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The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples n is smaller than the number of possible outcomes m. The goal of this paper is to find an appropriate criterion to analyze statistical tests in this setting. A suitable model for analysis is the high-dimensional model in which both n and m increase to infinity, and n=o(m). A new performance criterion based on large deviations analysis is proposed and it generalizes the classical error exponent applicable for large sample problems (in which m=O(n)). This generalized error exponent criterion provides insights that are not available from asymptotic consistency or central limit theorem analysis. The following results are established for the uniform null distribution: 1) The best achievable probability of error Pe decays as Pe=\exp \{-(n^{2}/m) J (1+o(1))\} for some J>0. 2) A class of tests based on separable statistics, including the coincidence-based test, attains the optimal generalized error exponents. 3) Pearson's chi-square test has a zero generalized error exponent and thus its probability of error is asymptotically larger than the optimal test. [ABSTRACT FROM PUBLISHER]

Consider a decision maker who is responsible to collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest. The policies under which the decision maker selects sensing actions can be categorized based on the following two factors: i) sequential versus non-sequential; ii) adaptive versus non-adaptive. Non-sequential policies collect a fixed number of observation samples and make the final decision afterwards; while under sequential policies, the sample size is not known initially and is determined by the observation outcomes. Under adaptive policies, the decision maker relies on the previous collected samples to select the next sensing action; while under non-adaptive policies, the actions are selected independent of the past observation outcomes. In this paper, performance bounds are provided for the policies in each category. Using these bounds, sequentiality gain and adaptivity gain, i.e., the gains of sequential and adaptive selection of actions are characterized. [ABSTRACT FROM PUBLISHER]

Optimal coding over the additive white Gaussian noise channel under the peak energy constraint is studied when there is noisy feedback over an orthogonal additive white Gaussian noise channel. As shown by Pinsker, under the peak energy constraint, the best error exponent for communicating an M-ary message, M\geq 3, with noise-free feedback is strictly larger than the one without feedback. This paper extends Pinsker's result and shows that if the noise power in the feedback link is sufficiently small, the best error exponent for communicating an M-ary message can be strictly larger than the one without feedback. The proof involves two feedback coding schemes. One is motivated by a two-stage noisy feedback coding scheme of Burnashev and Yamamoto for binary symmetric channels, while the other is a linear noisy feedback coding scheme that extends Pinsker's noise-free feedback coding scheme. When the feedback noise power \alpha is sufficiently small, the linear coding scheme outperforms the two-stage (nonlinear) coding scheme, and is asymptotically optimal as \alpha tends to zero. By contrast, when \alpha is relatively larger, the two-stage coding scheme performs better. [ABSTRACT FROM AUTHOR]

This paper studies the error exponent of block coding over an additive white Gaussian noise channel where a fraction (f) of the channel output symbols are revealed to the transmitter through noiseless feedback. If the code rate exceeds fC, where C is the channel capacity, then the probability of decoding error cannot decay faster than exponentially with block length. However, if the code rate is below fC, the error probability can decrease faster than exponentially with the block length, as with full feedback (f=1). This is achieved by combining a feedback code and a forward error control code, and jointly decoding them at the receiver. This scheme can attain higher reliability than rate splitting in which feedback and forward codes independently encode separate source messages. [ABSTRACT FROM AUTHOR]

We consider random network coding in noisy large-scale multiple-access relay networks in which the source packets that are correctly received at a relay are linearly combined with randomly chosen coefficients and forwarded to the destination. We derive the union bound on the average probability of decoding error at the destination with the maximum likelihood decoding, averaged over all possible node locations and relay encoding rules. The union bound provides an upper bound to the probability of decoding error with the best network coding scheme and enables us to determine the error exponent. From the error exponent, we determine the reliability-rate tradeoff and the achievable rate at the high node density regime. The high node density analysis is useful for understanding the performance of large-scale multiple access relay networks. The energy saving at a source node offered by the energy expenditure at a relay node and the optimum constellation size that minimizes the energy per information bit (E_b/N_0) are investigated as a function of reliability, rate, and node density. The effect of MIMO transmit modes at the relay nodes, when they are equipped with multiple antennas, on the network-wide reliability-rate tradeoff is investigated. The insight provided by the analysis is useful for understanding of the fundamental limit and tradeoffs in large-scale multiple-access relay networks with network coding. [ABSTRACT FROM PUBLISHER]

For a given linear code (ensemble), upper bounds on the error probability under maximum likelihood decoding are investigated at low rates. A class of symmetric memoryless channels suitable for Bhattacharyya-type bounds, which are particularly of importance at low rates, is introduced. Over a symmetric channel, a lower bound on the error exponent is derived for a given linear code. A sufficient condition for achieving the expurgated exponent, which is the best among known error exponents at low rates, within a fixed discrepancy is given. Over a general discrete memoryless channel, the same analysis provides a lower bound on the average error exponent for an ensemble of coset codes generated by a given linear code. The bounding technique is extended to the case of generalized maximum likelihood decoding with erasure and list- decoding options. [ABSTRACT FROM AUTHOR]

In this paper, the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white Gaussian noise channel. The performance analysis available in the literature for such a channel has been studied only under the use of the minimum Euclidean distance decoder that is commonly referred to as the lattice decoder. Lattice decoders based on solutions to the NP-hard closest vector problem are very complex to implement, and the search for low complexity receivers for the detection of lattice codes is considered a challenging problem. However, the low computational complexity advantage that sequential decoding promises, makes it an alternative solution to the lattice decoder. In this work, we characterize the performance and complexity tradeoff via the error exponent and the decoding complexity, respectively, of such a decoder as a function of the decoding parameter — the bias term. For the above channel, we derive the cut-off volume-to-noise ratio that is required to achieve a good error performance with low decoding complexity. [ABSTRACT FROM PUBLISHER]

We consider a distributed detection system, in which sensors send their decisions over orthogonal noisy channels to a fusion center (FC). We study how the optimal integrated fusion rule and its low signal-to-noise ratio (SNR) approximation, as well as the suboptimal non-integrated fusion rule, are related to the physical layer specifications (reception, modulation, channel model, and availability of channel state information (CSI) at FC). In particular, we consider training and non-training based systems and investigate the effect of imperfect CSI on the fusion rules, detection performance and error exponent, assuming that the sum of training and data symbol transmit powers is fixed. Our results show that the detection performance of the system with noncoherent reception is maximized when training symbol transmit power is zero. This performance is attainable with the statistics-based likelihood ratio test (LRT) rule for random channel model and the generalized LRT rule for deterministic channel model. For a system with BPSK modulation and coherent reception, subject to Rayleigh fading, the detection probability and error exponent are maximized when half of transmit power is allocated for training symbol. For Rician fading, however, optimal power allocation between training and decision symbols depends on the SNR and Rice factor. Comparing the integrated and non-integrated fusion rules, we show that the former always outperforms the latter. [ABSTRACT FROM PUBLISHER]

Consider the following unequal error protection scenario. One special message, dubbed the “red alert” message, is required to have an extremely small probability of missed detection. The remainder of the messages must keep their average probability of error and probability of false alarm below a certain threshold. The goal then is to design a codebook that maximizes the error exponent of the red alert message while ensuring that the average probability of error and probability of false alarm go to zero as the blocklength goes to infinity. This red alert exponent has previously been characterized for discrete memoryless channels. This paper completely characterizes the optimal red alert exponent for additive white Gaussian noise channels with block power constraints. [ABSTRACT FROM PUBLISHER]

This paper extends linear-complexity concatenated coding schemes to fountain communication over the discrete-time memoryless channel. Achievable fountain error exponents for one-level and multi-level concatenated fountain codes are derived. Several important properties of the concatenated coding schemes in multi-user fountain communication scenarios are demonstrated. [ABSTRACT FROM PUBLISHER]

We consider the decentralized binary hypothesis testing problem in networks with feedback, where some or all of the sensors have access to compressed summaries of other sensors' observations. We study certain two-message feedback architectures, in which every sensor sends two messages to a fusion center, with the second message based on full or partial knowledge of the first messages of the other sensors. We also study one-message feedback architectures, in which each sensor sends one message to a fusion center, with a group of sensors having full or partial knowledge of the messages from the sensors not in that group. Under either a Neyman–Pearson or a Bayesian formulation, we show that the asymptotically optimal (in the limit of a large number of sensors) detection performance (as quantified by error exponents) does not benefit from the feedback messages, if the fusion center remembers all sensor messages. However, feedback can improve the Bayesian detection performance in the one-message feedback architecture if the fusion center has limited memory; for that case, we determine the corresponding optimal error exponents. [ABSTRACT FROM AUTHOR]

A new channel coding approach was proposed by Luo and Ephremides for random multiple-access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the rate information among each other or with the receiver. The receiver will either decode the messages or report a collision depending on whether reliable message recovery is possible. It was shown that, asymptotically as the codeword length goes to infinity, the set of communication rates supporting reliable message recovery can be characterized by an achievable region which equals Shannon's information rate region without a convex hull operation. In this paper, we derive achievable bounds on error probabilities, including the decoding error probability and the collision miss detection probability, of random multiple-access systems with a finite codeword length. Achievable error exponents are obtained by taking the codeword length to infinity. [ABSTRACT FROM PUBLISHER]

We study the fundamental limits to secret key generation from an excited distributed source (EDS). In an EDS, a pair of terminals observe dependent sources of randomness excited by a pre-arranged signal. We first determine the secret key capacity for such systems with one-way public messaging. We then characterize a tradeoff between the secret key rate and exponential bounds on the probability of key agreement failure and on the secrecy of the key generated. We find that there is a fundamental tradeoff between reliability and secrecy. [ABSTRACT FROM AUTHOR]

This paper studies communication outages in multiple-input multiple-output (MIMO) block-fading channels with imperfect channel state information at the receiver (CSIR). Using mismatched decoding error exponents, we prove the achievability of the generalized outage probability, the probability that the generalized mutual information (GMI) is less than the data rate, and show that this probability is the fundamental limit for independent and identically distributed (i.i.d.) codebooks. Then, using nearest neighbor decoding, we study the generalized outage probability in the high signal-to-noise ratio (SNR) regime for random codes with Gaussian and discrete signal constellations. In particular, we study the SNR exponent, which is defined as the high-SNR slope of the error probability curve on a logarithmic-logarithmic scale. We show that the maximum achievable SNR exponent of the imperfect CSIR case is given by the SNR exponent of the perfect CSIR case times the minimum of one and the channel estimation error diversity. Random codes with Gaussian constellations achieve the optimal SNR exponent with finite block length as long as the block length is larger than a threshold. On the other hand, random codes with discrete constellations achieve the optimal SNR exponent with block length growing with the logarithm of the SNR. The results hold for many fading distributions, including Rayleigh, Rician, Nakagami-m, Nakagami-q and Weibull as well as for optical wireless scintillation distributions such as lognormal-Rice and gamma-gamma. [ABSTRACT FROM AUTHOR]

We investigate the two-hop multiple source-destination relay channels using the rate splitting transmission scheme where each source can split its message into private and public parts. We determine the system error probability via integrated exponent function under amplify-and-forward (AF) and decode-and-forward (DF) relay strategies. The most significant difference between AF and DF system error probability evaluations lies in a minimized cut-set bound of transmission rate under the DF strategy. There are many cases among transmission rate intervals for different system parameters (e.g. transmit power) and it is extremely complex to derive the system error probability for the DF strategy. We obtain a relatively simple result, which unifies various cases by a few expressions. Numerical results show that the system error probability decreases with the increase of the public message. Moreover, in order to draw deep insight into the reliability requirement of each source node in this network, we provide the error exponent region (EER) for different source nodes to show the trade-off of error probability among source nodes. [ABSTRACT FROM AUTHOR]

Inner and outer bounds are derived on the optimal performance of fixed-length block codes on discrete memoryless channels with feedback and errors-and-erasures decoding. First, an inner bound is derived using a two-phase encoding scheme with communication and control phases together with the optimal decoding rule for the given encoding scheme, among decoding rules that can be represented in terms of pairwise comparisons between the messages. Then, an outer bound is derived using a generalization of the straight-line bound to errors-and-erasures decoders and the optimal error-exponent tradeoff of a feedback encoder with two messages. In addition, upper and lower bounds are derived, for the optimal erasure exponent of error-free block codes in terms of the rate. Finally, a proof is provided for the fact that the optimal tradeoff between error exponents of a two-message code does not improve with feedback on discrete memoryless channels (DMCs). [ABSTRACT FROM PUBLISHER]

Random coding of channel decoding with an erasure option is studied. By analyzing the large deviations behavior of the code ensemble, we obtain exact single-letter formulas for the error exponents in lieu of Forney's lower bounds. The analysis technique we use is based on an enhancement and specialization of tools for assessing the statistical properties of certain distance enumerators. We specialize our results to the setup of the binary symmetric channel case with uniform random coding distribution and derive an explicit expression for the error exponent which, unlike Forney's bounds, does not involve optimization over two parameters. We also establish the fact that for this setup, the difference between the exact error exponent corresponding to the probability of undetected decoding error and the exponent corresponding to the erasure event is equal to the threshold parameter. Numerical calculations indicate that for this setup, as well as for a Z-channel, Forney's bound coincides with the exact random coding exponent. [ABSTRACT FROM AUTHOR]

In this paper, we study upper and lower bounds on the error exponents for joint source-channel coding with decoder side-information. The results in the paper are nontrivial extensions of Csiszár's classical paper “Joint Source-Channel Error Exponent”, Problems of Control and Information Theory, 1980. Unlike the joint source-channel coding result in Csiszár's paper, it is not obvious whether the lower bound and the upper bound are equivalent even if the channel coding error exponent is known. For a class of channels, including symmetric channels, we apply a game-theoretic result to establish the existence of a saddle point and, hence, prove that the lower and upper bounds are the same if the channel coding error exponent is known. More interestingly, we show that encoder side-information does not increase the error exponents in this case. [ABSTRACT FROM AUTHOR]

We consider multiple repetition strategies with fixed delay decoding for discrete memoryless channels with noiseless feedback. Existing binary schemes by Schalkwijk and Zigangirov are analyzed and their results are extended. The general error exponents are computed and presented by elegant expressions in the strictly symmetric case. An important class of precoded sequences, so-called flip sequences, is found and their degrading effect on the error exponent is investigated. This effect is shown negligible when the repetition parameters are chosen such that the transmission rate is maximized. Even when signalling at channel capacity, the error exponent is shown to be strictly positive. [ABSTRACT FROM AUTHOR]

The problem of detecting a wide-sense stationary Gaussian signal process embedded in white Gaussian noise, in which the power spectral density of the signal process exhibits uncertainty, is investigated. The performance of minimax robust detection is characterized by the exponential decay rate of the miss probability under a Neyman–Pearson criterion with a fixed false alarm probability, as the length of the observation interval grows without bound. A stochastic suppression condition is identified for the uncertainty set of spectral density functions, and it is established that, under the stochastic suppression condition, the resulting minimax problem possesses a saddle point, which is achievable by the likelihood ratio tests matched to a so-called suppressing power spectral density in the uncertainty set. No convexity condition on the uncertainty set is required to establish this result. [ABSTRACT FROM AUTHOR]

A distributed detection scheme where the sensors transmit with constant modulus signals over a Gaussian multiple access channel is considered. The deflection coefficient of the proposed scheme is shown to depend on the characteristic function of the sensing noise and the error exponent for the system is derived using large deviation theory. Optimization of the deflection coefficient and error exponent are considered with respect to a transmission phase parameter for a variety of sensing noise distributions including impulsive ones. The proposed scheme is also favorably compared with existing amplify-and-forward and detect-and-forward schemes. The effect of fading is shown to be detrimental to the detection performance through a reduction in the deflection coefficient depending on the fading statistics. Simulations corroborate that the deflection coefficient and error exponent can be effectively used to optimize the error probability for a wide variety of sensing noise distributions. [ABSTRACT FROM AUTHOR]

The Shannon cipher system is studied in the context of general sources using a notion of computational secrecy introduced by Merhav and Arikan. Bounds are derived on limiting exponents of guessing moments for general sources. The bounds are shown to be tight for i.i.d., Markov, and unifilar sources, thus recovering some known results. A close relationship between error exponents and correct decoding exponents for fixed rate source compression on the one hand and exponents for guessing moments on the other hand is established. [ABSTRACT FROM AUTHOR]

We study a decentralized detection architecture in which each of a set of sensors transmits a highly compressed summary of its observations (a binary message) to a fusion center, which then decides on one of two alternative hypotheses. In contrast to the star (or “parallel”) architecture considered in most of the literature, we allow a subset of the sensors to both transmit their messages to the fusion center and to also broadcast them to the remaining sensors. We focus on the following architectural question: Is there a significant performance improvement when we allow such a message broadcast? We consider the error exponent (asymptotically, in the limit of a large number of sensors) for the Neyman–Pearson formulation of the detection problem. We prove that the sharing of messages does not improve the optimal error exponent. [ABSTRACT FROM PUBLISHER]

The problem of maximum-likelihood (ML) estimation of discrete tree-structured distributions is considered. Chow and Liu established that ML-estimation reduces to the construction of a maximum-weight spanning tree using the empirical mutual information quantities as the edge weights. Using the theory of large-deviations, we analyze the exponent associated with the error probability of the event that the ML-estimate of the Markov tree structure differs from the true tree structure, given a set of independently drawn samples. By exploiting the fact that the output of ML-estimation is a tree, we establish that the error exponent is equal to the exponential rate of decay of a single dominant crossover event. We prove that in this dominant crossover event, a non-neighbor node pair replaces a true edge of the distribution that is along the path of edges in the true tree graph connecting the nodes in the non-neighbor pair. Using ideas from Euclidean information theory, we then analyze the scenario of ML-estimation in the very noisy learning regime and show that the error exponent can be approximated as a ratio, which is interpreted as the signal-to-noise ratio (SNR) for learning tree distributions. We show via numerical experiments that in this regime, our SNR approximation is accurate. [ABSTRACT FROM PUBLISHER]

We study the best exponential decay in the blocklength of the probability of error that can be achieved in the transmission of a single bit over the Gaussian channel with an active noisy Gaussian feedback link. We impose an expected block power constraint on the forward link and study both almost-sure and expected block power constraints on the feedback link. In both cases the best achievable error exponents are finite and grow approximately proportionally to the larger between the signal-to-noise ratios on the forward and feedback links. The error exponents under almost-sure block power constraints are typically strictly smaller than under expected constraints. Some of the results extend to communication at arbitrary rates below capacity and to general discrete memoryless channels. [ABSTRACT FROM PUBLISHER]

We consider a distributed detection system formed by a large number of local detectors and a data fusion center that performs a Neyman–Pearson fusion of the binary quantizations of the sensor observations. In the analyzed two-stage detection system the local decisions are taken with no kind of cooperation among the devices and they are transmitted to the fusion center over an error free parallel access channel. In addition, the sensors are randomly deployed along a straight line, and the corresponding sensor spacings are drawn independently from a common probability density function (pdf). For both hypothesis, \mbi H\bf 0 and \mbi H\bf 1, depending on the correlation structure of the observed phenomenon the local decisions might be dependent. In the case of being dependent, their correlation structure is modelled with a one-dimensional Markov random field with nearest neighbor dependency and binary state space. Under this scenario, we first derive a closed-form error exponent for the Neyman–Pearson fusion of the local decisions when the involved data fusion center only knows the distribution of the sensor spacings. Second, based on a single parameter that captures the mean correlation strength among the local decisions, some analytical properties of the error exponent are investigated. Finally, we develop a physical model for the conditional probabilities of the Markov random fields that might be present under each hypothesis. Using this model we characterize the error exponent for two well-known models of the sensor spacing: i) equispaced sensors with failures, and ii) exponentially spaced sensors with failures. [ABSTRACT FROM AUTHOR]

We investigate the performance of Neyman–Pearson detection of a stationary Gaussian process in noise, using a large wireless sensor network (WSN). In our model, each sensor compresses its observation sequence using a linear precoder and a final decision is taken by a fusion center (FC) based on the compressed information. Two families of precoders are studied: random i.i.d. precoders and orthogonal precoders. We analyse their performance under a regime where both the number of sensors k and the number of samples n per sensor tend to infinity at the same rate, that is, k/n\to c \in [0,1]. Contributions are as follows. 1) Using results from random matrix theory and large Toeplitz matrices, we prove that, when the above families of precoders are used, the miss probability of the Neyman–Pearson detector converges exponentially to zero. Closed form expressions of the corresponding error exponents are derived. 2) In particular, we propose a practical orthogonal precoding strategy, the Principal Frequencies Strategy (PFS), which achieves the best error exponent among all orthogonal strategies, and which requires very little signaling overhead between the central processor and the nodes of the network. 3) When the PFS is used, a simplified low-complexity testing procedure can be implemented at the FC. We show that the proposed suboptimal test enjoys the same error exponent as the Neyman–Pearson test, which indicates a similar asymptotic behavior of the performance. We illustrate our findings by numerical experiments on several examples. [ABSTRACT FROM AUTHOR]

Polar codes were recently introduced by Arıkan. They achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels under a low complexity successive cancellation decoding scheme. The original polar code construction is closely related to the recursive construction of Reed-Muller codes and is based on the 2\,\times\,2 matrix \biggl[\matrix1 &0 \cr 1& 1\biggr]. It was shown by Arıkan and Telatar that this construction achieves an error exponent of 1\over 2, i.e., that for sufficiently large blocklengths the error probability decays exponentially in the square root of the blocklength. It was already mentioned by Arıkan that in principle larger matrices can be used to construct polar codes. In this paper, it is first shown that any \ell \times \ell matrix none of whose column permutations is upper triangular polarizes binary-input memoryless channels. The exponent of a given square matrix is characterized, upper and lower bounds on achievable exponents are given. Using these bounds it is shown that there are no matrices of size smaller than 15\,\times\,15 with exponents exceeding 1\over 2. Further, a general construction based on BCH codes which for large \ell achieves exponents arbitrarily close to 1 is given. At size 16\,\times\,16, this construction yields an exponent greater than 1\over 2. [ABSTRACT FROM PUBLISHER]

Typical minimum distances and error exponents are analyzed on the 8-PSK Gaussian channel for two capacity- achieving code ensembles with different algebraic structure. It is proved that the typical group code over the cyclic group of order eight achieves both the Gilbert–Varshamov bound and the expurgated error exponent. On the other hand, the typical binary-coset codes (under any labeling) is shown to be bounded away both from the Gilbert–Varshamov bound (at any rate) and the expurgated exponent (at low rates). The reason for this phenomenon is shown to rely on the symmetry structure of the 8-PSK constellation, which is known to match the cyclic group of order eight, but not the direct product of three copies of the binary group. The presented results indicate that designing group codes matching the symmetry of the channel guarantees better typical-code performance than designing codes whose algebraic structure does not match the channel. This contrasts the well-known fact that the average binary-coset code achieves both the capacity and the random-coding error exponent of any discrete memoryless channel. [ABSTRACT FROM PUBLISHER]

One way to find near-matches in large datasets is to use hash functions. In recent years locality-sensitive hash functions for various metrics have been given; for the Hamming metric projecting onto k bits is simple hash function that performs well. In this paper, we investigate alternatives to projection. For various parameters hash functions given by complete decoding algorithms for error-correcting codes work better, and asymptotically random codes perform better than projection. [ABSTRACT FROM AUTHOR]

An approximate implementation is formulated and analyzed for the detection of wide-sense stationary Gaussian stochastic signals in white Gaussian noise. For scalar processes, the approximate detector can be realized as the correlation between the periodogram of the observations and an appropriately selected spectral mask, and thus is termed the frequency-domain correlation detector. Through the asymptotic properties of Toeplitz matrices, it is shown that, as the length of the observation interval grows without bound, the frequency-domain correlation detector and the optimum quadratic detector achieve identical asymptotic performance, characterized by the decay rate of the miss probability under the Neyman-Pearson criterion. The frequency-domain correlation detector is further extended to the detection of vector-valued wide-sense stationary Gaussian stochastic signals, and the asymptotic optimality of its performance is established through the asymptotic properties of block Hermitian Toeplitz matrices. [ABSTRACT FROM AUTHOR]

In this paper, we study distributed detection in ultrawideband (UWB) wireless sensor networks (WSNs) over frequency selective channels. Several schemes with different requirements on channel state information (CS!) are proposed, analyzed, and compared. We study the error exponent and asymptotic optimality for these schemes under different energy, and time-bandwidth product requirements. Our study shows that to achieve a nonzero error exponent, the no-feedback scheme requires large energy and time-bandwidth product but has advantages of no synchronization requirement and no feedback overhead. On the other hand, schemes requiring feedback are suitable for energy and bandwidth limited settings but require quasi-synchronization. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that each Slepian-Wolf coding problem is related to a dual channel coding problem the sense that the sphere packing exponents, random coding exponents, and correct decoding exponents in these two problems are mirror-symmetrical to each other. This mirror symmetry interpreted as a manifestation of the linear codebook-level duality between Slepian-Wolf coding and channel coding. Furthermore, this duality, in conjunction with a systematic analysis of expurgated exponents, reveals that nonlinear Slepian-Wolf codes can strictly outperform linear Slepian-Wolf codes in terms rate-error tradeoff at high rates. The linear codebook-level duality is also established for general sources and channels. [ABSTRACT FROM AUTHOR]

We study the detection performance of large scale sensor networks, configured as trees with bounded height, in which information is progressively compressed as it moves towards the root of the tree. We show that, under a Bayesian formulation, the error probability decays exponentially fast, and we provide bounds for the error exponent. We then focus on the case where the tree has certain symmetry properties. We derive the form of the optimal exponent within a restricted class of easily implementable strategies, as well as optimal strategies within that class. We also find conditions under which (suitably defined) majority rules are optimal. Finally, we provide evidence that in designing a network it is preferable to keep the branching factor small for nodes other than the neighbors of the leaves. [ABSTRACT FROM AUTHOR]

We establish random-coding lower bounds to the error exponent of discrete and Gaussian joint quantization and private watermarking systems. In the discrete system, both the covertext and the attack channel are memoryless and have finite alphabets. In the Gaussian system, the covertext is memoryless Gaussian and the attack channel has additive memoryless Gaussian noise. In both cases, our bounds on the error exponent are positive in the interior of the achievable quantization and watermarking rate region. [ABSTRACT FROM AUTHOR]

The error performance of the ensemble of typical low-definition parity-check (LDPC ) codes transmitted over the binary erasure channel (BEC) is analyzed. In the past, lower bounds on the error exponents were derived. In this paper, a probabilistic upper bound on this error exponent is derived. This bound holds with some confidence level. [ABSTRACT FROM AUTHOR]

The capacity of finite Abelian group codes over symmetric memoryless channels is determined. For certain important examples, such as m-PSK constellations over additive white Gaussian noise (AWGN) channels, with in a prime power, it is shown that this capacity coincides with the Shannon capacity; i.e., there is no loss in capacity using group codes. (This had previously been known for binary-linear codes used over binary-input output-symmetric memoryless channels.) On the other hand, a counterexample involving a three-dimensional geometrically uniform constellation is presented in which the use of Abelian group codes leads to a loss in capacity. The error exponent of the average group code is determined, and it is shown to be bounded away from, the random-coding error exponent, at low rates, for finite Abelian groups not admitting Galois field structure. [ABSTRACT FROM AUTHOR]