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In this paper, the finite-order autoregressive moving average (ARMA) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of signals in both forward and feedback channels. It is shown that the generalized Schalkwijk–Kailath scheme, a capacity-achieving coding scheme for the Gaussian feedback channel, achieves the same maximum rate for the same channel even with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the Gaussian feedback channel. Furthermore, the results are extended to the additive white Gaussian noise (AWGN) channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate. Our result implies that as the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel. [ABSTRACT FROM AUTHOR]

We investigate two closely related nonparametric hypothesis testing problems. In the first problem (i.e., the existence problem), we test whether a testing data stream is generated by one of a set of composite distributions. In the second problem (i.e., the association problem), we test which one of the multiple distributions generates a testing data stream. We assume that some distributions in the set are unknown, and instead, only training sequences generated by the corresponding distributions are available. For both problems, we construct the generalized likelihood tests and characterize the error exponents of the maximum error probabilities. For the existence problem, we show that the error exponent is mainly captured by the Chernoff information between the set of composite distributions and alternative distributions. For the association problem, we show that the error exponent is captured by the minimum Chernoff information between each pair of distributions as well as the Kullback-Leibler Divergences between the approximated distributions (via training sequences) and the true distributions. We also show that the ratio between the lengths of training and testing sequences plays an important role in determining the error decay rate. [ABSTRACT FROM AUTHOR]

This paper studies a two-user state-dependent Gaussian multiple-access channel (MAC) with state noncausally known at one encoder. Two scenarios are considered: 1) each user wishes to communicate an independent message to the common receiver; and 2) the two encoders send a common message to the receiver and the non-cognitive encoder (i.e., the encoder that does not know the state) sends an independent individual message (this model is also known as the MAC with degraded message sets). For both scenarios, new outer bounds on the capacity region are derived, which improve uniformly over the best known outer bounds. In the first scenario, the two corner points of the capacity region as well as the sum rate capacity are established, and it is shown that a single-letter solution is adequate to achieve both the corner points and the sum rate capacity. Furthermore, the full capacity region is characterized in situations in which the sum rate capacity is equal to the capacity of the helper problem. The proof exploits the optimal-transportation idea of Polyanskiy and Wu (which was used previously to establish an outer bound on the capacity region of the interference channel) and the worst case Gaussian noise result for the case in which the input and the noise are dependent. [ABSTRACT FROM AUTHOR]

The K -receiver degraded broadcast channel with secrecy outside a bounded range is studied, in which a transmitter sends K messages to K receivers, and the channel quality gradually degrades from receiver K to receiver 1. Each receiver k , for 1\leq k\leq K , and to be kept ignorant of W_{k+2},\ldots,W_{K} , for k=1,\ldots, K-2 . Thus, each message Wk is kept secure from receivers with at least two-level worse channel quality, i.e., receivers 1, \ldots , $k-2$ . The secrecy capacity region is fully characterized. The achievable scheme designates one superposition layer to each message with binning employed for each layer. Joint embedded coding and binning are employed to protect all upper-layer messages from lower-layer receivers. Furthermore, the scheme allows adjacent layers to share rates so that part of the rate of each message can be shared with its immediate upper-layer message to enlarge the rate region. More importantly, an induction approach is developed to perform Fourier-Motzkin elimination of 2K$ variables from the order of K^{2} bounds to obtain a close-form achievable rate region. An outer bound is developed that matches the achievable rate region, whose proof involves recursive construction of the rate bounds and exploits the intuition gained from the achievable scheme. [ABSTRACT FROM PUBLISHER]

A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally $n$ observed sequences out of which $s$ anomalous sequences are to be detected. Each typical sequence consists of $m$ independent and identically distributed (i.i.d.) samples drawn from a distribution $p$ , whereas each anomalous sequence consists of $m$ i.i.d. samples drawn from a distribution $q$ that is distinct from $p$ . The distributions $p$ and $q$ are assumed to be unknown in advance. Distribution-free tests are constructed by using the maximum mean discrepancy as the metric, which is based on mean embeddings of distributions into a reproducing kernel Hilbert space. The probability of error is bounded as a function of the sample size $m$, the number $s$ of anomalous sequences, and the number $n$ of sequences. It is shown that with $s$ known, the constructed test is exponentially consistent if $m$ is greater than a constant factor of $\log n$, for any $p$ and $q$ , whereas with $s$ unknown, $m$ should have an order strictly greater than $\log n$. Furthermore, it is shown that no test can be consistent for arbitrary $p$ and $q$ if $m$ is less than a constant factor of $\log n$. Thus, the order-level optimality of the proposed test is established. Numerical results are provided to demonstrate that the proposed tests outperform (or perform as well as) tests based on other competitive approaches under various cases. [ABSTRACT FROM PUBLISHER]

Nonparametric detection of the possible existence of an anomalous structure over a network is investigated. Nodes corresponding to the anomalous structure (if one exists) receive samples generated by a distribution $q$, which is different from a distribution $p$ generating samples for other nodes. If an anomalous structure does not exist, all nodes receive samples generated by $p$ . It is assumed that the distributions $p$ and $q$ are arbitrary and unknown. The goal is to design statistically consistent tests with probability of errors converging to zero as the network size becomes asymptotically large. Kernel-based tests are proposed based on maximum mean discrepancy, which measures the distance between mean embeddings of distributions into a reproducing kernel Hilbert space. Detection of an anomalous interval over a line network is first studied. Sufficient conditions on minimum and maximum sizes of candidate anomalous intervals are characterized in order to guarantee that the proposed test is consistent. It is also shown that certain necessary conditions must hold in order to guarantee that any test is universally consistent. Comparison of sufficient and necessary conditions yields that the proposed test is order-level optimal and nearly optimal respectively in terms of minimum and maximum sizes of candidate anomalous intervals. Generalization of the results to other networks is further developed. Numerical results are provided to demonstrate the performance of the proposed tests. [ABSTRACT FROM PUBLISHER]

The problem of simultaneously generating multiple keys for a cellular source model with a helper is investigated. In the model considered, there are four terminals, \mathcal X0 , \mathcal X1 , \mathcal X2 , and \mathcal X3 , each of which observes one component of a vector source. Terminal \mathcal X0 wishes to generate two secret keys K1 and K2 , respectively, with terminals \mathcal X1 and \mathcal X2 under the help of terminal \mathcal X3 . All terminals are allowed to communicate over a public channel. An eavesdropper is assumed to have access to the public discussion. Both symmetric and asymmetric key generations are considered. In symmetric key generation models, model 1a (with a trusted helper) requires that the two keys are concealed from the eavesdropper, and model 1b (with an untrusted helper) further requires that the two keys are concealed from the helper in addition to the eavesdropper. The asymmetric key generation models 2a and 2b are the same as symmetric key generation models 1a and 1b, respectively, except that the key K2 is further required to be concealed from terminal \mathcal X1 . For all models studied, the key capacity region is established by designing a unified achievable strategy to achieve the cut-set outer bounds. We also study the problem of generating more than two keys and characterize its key capacity region when all the cellular terminals are required to generate independent keys with the base station. [ABSTRACT FROM AUTHOR]

The state-dependent Gaussian interference channel (IC) and Z-IC are investigated, in which two receivers are corrupted by the same but differently scaled states. The state sequence is noncausally known at both transmitters, but not known at either receiver. Three interference regimes are studied, i.e., the very strong, strong, and weak regimes. In the very strong regime, the capacity region is characterized under certain channel parameters by designing a cooperative dirty paper coding between the two transmitters to fully cancel the state. In the strong regime, points on the capacity region boundary are characterized under certain channel parameters by designing an achievable scheme based on rate splitting, layered dirty paper coding, and successive state cancellation. In the weak regime, the sum capacity is obtained by independent dirty paper coding at two transmitters. For all the above regimes, the capacity achieves that of the IC/Z-IC without state. Comparison between the state-dependent regular IC and the Z-IC suggests that even with one interference-free link, the Z-IC does not necessarily perform better, because dirty paper coded interference in the regular IC facilitates to cancel the state through the cooperative dirty paper coding between the transmitters. [ABSTRACT FROM AUTHOR]

The kernel-based nonparametric approach proposed by Nguyen, Wainwright, and Jordan is further investigated for decentralized detection. In contrast with the uniform kernel used in the previous work, a weighted kernel is proposed, where weight parameters serve to selectively incorporate sensors’ information into the fusion center’s decision rule based on quality of sensors’ observations. Furthermore, weight parameters also serve as sensor selection parameters with nonzero parameters corresponding to sensors being selected. By introducing the l_1 regularization on weight parameters into the risk minimization framework, sensor selection is jointly performed with decision rules for sensors and the fusion center with the resulting optimal decision rule having only sparse nonzero weight parameters. A gradient projection algorithm and a Gauss-Seidel algorithm are developed to solve the risk minimization problem, which is nonconvex, and both algorithms are shown to converge to critical points. Conditions on the sample complexity to guarantee asymptotically small estimation error are characterized based on analysis of Rademacher complexity. Connection between the probability of error and the risk function is also studied. Numerical results are provided to demonstrate the advantages and properties of the proposed approach based on weighted kernel. [ABSTRACT FROM AUTHOR]

State-dependent parallel networks with a common state-cognitive helper is studied, in which $K$ transmitters wish to send $K$ messages to their corresponding receivers over $K$ state-corrupted parallel channels, and a helper who knows the state information noncausally wishes to assist these receivers to cancel state interference. Furthermore, the helper also has its own message to be sent simultaneously to its corresponding receiver. Since the state information is known only to the helper, but not to other transmitters, transmitter-side state cognition and receiver-side state interference are mismatched. Our focus is on the high state power regime, i.e., the state power goes to infinity. Three (sub)models are studied. Model I serves as a basic model, which consists of only one transmitter–receiver (with state corruption) pair in addition to a helper that assists the receiver to cancel state in addition to transmitting its own message. Model II consists of two transmitter–receiver pairs in addition to a helper, and only one receiver is interfered by a state sequence. Model III generalizes model I to include multiple transmitter–receiver pairs with each receiver corrupted by independent state. For all models, the inner and outer bounds on the capacity region are derived, and comparison of the two bounds yields characterization of either full or partial boundary of the capacity region under various channel parameters. [ABSTRACT FROM PUBLISHER]

A novel information theoretic approach is proposed to solve the secret sharing problem, in which a dealer distributes one or multiple secrets among a set of participants in such a manner that for each secret only qualified sets of users can recover this secret by pooling their shares together while nonqualified sets of users obtain no information about the secret even if they pool their shares together. While existing secret sharing systems (implicitly) assume that communications between the dealer and participants are noiseless, this paper takes a more practical assumption that the dealer delivers shares to the participants via a noisy broadcast channel. Thus, in contrast to the existing solutions that are mainly based on number theoretic tools, an information theoretic approach is proposed, which exploits the channel randomness during delivery of shares as additional resources to achieve secret sharing requirements. In this way, secret sharing problems can be reformulated as equivalent secure communication problems via wiretap channel models, and can hence be solved by employing the powerful information theoretic security techniques. This approach is first developed for the classic secret sharing problem, in which only one secret is to be shared. This classic problem is shown to be equivalent to a communication problem over a compound wiretap channel. Thus, the lower and upper bounds on the secrecy capacity of the compound channel provide the corresponding bounds on the secret sharing rate, and the secrecy scheme designed for the compound channel provides the secret sharing schemes. The power of the approach is further demonstrated by a more general layered multisecret sharing problem, which is shown to be equivalent to the degraded broadcast multiple-input multiple-output (MIMO) channel with layered decoding and secrecy constraints. The secrecy capacity region for the degraded MIMO broadcast channel is characterized, which provides the secret sharing capacity region. Furthermore, the secure encoding scheme that achieves the secrecy capacity region provides an information theoretic scheme for sharing the secrets. [ABSTRACT FROM AUTHOR]

The multi-design multi-response linear regression problem is investigated, in which design matrices are Gaussian with covariance matrices \Sigma ^(1:K)=\big (\Sigma ^(1),\ldots, \Sigma ^(K) \big) for K linear regression tasks. Design matrices across tasks are assumed to be independent. The support union of K~p -dimensional regression vectors (collected as columns of matrix B^* ) is recovered using l1/l2 -regularized lasso. Sufficient and necessary conditions on sample complexity are characterized as a sharp threshold to guarantee successful recovery of the support union. This model has been previously studied via l1/l\infty -regularized lassoand via l1/l1+l1/l\infty -regularized lasso, in which sharp threshold on sample complexity is characterized only for K=2 and under special conditions. In this paper, using l_{1}/l_{2} -regularized lasso, sharp threshold on sample complexity is characterized under standard regularization conditions. Namely, if n > c_{p1} \psi (B^{*},\Sigma ^{(1:K)})\log (p-s) where cp1 is a constant, and s is the size of the support set, then l1/l2 -regularized lasso correctly recovers the support union; and if n < cp2 \psi (B^{*},\Sigma ^{(1:K)})\log (p-s) where cp2 is a constant, then l1/l2 -regularized lasso fails to recover the support union. In particular, the function \psi (B^*,\Sigma ^(1:K)) captures the impact of the sparsity of $K$ regression vectors and the statistical properties of the design matrices on the threshold on sample complexity. Therefore, such threshold function also demonstrates the advantages of joint support union recovery using multitask lasso over individual support recovery using single-task lasso. [ABSTRACT FROM AUTHOR]

A class of cognitive interference channels with state are investigated, in which a primary transmitter sends a message to two receivers (receivers 1 and 2) with assistance of a cognitive transmitter (that knows the primary transmitter’s message), and the cognitive transmitter also sends a separate message to receiver 2. The channel is corrupted by an independent and identically distributed state sequence. The scenario, in which the state sequence is noncausally known at both the cognitive transmitter and receiver 2, is first studied. The capacity region is obtained for both the discrete memoryless and Gaussian channels. The second scenario, in which the state sequence is noncausally known only at the cognitive transmitter, is further studied. Inner and outer bounds on the capacity region are obtained for the discrete memoryless channel and its degraded version. The capacity region is characterized for the degraded semideterministic channel and for channels that satisfy a less noisy condition. The Gaussian channels are further studied, which are partitioned into two cases based on how the interference compares with the signal at receiver 1. For each case, inner and outer bounds on the capacity region are derived, and partial boundaries of the capacity region are characterized. The full capacity region is also characterized for channels that satisfy certain conditions. It is shown that certain Gaussian channels achieve the capacity of the same channels with state noncausally known at both the cognitive transmitter and receiver 2. [ABSTRACT FROM PUBLISHER]

The Poisson interference channel, which models optical communication systems with multiple transceivers in the short-noise-limited regime, is investigated. Conditions for the strong interference regime are characterized and the corresponding capacity region is derived, which is the same as that of the compound Poisson multiple-access channel with each receiver decoding both messages. For the cases when the strong interference conditions are not satisfied, inner and outer bounds on the capacity region are derived. The inner bound is derived via approximating the Poisson interference channel by a binary interference channel and then evaluating the corresponding Han–Kobayashi region. The outer bounds are obtained via various techniques, including noise reduction, genie-aided scheme, and channel transformation. The Poisson Z-interference channel is then studied. The sum rate capacity is obtained when the cross link coefficient is either sufficiently small or sufficiently large. [ABSTRACT FROM PUBLISHER]

A (layered) broadcast approach is studied for the fading wiretap channel without the channel state information (CSI) at the transmitter. Two broadcast schemes, based on superposition coding and embedded coding, respectively, are developed to encode information into a number of layers and use stochastic encoding to keep the corresponding information secret from an eavesdropper. The layers that can be successfully and securely transmitted are determined by the channel states to the legitimate receiver and the eavesdropper. The advantage of these broadcast approaches is that the transmitter does not need to know the CSI to the legitimate receiver and the eavesdropper, but the scheme still adapts to the channel states of the legitimate receiver and the eavesdropper. Three scenarios of block fading wiretap channels with stringent delay constraints are studied, in which either the legitimate receiver's channel, the eavesdropper's channel, or both channels are fading. For each scenario, the secrecy rate that can be achieved via the broadcast approach developed in this paper is derived, and the optimal power allocation over the layers (or the conditions on the optimal power allocation) is also characterized. A notion of probabilistic secrecy, which characterizes the probability that a certain secrecy rate of decoded messages is achieved during one block, is also introduced and studied for scenarios when the eavesdropper's channel is fading. Numerical examples are provided to demonstrate the impact of the CSI at the transmitter and the channel fluctuations of the eavesdropper on the average secrecy rate. These examples also demonstrate the advantage of the proposed broadcast approach over the compound channel approach. [ABSTRACT FROM AUTHOR]

The secrecy throughput of mobile ad hoc networks (MANETs) with malicious nodes is investigated. The MANET consists of n legitimate mobile nodes and m malicious nodes. Transmissions between legitimate nodes are subject to a delay constraint D. A model under passive attack is first studied, in which the malicious nodes are assumed to be eavesdroppers that only listen to transmission without actively injecting signals. An information-theoretic approach for security is applied to achieve secure communication among legitimate nodes in MANETs with transmissions being kept perfectly secure from eavesdroppers. A critical threshold on the number of malicious nodes (m) is identified such that when m=o(\sqrt nD), i.e., \lim n\rightarrow \infty m/\sqrt {nD}=0, the optimal secrecy throughput equals that of MANETs without malicious nodes, i.e., the impact of the presence of malicious nodes on the network throughput is negligible; and when m=\Omega \left (\sqrt nDpoly(n)\right ), i.e., \lim n\rightarrow \infty m/\left (\sqrt {nD}poly(n)\right ) \geq c for a positive constant c, the optimal secrecy throughput is limited by the number of malicious nodes. A model under active attack is further studied, in which the malicious nodes actively attack the network by transmitting modified packets to the destination nodes. It is shown that to guarantee the same throughput as the model under passive attack, the model under active attack needs to satisfy more stringent condition on the number of malicious nodes. [ABSTRACT FROM AUTHOR]

The fading cognitive multiple-access channel with confidential messages (CMAC-CM) is investigated, in which two users (users 1 and 2) wish to transmit a common message to a destination and user 1 also has a confidential message intended for the destination. The two users transmit to the destination via a multiple access channel, and user 2 also receives noisy channel outputs. Such channel outputs potentially help user 2 to learn user 1's confidential information (although they are not exploited by user 2 for channel transmission). Hence, user 1 views user 2 as an eavesdropper and wishes to keep its confidential message as secret as possible from user 2. A parallel CMAC-CM with independent subchannels is first studied. The secrecy capacity region of the parallel CMAC-CM is established, which yields the secrecy capacity regions of the parallel CMAC-CM with degraded subchannels and the parallel Gaussian CMAC-CM. These results are then applied to study the fading CMAC-CM, in which both the user-to-user channel and the user-to-destination channel are corrupted by multiplicative fading gain coefficients in addition to additive white Gaussian noise. The channel state information (CSI) is assumed to be known at both the users and the destination. With the CSI, users can dynamically change their transmission powers with the channel realization to achieve the optimal performance. The closed-form power allocation function that achieves every boundary point of the secrecy capacity region is derived. [ABSTRACT FROM PUBLISHER]

The problem of optimal resource allocation is studied for ergodic fading orthogonal multi-access relay channels (MARCs) in which the users (sources) communicate with a destination with the aid of a half-duplex relay that transmits and receives on orthogonal channels. Under the assumption that the instantaneous fading state information is available at all nodes, the maximum sum-rate and the optimal user and relay power allocations (policies) are developed for a decode-and-forward (DF) relay. A known lemma on the sum-rate of two intersecting polymatroids is used to determine the DF sum-rate and the optimal user and relay policies, and to classify fading MARCs into one of three types: (i) partially clustered MARCs in which a user is clustered either with the relay or with the destination, (ii) clustered MARCs in which all users are either proximal to the relay or to the destination, and (iii) arbitrarily clustered MARCs which are a combination of the first two types. Cutset outer bounds are used to show that DF achieves the capacity region for a sub-class of clustered orthogonal MARCs. [ABSTRACT FROM AUTHOR]

A recent inner bound on the capacity region of the two-receiver discrete memoryless broadcast channel is shown to be equivalent to the Marton-Gelfand-Pinsker region. The proof method is based on a result of Gelfand and Pinsker concerning channel input distributions. [ABSTRACT FROM AUTHOR]

The capacity of the multiple-input multiple-output (MIMO) wireless channel with uniform linear arrays (ULAs) of antennas at the transmitter and receiver is investigated. It is assumed that the receiver knows the channel perfectly but that the transmitter knows only the channel statistics. The analysis is carried out using an equivalent virtual representation of the channel that is obtained via a spatial discrete Fourier transform. A key property of the virtual representation that is exploited is that the components of virtual channel matrix are approximately independent. With this approximation, the virtual representation allows for a general capacity analysis without the common simplifying assumptions of Gaussian statistics and product-form correlation (Kronecker model) for the channel matrix elements. A deterministic line-of-sight (LOS) component in the channel is also easily incorporated in much of the analysis. It is shown that in the virtual domain, the capacity-achieving input vector consists of independent zero-mean proper-complex Gaussian entries, whose variances can be computed numerically using standard convex programming algorithms based on the channel statistics. Further- more, in the asymptotic regime of low signal-to-noise ratio (SNR), it is shown that beamforming along one virtual transmit angle is asymptotically optimal. Necessary and sufficient conditions for the optimality of beamforming, and the value of the corresponding optimal virtual angle, are also derived based on only the second moments of the virtual channel coefficients. Numerical results indicate that beamforming may be close to optimum even at moderate values of SNR for sparse scattering environments. Finally, the capacity is investigated in the asymptotic regime where the numbers of receive and transmit antennas go to infinity, with their ratio being kept constant. Using a result of Girko, an expression for the asymptotic capacity scaling with the number of antennas is obtained in terms of the two-dimensional spatial scattering function of the channel. This asymptotic formula for the capacity is shown to be accurate even for small numbers of transmit and receive antennas in numerical examples. [ABSTRACT FROM AUTHOR]

The capacity of noncoherent time-selective Rayleigh-fading channels is studied under various models for the variations in time. The study includes both single-input and single-output (SISO) and multiple-input and multiple-output (MIMO) systems. A block-fading model is first considered where the channel changes correlatively over each block period of length T, and independently across blocks. The predictability of the channel is characterized through the rank Q of the correlation matrix of the vector of channel gains in each block. This model includes, as special cases, the standard block-fading model where the channel remains constant over block periods (Q = 1), and models where the fading process has finite differential entropy rate (Q = T). The capacity is initially studied for long block lengths and some straightforward but interesting asymptotes are established. For the case where Q is kept fixed as T → ∞, it is shown that the non-coherent capacity converges to the coherent capacity. For the case where both T, Q → ∞, with Q/T being held constant, a bound on the capacity loss due to channel unpredictability is established. The more interesting scenario of large signal-to-noise ratio (SNR) is then explored in detail. For SISO systems, useful upper and lower bounds on the large SNR asymptotic capacity are derived, and it is shown that the capacity grows logarithmically with SNR with a slope of T-Q/T, for Q < T. Next, in order to facilitate the analysis of MIMO systems, the rank-Q block-fading model is specialized to the case where each T-symbol block consists of Q subblocks of length L, with the channel remaining constant over each subblock and changing correlatively across subblocks. For this model, it is shown that the log SNR growth behavior of the capacity is the same as that of the standard block-fading model with block length L. Finally, the SISO and MIMO channel models are generalized to allow the fading process to be correlated across blocks in a stationary and ergodic manner. It is shown that the log SNR growth behavior of the capacity is not affected by the correlation across blocks. [ABSTRACT FROM AUTHOR]

This article investigates the estimation and generalization errors of the generative adversarial network (GAN) training. On the statistical side, we develop an upper bound as well as a minimax lower bound on the estimation error for training GANs. The upper bound incorporates the roles of both the discriminator and the generator of GANs, and matches the minimax lower bound in terms of the sample size and the norm of the parameter matrices of neural networks under ReLU activation. On the algorithmic side, we develop a generalization error bound for the stochastic gradient method (SGM) in training GANs. Such a bound justifies the generalization ability of the GAN training via SGM after multiple passes over the data and reflects the interplay between the discriminator and the generator. Our results imply that the training of the generator requires more samples than the training of the discriminator. This is consistent with the empirical observation that the training of the discriminator typically converges faster than that of the generator. The experiments validate our theoretical results. [ABSTRACT FROM AUTHOR]

We investigate the state-dependent Gaussian wiretap channel with noncausal channel state information at the transmitter (GWTC-N-CSIT), and explore whether three strategies (i.e., taking action on the state, legitimate receiver’s channel output feedback, and combining the former two strategies together) help to enhance the secrecy capacity of the GWTC-N-CSIT. To be specific, we first determine the secrecy capacity of the GWTC-N-CSIT with noiseless feedback. Next, we derive lower and upper bounds on the secrecy capacity of the GWTC-N-CSIT with action-dependent state. Finally, we derive lower and upper bounds on the secrecy capacity of the GWTC-N-CSIT with both action-dependent state and noiseless feedback, and show that these bounds meet for a special case. Numerical results of this paper indicate that all three strategies enhance the secrecy capacity of the GWTC-N-CSIT. The study of this paper offers new options for enhancing the secrecy rates of the state-dependent wiretap channel models. [ABSTRACT FROM AUTHOR]

Physical layer security (PLS), which is based on information-theoretic principles of message confidentiality, has attracted considerable attention in recent years. This paper provides a comprehensive survey of using channel feedback (CF) to enhance the quality of PLS of various communication models. To be specific, the survey starts from the secret key-based CF scheme and its variations for the wiretap channel (WTC) and other communication models. Then, for the WTC and its generalized models, an improved feedback scheme and its variations are respectively introduced, where the improved scheme combines the secret key-based CF scheme with the Wyner-Ziv scheme for source coding with side information. It has been shown that these improved schemes perform better than the original secret key-based schemes for several cases. Next, the Schalkwijk-Kailath (SK) feedback scheme and its variations are introduced, which are optimal for the Gaussian WTC and its variations. Finally, the already existing CF schemes are summarized and the future challenges of using CF to enhance PLS are discussed. [ABSTRACT FROM AUTHOR]

This paper investigates the Gaussian state-dependent interference channel (IC) and Z-IC, in which two receivers are corrupted respectively by two different but correlated states that are noncausally known to two transmitters but are unknown to the receivers. Three interference regimes are studied, and the capacity region boundary or the sum capacity boundary is characterized either fully or partially under various channel parameters. In particular, the impact of the correlation between states on cancellation of state and interference as well as achievability of capacity is explored with numerical illustrations. For the very strong interference regime, the capacity region is achieved by the scheme where the two transmitters implement a cooperative dirty paper coding. For the strong but not very strong interference regime, the sum-rate capacity is characterized by rate splitting, layered dirty paper coding, and successive cancellation. For the weak interference regime, the sum-rate capacity is achieved via dirty paper coding individually at two receivers as well as treating interference as noise. This paper also provides the achievable region for the state-dependent IC with each state known at its corresponding transmitter. [ABSTRACT FROM AUTHOR]

This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements are corrupted by sparse outliers that can take arbitrary values. We propose a novel approach to robustify the gradient descent algorithm by using the sample median as a guide for pruning spurious samples in initialization and local search. Adopting a Poisson loss and a reshaped quadratic loss, respectively, we obtain two algorithms termed median-truncated Wirtinger flow and median-reshaped Wirtinger flow, both of which provably recover the signal from a near-optimal number of measurements when the measurement vectors are composed of independent and identically distributed Gaussian entries, up to a logarithmic factor, even when a constant fraction of the measurements is adversarially corrupted. We further show that both algorithms are stable in the presence of additional dense bounded noise. Our analysis is accomplished by developing non-trivial concentration results of median-related quantities, which may be of independent interest. We provide numerical experiments to demonstrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements are corrupted by sparse outliers that can take arbitrary values. We propose a novel approach to robustify the gradient descent algorithm by using the sample median as a guide for pruning spurious samples in initialization and local search. Adopting a Poisson loss and a reshaped quadratic loss, respectively, we obtain two algorithms termed median-truncated Wirtinger flow and median-reshaped Wirtinger flow, both of which provably recover the signal from a near-optimal number of measurements when the measurement vectors are composed of independent and identically distributed Gaussian entries, up to a logarithmic factor, even when a constant fraction of the measurements is adversarially corrupted. We further show that both algorithms are stable in the presence of additional dense bounded noise. Our analysis is accomplished by developing non-trivial concentration results of median-related quantities, which may be of independent interest. We provide numerical experiments to demonstrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

The problem of estimating the Kullback–Leibler divergence $D(P\|Q)$ between two unknown distributions P$ and Q$ is studied, under the assumption that the alphabet size k$ of the distributions can scale to infinity. The estimation is based on m$ independent samples drawn from P$ and n$ independent samples drawn from , if m$ and n$ exceed a constant factor of k$ and kf(k) , if $m$ and $n$ exceed a constant factor of $k/\log (k)$ and $kf(k)/\log k$ , respectively. The lower bound on the minimax quadratic risk is characterized by employing a generalized Le Cam’s method. A minimax optimal estimator is then constructed by employing both the polynomial approximation and the plug-in approaches. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the sum-rate capacity of two-user Poisson multiple input multiple output multiple-access channels (MACs), when both the transmitters and the receiver are equipped with multiple antennas. Although the sum-rate capacity of Poisson MISO MAC when the receiver is equipped with a single antenna has been characterized by us, the inclusion of multiple antennas at the receiver makes the problem more challenging and requires the development of new analytical tools. We first characterize the sum-rate capacity of the Poisson MAC when each transmitter has a single antenna and the receiver has multiple antennas. We obtain the optimal input that achieves the sum-rate capacity by solving a non-convex optimization problem. We show that, for certain channel parameters, it is optimal for a single user to transmit to achieve the sum-rate capacity, and for certain channel parameters, it is optimal for both users to transmit. We then characterize the sum-rate capacity of the channel where both the transmitters and the receiver are equipped with multiple antennas. We show that the sum-rate capacity of the Poisson MAC with multiple transmit antennas is equivalent to a properly constructed Poisson MAC with a single antenna at each transmitter, and has thus been characterized by the former case. We show this by developing a novel channel transformation argument. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the sum-rate capacity of two-user Poisson multiple access channels (MAC), when the receiver is equipped with single antenna. We first characterize the sum-rate capacity of the non-symmetric Poisson MAC when each transmitter has a single antenna. While the sum-rate capacity of the symmetric Poisson MAC with single antenna at each transmitter has been characterized in the literature, the special property exploited in the existing method for the symmetric case does not hold for the non-symmetric channel anymore. We obtain the optimal input that achieves the sum-rate capacity by solving a non-convex optimization problem. We show that, for certain channel parameters, it is optimal for a single user to transmit to achieve the sum-rate capacity. This is in sharp contrast to the Gaussian MAC, in which both users must transmit, either simultaneously or at different times, in order to achieve the sum-rate capacity. We then characterize the sum-rate capacity of the Poisson multiple-input single-output (MISO) MAC with multiple antennas at each transmitter and single antenna at the receiver. By converting a non-convex optimization problem with a large number of variables into a non-convex optimization problem with two variables, we show that the sum-rate capacity of the Poisson MISO MAC with multiple transmit antennas is equivalent to a properly constructed Poisson MAC with a single antenna at each transmitter. [ABSTRACT FROM PUBLISHER]

The state-dependent point-to-point Gaussian channel with a helper is first studied, in which a transmitter communicates with a receiver via a state-corrupted channel. The state is not known to the transmitter nor to the receiver, but known to a helper noncausally, which then wishes to assist the receiver to cancel the state. Differently from the previous work that characterized the capacity only in the infinite state power regime, this paper explores the general case with arbitrary state power. A lower bound on the capacity is derived based on an achievable scheme that integrates direct state subtraction and single-bin dirty paper coding. By analyzing this lower bound and further comparing it with the existing upper bounds, the capacity of the channel is characterized for a wide range of channel parameters. Such an idea of characterizing the capacity is further extended to study the two-user state-dependent multiple access channel with a helper. By comparing the derived inner and outer bounds, the channel parameters are partitioned into appropriate cases, and for each case, either segments on the capacity region boundary or the full capacity region are characterized. [ABSTRACT FROM PUBLISHER]

In this paper, we study Poisson fading channels with time-varying background light. Different from most of the existing work on fading Poisson channel that focus on the case with time-varying channel gain, our model is motivated by indoor optical wireless communication systems, in which the noise level is affected by the strength of the background light. We study both the single-input single-output and the multiple-input and multiple-output channels. For each channel, we consider scenarios with and without delay constraints. For the case without a delay constraint, we characterize the optimal power allocation scheme that maximizes the ergodic capacity. For the case with a strict delay constraint, we characterize the optimal power allocation scheme that minimizes the outage probability. We also provide several numerical examples to demonstrate the analytic results. [ABSTRACT FROM PUBLISHER]

The problem of simultaneously generating a secret key (SK) and private key (PK) pair among three terminals via public discussion is investigated. In this problem, each terminal observes a component of correlated sources. All three terminals are required to generate the common SK to be concealed from an eavesdropper that has access to the public discussion, while two designated terminals are required to generate an extra PK to be concealed from both the eavesdropper and the remaining terminal. An outer bound on the SK-PK capacity region was established by Ye and Narayan, and was shown to be achievable for a special case. In this paper, the SK-PK capacity region is established in general by developing schemes to achieve the outer bound for the remaining two cases. The main technique lies in the novel design of a random binning-joint decoding scheme that achieves the existing outer bound. [ABSTRACT FROM AUTHOR]

We study the implicit bias of gradient descent methods in solving a binary classification problem over a linearly separable data set. The classifier is described by a non‐linear ReLU model and the objective function adopts the exponential loss function. We first characterize the landscape of the loss function and show that there can exist spurious asymptotic local minima besides asymptotic global minima. We then show that gradient descent (GD) can converge to either a global or a local max‐margin direction or may diverge from the desired max‐margin direction in a general context. For stochastic gradient descent (SGD), we show that it converges in expectation to either the global or the local max‐margin direction if SGD converges. We further explore the implicit bias of these algorithms in learning a multineuron network under certain stationary conditions and show that the learned classifier maximizes the margins of each sample pattern partition under the ReLU activation. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the multiple-input multiple-output (MIMO) Gaussian broadcast channel with two receivers (receivers 1 and 2) and two messages: a common message intended for both receivers and a confidential message intended only for receiver 1 but needing to be kept asymptotically perfectly secure from receiver 2. A matrix characterization of the secrecy capacity region is established via a channel enhancement argument. The enhanced channel is constructed by first splitting receiver 1 into two virtual receivers and then enhancing only the virtual receiver that decodes the confidential message. The secrecy capacity region of the enhanced channel is characterized using an extremal entropy inequality previously established for characterizing the capacity region of a degraded compound MIMO Gaussian broadcast channel. [ABSTRACT FROM PUBLISHER]

Recent work has demonstrated the effectiveness of gradient descent for directly recovering the factors of low-rank matrices from random linear measurements in a globally convergent manner when initialized properly. However, the performance of existing algorithms is highly sensitive in the presence of outliers that may take arbitrary values. In this paper, we propose a truncated gradient descent algorithm to improve the robustness against outliers, where the truncation is performed to rule out the contributions of samples that deviate significantly from the sample median of measurement residuals adaptively in each iteration. We demonstrate that, when initialized in a basin of attraction close to the ground truth, the proposed algorithm converges to the ground truth at a linear rate for the Gaussian measurement model with a near-optimal number of measurements, even when a constant fraction of the measurements are arbitrarily corrupted. In addition, we propose a new truncated spectral method that ensures an initialization in the basin of attraction at slightly higher requirements. We finally provide numerical experiments to validate the superior performance of the proposed approach. [ABSTRACT FROM AUTHOR]

We consider the problem of channel coding over multiterminal state-dependent channels in which neither transmitters nor receivers but only a helper node has a non-causal knowledge of the state. Such channel models arise in many emerging communication schemes. We start by investigating the parallel state-dependent channel with the same but differently scaled state corrupting the receivers. A cognitive helper knows the state in a non-causal manner and wishes to mitigate the interference that impacts the transmission between two transmit–receive pairs. Outer and inner bounds are derived. In our analysis, the channel parameters are partitioned into various cases, and segments on the capacity region boundary are characterized for each case. Furthermore, we show that for a particular set of channel parameters, the capacity region is entirely characterized. In the second part of this work, we address a similar scenario, but now each channel is corrupted by an independent state. We derive an inner bound using a coding scheme that integrates single-bin Gel'fand–Pinsker coding and Marton's coding for the broadcast channel. We also derive an outer bound and further partition the channel parameters into several cases for which parts of the capacity region boundary are characterized. [ABSTRACT FROM AUTHOR]

This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from unknown continuous distributions, which form clusters with each cluster containing a composite set of closely located distributions (based on a certain distance metric between distributions). The maximum intracluster distance is assumed to be smaller than the minimum intercluster distance, and both values are assumed to be known. The goal is to group the data sequences together if their underlying generative distributions (which are unknown) belong to one cluster. Distribution distance metrics based k-medoids algorithms are proposed for known and unknown number of distribution clusters. Upper bounds on the error probability and convergence results in the large sample regime are also provided. It is shown that the error probability decays exponentially fast as the number of samples in each data sequence goes to infinity. The error exponent has a simple form regardless of the distance metric applied when certain conditions are satisfied. In particular, the error exponent is characterized when either the Kolmogrov–Smirnov distance or the maximum mean discrepancy are used as the distance metric. Simulation results are provided to validate the analysis. [ABSTRACT FROM AUTHOR]