot//spl middot/,x/sub v-1/)/spl isin/C and any integer i not equivalent 0 mod v; and (2) /spl Sigma//sub 0/spl les/t/spl les/v-1/x/sub t/y/sub t+i//spl les//spl lambda//sub b/ for any x=(x/sub 0/,x/sub 1/,/spl middot//spl middot//spl middot/, x/sub v-1/) /spl isin/ C, y=(y/sub 0/,y/sub 1/,/spl middot//spl middot//spl middot/,y/sub v-1/) /spl isin/C with x/spl ne/y, and any integer i, where the subscripts are taken modulo v. The study of optical orthogonal codes is motivated by an application in optical code-division multiple-access communication systems. In this paper, upper bounds on the size of an optical orthogonal code are discussed. Several new constructions for optimal optical orthogonal codes with weight k/spl ges/4 and correlation constraints /spl lambda//sub a/=/spl lambda//sub c/=1 are described by means of optimal cyclic packings. Many new infinite series of such optimal optical orthogonal codes are thus produced.