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This paper examines near-capacity dirty-paper code designs based on source-channel coding. We first point out that the performance loss in signal-to-noise ratio (SNR) in our code designs can be broken into the sum of the packing loss from channel coding and a modulo loss, which is a function of the granular loss from source coding and the target dirty-paper coding rate (or SNR). We then examine practical designs by combining trellis-coded quantization (TCQ) with both systematic and nonsystematic irregular repeat-accumulate (IRA) codes. Like previous approaches, we exploit the extrinsic information transfer (EXIT) chart technique for capacity-approaching IRA code design; but unlike previous approaches, we emphasize the role of strong source coding to achieve as much granular gain as possible using TCQ. Instead of systematic doping, we employ two relatively shifted TCQ codebooks, where the shift is optimized (via tuning the EXIT charts) to facilitate the IRA code design. Our designs synergistically combine TCQ with IRA codes so that they work together as well as they do individually. By bringing together TCQ (the best quantizer from the source coding community) and EXIT chart-based IRA code designs (the best from the channel coding community), we are able to approach the theoretical limit of dirty-paper coding. For example, at 0.25 bit per symbol (b/s), our best code design (with 2048-state TCQ) performs only 0.630 dB away from the Shannon capacity. [ABSTRACT FROM AUTHOR]

The "writing on dirty paper"-channel model offers an information-theoretic framework for precoding techniques for canceling arbitrary interference known at the transmitter. It indicates that lossless precoding is theoretically possible at any signal-to-noise ratio (SNR), and thus dirty-paper coding may serve as a basic building block in both single-user and multiuser communication systems. We design an end-to-end coding realization of a system materializing a significant portion of the promised gains. We employ multidimensional quantization based on trellis shaping at the transmitter. Coset decoding is implemented at the receiver using "virtual bits." Combined with iterative decoding of capacity-approaching codes we achieve an improvement of 2 dB over the best scalar quantization scheme. Code design is done using the EXIT chart technique. [ABSTRACT FROM AUTHOR]

A bound on the capacity of the causal dirty-paper channel with arbitrary interference and general independent identically distributed additive noise is derived. In particular, it is shown that for the case of Gaussian noise, the capacity is upper bounded by \log_2\left(1+SNR/e\right) bits per real dimension. This bound is useful for SNR\leq e(e-2). [ABSTRACT FROM AUTHOR]

In this correspondence, we compare the achievable throughput for the optimal strategy of dirty paper coding (DPC) to that achieved with suboptimal and lower complexity linear precoding techniques (zero-forcing and block diagonalization). Both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain, but an absolute difference in terms of throughput does exist. The sum rate difference between the two strategies is analytically computed at asymptotically high SNR. Furthermore, the difference is not affected by asymmetric channel behavior when each user has a different average SNR. Weighted sum rate maximization is also considered. In the process, it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate. [ABSTRACT FROM AUTHOR]

In wireless networks, the link connectivity may be intermittent due to shadowing, burstiness of data arrival, or uncoordinated resource allocation. In this paper, we model the intermittence of links as Bernoulli distributed random channel states, termed intermittence channel states, and study the impact of the corresponding channel state information at the transmitter (CSIT) in a two-user Gaussian broadcast channel (BC). Moreover, due to the heterogeneous timeliness of intermittence channel states, the CSIT considered in this paper is hybrid. More specifically, the CSIT of each link can be perfectly (causally or non-causally) available, delayed, or not available. When the links are connected, we adopt a general setting that the received signal-to-noise ratios can be different. Our contribution is the characterization of the capacity regions of intermittent Gaussian BC to within bounded gaps for all combinations of hybrid CSIT, except for scenario DN (delayed CSIT of receiver 1, no CSIT of receiver 2). For scenario DN, we propose an opportunistic physical layer network coding scheme that achieves a strictly larger degree-of-freedom (DoF) region than the no-CSIT DoF region. As a corollary, single-user CSIT is able to increase the sum DoF for intermittent Gaussian BC (also the capacity region for the erasure BC, as a by-product). This result is in sharp contrast to the recent negative result by Davoodi and Jafar, where it is shown that for fast-fading multiple-input single-output BC with continuous channel states, single-user CSIT does not help at all in terms of sum DoF. [ABSTRACT FROM AUTHOR]

Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers; the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink. [ABSTRACT FROM AUTHOR]

In this paper, we study the estimation of a rank-one spiked tensor in the presence of heavy tailed noise. Our results highlight some of the fundamental similarities and differences in the tradeoff between statistical and computational efficiencies under heavy tailed and Gaussian noise. In particular, we show that, for $p$ th order tensors, the tradeoff manifests in an identical fashion as the Gaussian case when the noise has finite $4(p-1)$ th moment. The difference in signal strength requirements, with or without computational constraints, for us to estimate the singular vectors at the optimal rate, interestingly, narrows for noise with heavier tails and vanishes when the noise only has finite fourth moment. Moreover, if the noise has less than fourth moment, tensor SVD, perhaps the most natural approach, is suboptimal even though it is computationally intractable. Our analysis exploits a close connection between estimating the rank-one spikes and the spectral norm of a random tensor with iid entries. In particular, we show that the order of the spectral norm of a random tensor can be precisely characterized by the moment of its entries, generalizing classical results for random matrices. In addition to the theoretical guarantees, we propose estimation procedures for the heavy tailed regime, which are easy to implement and efficient to run. Numerical experiments are presented to demonstrate their practical merits. [ABSTRACT FROM AUTHOR]

In high-dimensional sparse regression, would increasing the signal-to-noise ratio while fixing the sparsity level always lead to better model selection? For high-dimensional sparse regression problems, surprisingly, in this paper we answer this question in the negative in the regime of linear sparsity for the Lasso method, relying on a new concept we term effect size heterogeneity. Roughly speaking, a regression coefficient vector has high effect size heterogeneity if its nonzero entries have significantly different magnitudes. From the viewpoint of this new measure, we prove that the false and true positive rates achieve the optimal trade-off uniformly along the Lasso path when this measure is maximal in a certain sense, and the worst trade-off is achieved when it is minimal in the sense that all nonzero effect sizes are roughly equal. Moreover, we demonstrate that the first false selection occurs much earlier when effect size heterogeneity is minimal than when it is maximal. The underlying cause of these two phenomena is, metaphorically speaking, the “competition” among variables with effect sizes of the same magnitude in entering the model. Taken together, our findings suggest that effect size heterogeneity shall serve as an important complementary measure to the sparsity of regression coefficients in the analysis of high-dimensional regression problems. Our proofs use techniques from approximate message passing theory as well as a novel technique for estimating the rank of the first false variable. [ABSTRACT FROM AUTHOR]

In this paper we study the problem of signal detection in Gaussian noise in a distributed setting where the local machines in the star topology can communicate a single bit of information. We derive a lower bound on the Euclidian norm that the signal needs to have in order to be detectable. Moreover, we exhibit optimal distributed testing strategies that attain the lower bound. [ABSTRACT FROM AUTHOR]

In Costa's dirty-paper channel, Gaussian random binning is able to eliminate the effect of interference which is known at the transmitter, and thus achieve capacity. We examine a generalization of the dirty-paper problem to a multiple access channel (MAC) setup, where structured (lattice-based) binning seems to be necessary to achieve capacity. In the dirty-MAC, two additive interference signals are present, one known to each transmitter but none to the receiver. The achievable rates using Costa's Gaussian binning vanish if both interference signals are strong. In contrast, it is shown that lattice-strategies (“lattice precoding”) can achieve positive rates, independent of the interference power. Furthermore, in some cases—which depend on the noise variance and power constraints—high-dimensional lattice strategies are in fact optimal. In particular, they are optimal in the limit of high SNR—where the capacity region of the dirty MAC with strong interference approaches that of a clean MAC whose power is governed by the minimum of the users' powers rather than their sum. The rate gap at high SNR between lattice-strategies and optimum (rather than Gaussian) random binning is conjectured to be 1\over 2\log_2(\pi e/6)\approx 0.254 bit. Thus, the doubly dirty MAC is another instance of a network setting, like the Körner-Marton problem, where (linear) structured coding is potentially better than random binning. [ABSTRACT FROM PUBLISHER]

This study investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e., simultaneous and successive relaying, associated with two possible relay schedulings are proposed. The simultaneous relaying protocol is based on the Broadcast-Multiaccess with Common Message (BCM) scheme considered in [34]. For the successive relaying protocol: (i) a non-cooperative scheme based on the Dirty Paper Coding (DPC) and (ii) a cooperative scheme based on the Block Markov Encoding (BME) are considered. The composite scheme of employing BME in at most one relay and DPC in at least another one is also proposed. It is proved that this scheme achieves at least the same rate when compared to the cooperative and non-cooperative schemes for the Gaussian case. A Simultaneous-Successive Relaying based on Dirty Paper Coding scheme (SSRD) is also proposed. The optimum scheduling of the relays, and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios, is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network. [ABSTRACT FROM AUTHOR]

The MAC-IC-MAC is a class of multiple-access interference channels consisting of two multiple-access channels (MACs) that are mutually interfering but in which there is interference only from one transmitter of each MAC to the receiver of the other MAC. Two achievable rate regions that are within a quantifiable gap of the capacity region for the discrete-memoryless semi-deterministic MAC-IC-MAC were obtained in a previous companion work by the authors using inner and outer bounds that are unions of polytopes over admissible random coding distributions. In this paper, we obtain single-distribution—and hence explicit—inner and outer bounds that characterize the capacity region of the MIMO Gaussian MAC-IC-MAC to within a constant gap. We also evaluate and study the generalized degrees of freedom (GDoF) region via multidimensional signal-level partitioning for MIMO networks. Through its lens, the achievability of the key vertices of the GDoF region are examined. This analysis as well as the symmetric GDoF curve reveal that, at high SNR, when the ratio of the interference-to-noise to the signal-to-noise ratios, both taken in dB, is within a certain range, non-interfering transmitters in that cell can fully occupy the receivers’ signal partitions in one or more dimensions that cannot otherwise be utilized by the interfering transmitter alone. This extends the same finding in the companion paper which established the results of this work for the scalar Gaussian MAC-IC-MAC. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the high-SNR regime of the $M\times K$ Network MISO channel in which each transmitter has access to a different channel estimate, possibly with different precision. It has been recently shown that, for some regimes, this setting attains the same Degrees-of-Freedom as the ideal centralized setting with perfect Channel State Information (CSI) sharing, in which all the transmitters are endowed with the best estimate available at any transmitter. This result is restricted by the limitations of the Degrees-of-Freedom metric, as it only provides information about the slope of growth of the capacity as a function of the SNR, without any insight about the possible performance at a given SNR. In order to overcome this limitation, we analyze the affine approximation of the rate on the high-SNR regime for this decentralized Network MISO setting for the antenna configurations in which it achieves the Degrees-of-Freedom of the centralized setting. We show that, for a regime of antenna configurations, it is possible to asymptotically attain the same achievable rate as in the ideal centralized scenario. Consequently, it is possible to achieve the beamforming gain of the ideal perfect-CSI-sharing setting even if only a subset of transmitters is endowed with precise CSI, which can be exploited in scenarios such as distributed massive MIMO where the number of transmit antennas is much bigger than the number of served users. This outcome is a consequence of the synergistic compromise between CSI precision at the transmitters and consistency between the locally-computed precoders, which is an inherent trade-off of decentralized settings that does not exist in the centralized CSI configuration. We propose a precoding scheme achieving the previous result, which is built on an uneven structure in which some transmitters reduce the precision of their own precoding vector for the sake of using transmission parameters that can be more easily predicted by the other transmitters. [ABSTRACT FROM AUTHOR]

This paper studies the performance and key structural properties of the optimum location-based relay selection policy for wireless networks consisting of homogeneous Poisson distributed relays. The distribution of the channel quality indicator at the optimum relay location is obtained. A threshold-based distributed selective feedback policy is proposed for the discovery of the optimum relay location with finite average feedback load. It is established that the total number of relays feeding back obeys a Poisson distribution and an analytical expression for the average feedback load is derived. The analytical expressions for the average rate and outage probability with and without selective feedback are obtained for general path-loss models. It is shown that the optimum location-based relay selection policy outperforms other common relay selection strategies notably. It is also shown that utilizing location information from five relays on average is enough to achieve almost the same performance with the infinite feedback load case. As generalizations, isotropic Poisson point processes and heterogeneous source-to-relay and relay-to-destination links are also studied. [ABSTRACT FROM AUTHOR]

Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the theoretical understanding of this problem is still elusive. In this paper, we introduce and quantitatively characterize the two resolution limits for the line spectral estimation problem under deterministic noise: one is the minimum separation distance between the line spectra that is required for exact detection of their number, and the other is the minimum separation distance between the line spectra that is required for a stable recovery of their supports. The quantitative results imply a phase transition phenomenon in each of the two recovery problems, and also the subtle difference between the two. We further propose a sweeping singular-value-thresholding algorithm for the number detection problem and conduct numerical experiments. The numerical results confirm the phase transition phenomenon in the number detection problem. [ABSTRACT FROM AUTHOR]

In this paper, we propose a systematic low density generator matrix (LDGM) code ensemble, which is defined by the Bernoulli process. We prove that, under maximum likelihood (ML) decoding, the proposed ensemble can achieve the capacity of binary-input output symmetric (BIOS) memoryless channels in terms of bit error rate (BER). The proof technique reveals a new mechanism, different from lowering down frame error rate (FER), that the BER can be lowered down by assigning light codeword vectors to light information vectors. The finite length performance is analyzed by deriving an upper bound and a lower bound, both of which are shown to be tight in the high signal-to-noise ratio (SNR) region. To improve the waterfall performance, we construct the systematic convolutional LDGM (SysConv-LDGM) codes by a random splitting process. The SysConv-LDGM codes are easily configurable in the sense that any rational code rate can be realized without complex optimization. As a universal construction, the main advantage of the SysConv-LDGM codes is their near-capacity performance in the waterfall region and predictable performance in the error-floor region that can be lowered down to any target as required by increasing the density of the uncoupled LDGM codes. Numerical results are also provided to verify our analysis. [ABSTRACT FROM AUTHOR]

This paper studies the related problems of prediction, covariance estimation, and principal component analysis for the spiked covariance model with heteroscedastic noise. We consider an estimator of the principal components based on whitening the noise, and we derive optimal singular value and eigenvalue shrinkers for use with these estimated principal components. Underlying these methods are new asymptotic results for the high-dimensional spiked model with heteroscedastic noise, and consistent estimators for the relevant population parameters. We extend previous analysis on out-of-sample prediction to the setting of predictors with whitening. We demonstrate certain advantages of noise whitening. Specifically, we show that in a certain asymptotic regime, optimal singular value shrinkage with whitening converges to the best linear predictor, whereas without whitening it converges to a suboptimal linear predictor. We prove that for generic signals, whitening improves estimation of the principal components, and increases a natural signal-to-noise ratio of the observations. We also show that for rank one signals, our estimated principal components achieve the asymptotic minimax rate. [ABSTRACT FROM AUTHOR]

Cooperative beamforming is a potentially useful technique for enhancing link reliability in modern wireless relay communications. To aid the beamforming design, the signal-to-noise ratio (SNR) of the source-to-relay (S-R) channel links must be known at the destination node. Abdallah and Papadopoulos in IEEE Trans. Signal Processing, vol. 56, no. 10, 2008, proposed a beamforming system with relay-assisted SNR acquisition; that is, the S-R link SNR is first quantized at each relay and is then forwarded to the destination. An optimal quantizer design problem was proposed in that paper, aiming at reducing the system bit error rate; however, only the binary quantization case was considered therein, with the quantization threshold computed by a suggested rule of thumb. In this paper, we study the aforementioned quantizer design problem in the general multiple-bit setting. We show that the solutions to the first-order necessary condition for optimality can be obtained as a fixed point of a certain nonlinear map over the feasible threshold set. The existence and uniqueness of the fixed point are established by using, respectively, the Brouwer’s and Schauder’s fixed point theorems. Finally, we show that the fixed point thus obtained yields the globally optimal set of quantization thresholds. To the best of our knowledge, this paper is the first which leverages fixed point theories to rigorously solve SNR quantization problems in the context of wireless relay communication. [ABSTRACT FROM AUTHOR]

Fundamental relations between information and estimation have been established in the literature for the continuous time Gaussian and Poisson channels. In this paper, we demonstrate that such relations hold for a much larger family of continuous-time channels. We introduce the family of semi-martingale channels where the channel output is a semi-martingale stochastic process, and the channel input modulates the characteristics of the semi-martingale. For these channels, which includes as a special case the continuous time Gaussian and Poisson models, we establish new representations relating the mutual information between the channel input and output to an optimal causal filtering loss, thereby unifying and considerably extending results from the Gaussian and Poisson settings. Extensions to the setting of mismatched estimation are also presented where the relative entropy between the laws governing the output of the channel under two different input distributions is equal to the cumulative difference between the estimation loss incurred by using the mismatched and optimal causal filters, respectively. The main tool underlying these results is the Doob–Meyer decomposition of a class of sub-martingales. The results in this paper can be viewed as the continuous-time analogues of recent generalizations for relations between information and estimation for discrete-time Lévy channels. [ABSTRACT FROM AUTHOR]

Let X and Y be dependent random variables. This paper considers the problem of designing a scalar quantizer for Y to maximize the mutual information between the quantizer’s output and X, and develops fundamental properties and bounds for this form of quantization, which is connected to the log-loss distortion criterion. The main focus is the regime of low ${I}({X};{Y})$ , where it is shown that, if X is binary, a constant fraction of the mutual information can always be preserved using $\mathcal {O}(\log (1/{I}({X};{Y})))$ quantization levels, and there exist distributions for which this many quantization levels are necessary. Furthermore, for larger finite alphabets $2 < |\mathcal {X}| < \infty $ , it is established that an $\eta $ -fraction of the mutual information can be preserved using roughly $(\log (| \mathcal {X} | /{I}({X};{Y})))^{\eta \cdot (|\mathcal {X}| - 1)}$ quantization levels. [ABSTRACT FROM AUTHOR]

The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy phaseless measurements, which arises in a diverse range of settings such as optical detection, X-ray crystallography, electron microscopy, and coherent diffractive imaging. Our focus is on information-theoretic fundamental limits under an approximate recovery criterion, considering both discrete and Gaussian models for the sparse non-zero entries, along with Gaussian measurement matrices. In both cases, our bounds provide sharp thresholds with near-matching constant factors in several scaling regimes on the sparsity and signal-to-noise ratio. As a key step towards obtaining these results, we develop new concentration bounds for the conditional information content of log-concave random variables, which may be of independent interest. [ABSTRACT FROM AUTHOR]

This paper considers a Gaussian channel with one transmitter and two receivers. The goal is to maximize the communication rate at the intended/primary receiver subject to a disturbance constraint at the unintended/secondary receiver. The disturbance is measured in terms of the minimum mean square error (MMSE) of the interference that the transmission to the primary receiver inflicts on the secondary receiver. This paper presents a new upper bound for the problem of maximizing the mutual information subject to an MMSE constraint. The new bound holds for vector inputs of any length and recovers a previously known limiting (when the length of the vector input tends to infinity) expression from the work of Bustin et al. The key technical novelty is a new upper bound on the MMSE. This bound allows one to bound the MMSE for all signal-to-noise ratio (SNR) values below a certain SNR at which the MMSE is known (which corresponds to the disturbance constraint). The bound also complements the “single-crossing point property” of the MMSE that upper bounds the MMSE for all SNR values above a certain value at which the MMSE value is known. The MMSE upper bound provides a refined characterization of the phase-transition phenomenon, which manifests, in the limit as the length of the vector input goes to infinity, as a discontinuity of the MMSE for the problem at hand. For vector inputs of size n=1 , a matching lower bound, to within an additive gap of order O ( \log \log ({1}/{\sf MMSE}) ) (where {\sf MMSE}$ is the disturbance constraint), is shown by means of the mixed inputs technique recently introduced by Dytso et al. [ABSTRACT FROM PUBLISHER]

This paper studies the capacity of a general multiple-input multiple-output (MIMO) free-space optical intensity channel under a per-input-antenna peak-power constraint and a total average-power constraint over all input antennas. The focus is on the scenario with more transmit than receive antennas. In this scenario, different input vectors can yield identical distributions at the output, when they result in the same image vector under multiplication by the channel matrix. We first determine the most energy-efficient input vectors that attain each of these image vectors. Based on this, we derive an equivalent capacity expression in terms of the image vector, and establish new lower and upper bounds on the capacity of this channel. The bounds match when the signal-to-noise ratio (SNR) tends to infinity, establishing the high-SNR asymptotic capacity. We also characterize the low-SNR slope of the capacity of this channel. [ABSTRACT FROM AUTHOR]

We study the generalized degrees of freedom (gDoF) of the noncoherent diamond (parallel relay) wireless network with asymmetric distributions of link strengths. We use the noncoherent block-fading model introduced by Marzetta and Hochwald, where no channel state information is available at the transmitters or at the receivers and the channels remain constant for a coherence time of $T$ symbol durations. We first derive an upper bound for the capacity of this channel and then derive the optimal structure for the solution of the upper bound optimization problem. Using the optimal structure, we solve the upper bound optimization problem in terms of its gDoF. Using insights from our upper bound signaling solution, we devise an achievability strategy based on a novel scheme that we call train-scale quantize-map-forward (TS-QMF). This scheme uses training in the links from the source to the relays, scaling and quantizing at the relays combined with nontraining-based schemes. We show the optimality of this scheme by comparing it to the upper bound in terms of the gDoF. In noncoherent point-to-point multiple-input-multiple-output (MIMO) channels, where the fading realization is unknown to the transmitter and the receiver, an important tradeoff between communication and channel learning was revealed by Zheng and Tse, by demonstrating that not all the available antennas might be used, as it is suboptimal to learn all their channel parameters. Our results in this paper for the diamond network demonstrate that in certain regimes of relative channel strengths, the gDoF-optimal scheme uses a subnetwork, demonstrating a similar tradeoff between channel learning and communication. In some regimes, it is gDoF-optimal to do relay selection, i.e., use a part of the network. In the other regimes, even when it is essential to use the entire network, it is suboptimal to learn the channel states for all the links in the network, i.e., traditional training-based schemes are suboptimal in these regimes. [ABSTRACT FROM AUTHOR]

This paper studies the transceiver design of the Gaussian two-pair two-way relay channel (TWRC), where two pairs of users exchange information through a common relay in a pairwise manner. Our main contribution is to show that the capacity of the Gaussian two-pair TWRC is achievable to within $\frac{1}{ 2}$ bit for arbitrary channel conditions. For the outer bound, we derive a genie-aided bound of the Gaussian two-pair TWRC, which is tighter than the cut-set bound. For the inner bound, we develop a hybrid coding scheme involving Gaussian random coding, nested lattice coding, superposition coding, and network-coded decoding. We further present a message-reassembling strategy to decouple the coding design for the user-to-relay and relay-to-user links, so as to provide flexibility to fully exploit the channel randomness. We show that judicious power allocation at the users and at the relay is necessary to approach the channel capacity under various channel conditions. [ABSTRACT FROM AUTHOR]

Shannon’s mutual information of a random multiple antenna and multipath time varying channel is studied in the general case where the process constructed from the channel coefficients is an ergodic and stationary process which is assumed to be available at the receiver. From this viewpoint, the channel can also be represented by an ergodic self-adjoint block-Jacobi operator, which is close in many aspects to a block version of a random Schrödinger operator. The mutual information is then related to the so-called density of states of this operator. In this paper, it is shown that under the weakest assumptions on the channel, the mutual information can be expressed in terms of a matrix-valued stochastic process coupled with the channel process. This allows numerical approximations of the mutual information in this general setting. Moreover, assuming further that the channel coefficient process is a Markov process, a representation for the mutual information offset in the large signal to noise ratio regime is obtained in terms of another related Markov process. This generalizes previous results from Levy et al.. It is also illustrated how the mutual information expressions that are closely related to those predicted by the random matrix theory can be recovered in the large dimensional regime. [ABSTRACT FROM AUTHOR]

The characterization of fundamental performance bounds of many-to-many communication systems in which participating nodes are active in an intermittent way is one of the major challenges in communication theory. In order to address this issue, we introduce the multiple-input multiple-output (MIMO) three-way channel (3WC) with an intermittent node and study its degrees-of-freedom (DoF) region and sum-DoF. We devise a non-adaptive encoding scheme based on zero-forcing, interference alignment, and erasure coding, and show its DoF region (and thus sum-DoF) optimality for non-intermittent 3WCs and its sum-DoF optimality for (node-) intermittent 3WCs. However, we show by example that in general some DoF tuples in the intermittent 3WC can only be achieved by adaptive schemes such as decode-forward relaying. This shows that non-adaptive encoding is sufficient for the non-intermittent 3WC and for the sum-DoF of intermittent 3WCs but adaptive encoding is necessary for the DoF region of intermittent 3WCs. This paper contributes to a better understanding of the fundamental limits of multi-way communication systems with intermittency and the impact of adaptation therein. [ABSTRACT FROM AUTHOR]

In fog-aided cellular systems, content delivery latency can be minimized by jointly optimizing edge caching and transmission strategies. In order to account for the cache capacity limitations at the edge nodes (ENs), transmission generally involves both fronthaul transfer from a cloud processor with access to the content library to the ENs and wireless delivery from the ENs to the users. In this paper, the resulting problem is studied from an information-theoretic viewpoint by making the following practically relevant assumptions: 1) the ENs have multiple antennas; 2) only uncoded fractional caching is allowed; 3) the fronthaul links are used to send fractions of contents; and 4) the ENs are constrained to use one-shot linear zero-forcing precoding on the wireless channel. Assuming off-line proactive caching and focusing on a high signal-to-noise ratio (SNR) latency metric, the optimal information-theoretic performance is investigated under both serial and pipelined fronthaul-edge transmission modes. The analysis characterizes the minimum high-SNR latency in terms of normalized delivery time (NDT) for worst case users’ demands. The characterization is exact for a subset of system parameters and is generally optimal within a multiplicative factor of 3/2 for the serial case and 2 for the pipelined case. The results bring insights into the optimal interplay between edge and cloud processing in fog-aided wireless networks as a function of system resources, including the number of antennas at the ENs, the ENs’ cache capacity, and the fronthaul capacity. [ABSTRACT FROM AUTHOR]

This paper addresses the question of achieving capacity with lattice codes in multi-antenna block fading channels when the number of fading blocks tends to infinity. A design criterion based on the normalized minimum determinant is proposed for division algebra multi-block space-time codes over fading channels; this plays a similar role to the Hermite invariant for Gaussian channels. Under maximum likelihood decoding, it is shown that this criterion is sufficient to guarantee transmission rates within a constant gap from capacity both for deterministic channels and ergodic fading channels. Moreover, if the number of receive antennas is greater than or equal to the number of transmit antennas, the same constant gap is achieved under naive lattice decoding as well. In the case of independent identically distributed Rayleigh fading, the error probability vanishes exponentially fast. In contrast to the standard approach in the literature, which employs random lattice ensembles, the existence results in this paper are derived from the number theory. First, the gap to capacity is shown to depend on the discriminant of the chosen division algebra; then, class field theory is applied to build families of algebras with small discriminants. The key element in the construction is the choice of a sequence of division algebras whose centers are number fields with small root discriminants. [ABSTRACT FROM AUTHOR]

This paper is about deriving lower bounds on the error exponents for the two-user interference channel under the random coding regime for several ensembles. Specifically, we first analyze the standard random coding ensemble, where the codebooks are comprised of independently and identically distributed (i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is in contrast to other, suboptimal decoding rules that have been used in the literature (e.g., joint typicality decoding, treating interference as noise, and so on). The fact that the interfering signal is a codeword, rather than an i.i.d. noise process, complicates the application of conventional techniques of performance analysis of the optimum decoder. In addition, unfortunately, these conventional techniques result in loose bounds. Using analytical tools rooted in statistical physics, as well as advanced union bounds, we derive single-letter formulas for the random coding error exponents. We compare our results with the best known lower bound on the error exponent, and show that our exponents can be strictly better. Then, in the second part of this paper, we consider more complicated coding ensembles and find a lower bound on the error exponent associated with the celebrated Han–Kobayashi random coding ensemble, which is based on superposition coding. [ABSTRACT FROM AUTHOR]

In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal’s orbit by accessing multiple independent observations. Of particular interest is the sample complexity, i.e., the number of observations/samples needed in terms of the signal-to-noise ratio (SNR) (the signal energy divided by the noise variance) in order to drive the mean-square error to zero. Previous work showed that if the translations are drawn from the uniform distribution, then, in the low SNR regime, the sample complexity of the problem scales as $\omega (1/ \mathrm {SNR}^{3})$. In this paper, using a generalization of the Chapman–Robbins bound for orbits and expansions of the $\chi ^{2}$ divergence at low SNR, we show that in the same regime the sample complexity for any aperiodic translation distribution scales as $\omega (1/ \mathrm {SNR}^{2})$. This rate is achieved by a simple spectral algorithm. We propose two additional algorithms based on non-convex optimization and expectation–maximization. We also draw a connection between the multireference alignment problem and the spiked covariance model. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general framework for tensor singular value decomposition (tensor singular value decomposition (SVD)), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive results are developed on both the statistical and computational limits for tensor SVD. This problem exhibits three different phases according to the signal-to-noise ratio (SNR). In particular, with strong SNR, we show that the classical higher-order orthogonal iteration achieves the minimax optimal rate of convergence in estimation; with weak SNR, the information-theoretical lower bound implies that it is impossible to have consistent estimation in general; with moderate SNR, we show that the non-convex maximum likelihood estimation provides optimal solution, but with NP-hard computational cost; moreover, under the hardness hypothesis of hypergraphic planted clique detection, there are no polynomial-time algorithms performing consistently in general. [ABSTRACT FROM AUTHOR]

This paper derives upper and lower bounds on the capacity of the multiple-input single-output free-space optical intensity channel with signal-independent additive Gaussian noise subject to both an average-intensity and a peak-intensity constraint. In the limit where the signal-to-noise ratio (SNR) tends to infinity, the asymptotic capacity is specified, while in the limit where the SNR tends to zero, the exact slope of the capacity is given. [ABSTRACT FROM AUTHOR]

This paper introduces an estimator of the signal-to-noise ratio in the framework where a noisy source emits the same signal a number $n$ of times. The estimator has the structure of a $U$ -statistic from which derives many desirable properties: it is unbiased, consistent and, being a Rao-Blackwellisation of existing proposals, is closer to optimal variance-wise. However, its variance is numerically difficult to evaluate and two approximations are obtained to facilitate its use in practice. These allow quantifying the improvement in variance, which is found to be substantial as the estimator needs roughly one-third of the data previously required to perform similarly. Moreover, a simulation shows that the estimator is approximately normally distributed for $n$ as small as 10, which allows for accurate inference. The estimator is then applied to data arising in a cryptanalysis, where the numerical security of a cryptoprocessor is tested against a side-channel attack. This problem is a representative of situations where the signal-to-noise ratio must be precisely estimated for small $n$. We derive a rigorous data-driven approach that is shown to much enhance the efficiency of standard side-channel attacks. [ABSTRACT FROM AUTHOR]

This paper considers the signal-to-noise ratio (SNR)-evolution, meaning the behavior as a function of the SNR, of the minimum mean-square error (MMSE) function of code sequences in several multi-user settings in the additive white Gaussian noise regime. The settings investigated in this context include the Gaussian wiretap channel, the Gaussian broadcast channel (BC), and the Gaussian BC with confidential messages (BCC). This paper shows that the specific properties of the SNR-evolution of the MMSE and conditional MMSE functions are necessary and sufficient conditions for capacity or equivocation achieving code sequences. In some cases, the complete SNR-evolution of a family of code sequences can be determined, providing significant insight into the disturbance (in terms of MMSE) such codes have on unintended receivers at other SNRs. Moreover, the effects of an additional MMSE constraint on the capacity region and on the SNR-evolution of code sequences are considered in the BC and BCC settings. Such an analysis emphasizes the tradeoff between rates and limited disturbance on unintended receivers. [ABSTRACT FROM AUTHOR]

This paper investigates the design of codes for multiple-input multiple-output (MIMO) multiple access channel (MAC). If a joint maximum-likelihood decoding is to be performed at the receiver, then every MIMO-MAC code can be regarded as a single-user code, where the minimum determinant criterion proposed by Tarokh et al. is useful for designing such codes and for upper bounding the maximum pairwise error probability (PEP), whenever the codes are of finite rate and operate in finite signal-to-noise ratio range. Unlike the case of single-user codes where the minimum determinant can be lower bounded by a fixed constant as code-rate grows, it was proved by Lahtonen et al. that the minimum determinant of MIMO-MAC codes decays as a function of the rates. This decay phenomenon is further investigated in this paper, and upper bounds for the decays of minimum determinant corresponding to each error event are provided. Lower bounds for the optimal decay are established and are based on an explicit construction of codes using algebraic number theory and Diophantine approximation. For some error profiles, the constructed codes are shown to meet the aforementioned upper bounds, hence they are optimal finite-rate codes in terms of PEPs associated with such error events. An asymptotic diversity-multiplexing gain tradeoff (DMT) analysis of the proposed codes is also given. It is shown that these codes are DMT optimal when the values of multiplexing gains are small. [ABSTRACT FROM PUBLISHER]

The Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) is considered. The dirty-paper coding (DPC) rate region is shown to coincide with the capacity region. To that end, a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality, to show that a superposition of Gaussian codes is optimal for the degraded vector broadcast channel and that DPC is optimal for the nondegraded case. Furthermore, the capacity region is characterized under a wide range of input constraints, accounting, as special cases, for the total power and the per-antenna power constraints. [ABSTRACT FROM AUTHOR]

In 1975, Carleial presented a special case of an interference channel, called the very strong interference regime, in which the interference does not reduce the capacity of the constituent point-to-point Gaussian channels. In this paper, we show that in the strictly very strong interference regime, the dispersions are similarly unaffected. More precisely, in this paper, we characterize the second-order coding rates of the Gaussian interference channel in the strictly very strong interference regime. In other words, we characterize the speed of convergence of rates of optimal block codes toward a boundary point of the (rectangular) capacity region. These second-order coding rates are expressed in terms of the average probability of error and variances of appropriately defined information densities which coincide with the dispersion of the (single-user) Gaussian channel. This allows us to conclude that the dispersions are unaffected by interference in this channel model. [ABSTRACT FROM AUTHOR]

In multiuser information theory, it is often assumed that every node in the network possesses all codebooks used in the network. This assumption may be impractical in distributed ad hoc, cognitive, or heterogeneous networks. This paper considers the two-user interference channel with one oblivious receiver (IC-OR), i.e., one receiver lacks knowledge of the interfering cookbook, whereas the other receiver knows both codebooks. This paper asks whether, and if so how much, the channel capacity of the IC-OR is reduced compared with that of the classical IC where both receivers know all codebooks. A novel outer bound is derived and shown to be achievable to within a gap for the class of injective semideterministic IC-ORs; the gap is shown to be zero for injective fully deterministic IC-ORs. An exact capacity result is shown for the general memoryless IC-OR when the nonoblivious receiver experiences very strong interference. For the linear deterministic IC-OR that models the Gaussian noise channel at high SNR, nonindependent identically distributed. Bernoulli(1/2) input bits are shown to achieve points not achievable by i.i.d. Bernoulli(1/2) input bits used in the same achievability scheme. For the real-valued Gaussian IC-OR, the gap is shown to be at most 1/2 bit per channel use, even though the set of optimal input distributions for the derived outer bound could not be determined. Toward understanding the Gaussian IC-OR, an achievability strategy is evaluated in which the input alphabets at the nonoblivious transmitter are a mixture of discrete and Gaussian random variables, where the cardinality of the discrete part is appropriately chosen as a function of the channel parameters. Surprisingly, as the oblivious receiver intuitively should not be able to jointly decode the intended and interfering messages (whose codebook is unavailable), it is shown that with this choice of input, the capacity region of the symmetric Gaussian IC-OR is to within 1/2\log \left (12\pi \mathrm e \right )\approx 3.34 bits (per channel use per user) of an outer bound for the classical Gaussian IC with full codebook knowledge at both receivers. [ABSTRACT FROM PUBLISHER]

Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code, which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multiuser uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean-squared error receiver. In the high signal-to-noise ratio regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard multiple-input multiple-output (MIMO) channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees of freedom. [ABSTRACT FROM AUTHOR]

This paper studies the zero-delay source-channel coding problem, and specifically the problem of obtaining the vector transformations that optimally map between the $m$ -dimensional source space and $k$ -dimensional channel space, under a given transmission power constraint and for the mean square error distortion. The functional properties of the cost are studied and the necessary conditions for the optimality of the encoder and decoder mappings are derived. An optimization algorithm that imposes these conditions iteratively, in conjunction with the noisy channel relaxation method to mitigate poor local minima, is proposed. The numerical results show strict improvement over prior methods. The numerical approach is extended to the scenario of source-channel coding with decoder side information. The resulting encoding mappings are shown to be continuous relatives of, and in fact subsume as special case, the Wyner–Ziv mappings encountered in digital distributed source coding systems. A well-known result in information theory pertains to the linearity of optimal encoding and decoding mappings in the scalar Gaussian source and channel setting, at all channel signal-to-noise ratios (CSNRs). In this paper, the linearity of optimal coding, beyond the Gaussian source and channel, is considered and the necessary and sufficient condition for linearity of optimal mappings, given a noise (or source) distribution, and a specified a total power constraint are derived. It is shown that the Gaussian source-channel pair is unique in the sense that it is the only source-channel pair for which the optimal mappings are linear at more than one CSNR values. Moreover, the asymptotic linearity of optimal mappings is shown for low CSNR if the channel is Gaussian regardless of the source and, at the other extreme, for high CSNR if the source is Gaussian, regardless of the channel. The extension to the vector settings is also considered where besides the conditions inherited from the scalar case, additional constraints must be satisfied to ensure linearity of the optimal mappings. [ABSTRACT FROM AUTHOR]

This paper deals with Low-Density Construction-A (LDA) lattices, which are obtained via Construction A from non-binary low-density parity-check codes. More precisely, a proof is provided that Voronoi constellations of LDA lattices achieve capacity of the AWGN channel under lattice encoding and decoding for every signal-to-noise ratio greater than 1. This is obtained after showing the same result for more general Construction-A lattice constellations. The theoretical analysis is carried out in a way that allows to describe how the prime number underlying Construction A behaves as a function of the lattice dimension. Moreover, no dithering is required in the transmission scheme, simplifying some previous solutions of the problem. Remarkably, capacity is achievable with LDA lattice codes whose parity-check matrices have constant row and column Hamming weights. Some expansion properties of random bipartite graphs constitute an extremely important tool for dealing with sparse matrices and allow to find a lower bound for the minimum Euclidean distance of LDA lattices in our ensemble. [ABSTRACT FROM PUBLISHER]

This paper focuses on the modeling and analysis of the temporal performance variation experienced by a mobile user in a wireless network and its impact on system-level design. We consider a simple stochastic geometry model: the infrastructure nodes are Poisson distributed while the user’s motion is the simplest possible, i.e., constant velocity on a straight line. We first characterize variations in the signal-to-noise ratio (SNR) process and associated downlink Shannon rate, resulting from variations in the infrastructure geometry seen by the mobile. Specifically, by making a connection between stochastic geometry and queuing theory, the level crossings of the SNR process are shown to form an alternating renewal process whose distribution is completely characterized. For large/small SNR levels, and associated rare events, we further derive simple distributional (exponential) models. We then characterize the second major contributor to such variations, namely, changes in the number of other users sharing the infrastructure. Combining these two phenomena, we study what are the dominant factors (infrastructure geometry or sharing number) when a mobile experiences a very high/low shared rate. These results are then used to evaluate and optimize the system-level quality of experience of the mobile users sharing such a wireless infrastructure, including mobile devices streaming video which proactively buffer content to prevent rebuffering and mobiles which are downloading large files. Finally, we use simulation to assess the fidelity of this model and its robustness to factors which are presently not taken into account. [ABSTRACT FROM PUBLISHER]

Usually, it is very difficult to determine the exact distribution for a test statistic. In this paper, asymptotic distributions of locally most powerful invariant test for independence of complex Gaussian vectors are developed. In particular, its cumulative distribution function (CDF) under the null hypothesis is approximated by a function of chi-squared CDFs. Moreover, the CDF corresponding to the non-null distribution is expressed in terms of non-central chi-squared CDFs for close hypothesis, and Gaussian CDF as well as its derivatives for far hypothesis. The results turn out to be very accurate in terms of fitting their empirical counterparts. Closed-form expression for the detection threshold is also provided. Numerical results are presented to validate our theoretical findings. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce new Stein identities for gamma target distribution as well as a new non-linear channel specifically designed for gamma inputs. From these two ingredients, we derive an explicit and simple formula for the derivative of the input-output mutual information of this non-linear channel with respect to the channel quality parameter. This relation is reminiscent of the well-known link between the derivative of the input-output mutual information of additive Gaussian noise channel with respect to the signal-to-noise ratio and the minimum mean-square error. The proof relies on a rescaled version of De Bruijn identity for gamma target distribution together with a stochastic representation for the gamma-specific Fisher information. Finally, we are able to derive precise bounds and asymptotics for the input-output mutual information of the non-linear channel with gamma inputs. [ABSTRACT FROM AUTHOR]

A classical problem in digital communications is to evaluate the symbol error probability (SEP) and bit error probability (BEP) of a multidimensional constellation over an additive white Gaussian noise channel. In this paper, we revisit this problem for nonequally likely symbols and study the behavior of the optimal maximum a posteriori (MAP) detector at asymptotically high signal-to-noise ratios. Exact closed-form asymptotic expressions for SEP and BEP for arbitrary constellations and input distributions are presented. The well-known union bound is proven to be asymptotically tight under general conditions. The performance of the practically relevant maximum likelihood (ML) detector is also analyzed. Although the decision regions with MAP detection converge to the ML regions at high signal-to-noise ratios, the ratio between the MAP and ML detectors in terms of both SEP and BEP approaches a constant, which depends on the constellation and a priori probabilities. Necessary and sufficient conditions for asymptotic equivalence between the MAP and ML detectors are also presented. [ABSTRACT FROM AUTHOR]

The fast Fourier transform is the most efficiently known way to compute the discrete Fourier transform (DFT) of an arbitrary n -length signal, and has a computational complexity of O( n\log n) . If the DFT \vec X of the signal \vec x has only $k$ non-zero coefficients (where k< n$ ), can we do better? We addressed this question and presented a novel fast Fourier aliasing-based sparse transform (FFAST) algorithm that cleverly induces sparse-graph alias codes in the DFT domain, via a Chinese-remainder-theorem-guided sub-sampling operation in the time-domain. The induced sparse-graph alias codes are then exploited to devise a fast and iterative onion-peeling style decoder that computes k$ -sparse DFT of an n$ -length signal using only O( k)$ time-domain samples and O( k\log k)$ computations. In this paper, we generalize the FFAST framework by Pawar and Ramchandran to the noisy setting where the time-domain samples are corrupted by white Gaussian noise. We show that the noise-robust R-FFAST algorithm computes a k noise-corrupted time-domain samples in O( k\log ^{4} n) complexity, i.e., sub-linear sample and time complexity. In Section IX, we provide extensive simulation results validating the empirical performance of the R-FFAST algorithm, e.g., we show that the R-FFAST algorithm computes a 50-sparse DFT of an ≈ 10 million length signal using only 4800 noisy samples with an effective signal-to-noise ratio of 5 dB. We also provide comparison of the run-time performance of several existing sparse Fourier transform implementations with that of the R-FFAST and show that it is almost 20 times faster, for comparable settings, than the state-of-the-art algorithm, while simultaneously providing better support recovery guarantees. While our theoretical results are for signals with a uniformly random support of the non-zero DFT coefficients and additive white Gaussian noise, we provide simulation results, which demonstrate that the R-FFAST algorithm performs well even for signals like magnetic resonance images, that have an approximately sparse Fourier spectrum with a non-uniform support for the dominant DFT coefficients. [ABSTRACT FROM PUBLISHER]

The capacity region of the $K$ -user Gaussian interference channel (GIC) is a long-standing open problem and even capacity outer bounds are little known in general. A significant progress on degrees-of-freedom (DoF) analysis, a first-order capacity approximation, for the $K$ -user GIC has provided new important insights into the problem of interest in the high signal-to-noise ratio (SNR) limit. However, such capacity approximation has been observed to have some limitations in predicting the capacity at finite SNR. In this paper, we develop a new upper-bounding technique that utilizes a new type of genie signal and applies time sharing to genie signals at $K$ receivers. Based on this technique, we derive new upper bounds on the sum capacity of the three-user GIC with constant, complex channel coefficients and then generalize to the $K$ -user case to better understand sum-rate behavior at finite SNR. We also provide closed-form expressions of our upper bounds on the capacity of the $K$ -user symmetric GIC easily computable for any $K$ . From the perspectives of our results, some sum-rate behavior at finite SNR is in line with the insights given by the known DoF results, while some others are not. In particular, the well-known $K/2$ DoF achievable for almost all constant real channel coefficients turns out to be not embodied as a substantial performance gain over a certain range of the cross-channel coefficient in the $K$ -user symmetric real case especially for large $K$ . We further investigate the impact of phase offset between the direct-channel coefficient and the cross-channel coefficients on the sum-rate upper bound for the three-user complex GIC. As a consequence, we aim to provide new findings that could not be predicted by the prior works on DoF of GICs. [ABSTRACT FROM PUBLISHER]

In this paper, we study a support set reconstruction problem for multiple measurement vectors (MMV) with different sensing matrices, where the signals of interest are assumed to be jointly sparse and each signal is sampled by its own sensing matrix in the presence of noise. Using mathematical tools, we develop upper and lower bounds of the failure probability of the support set reconstruction in terms of the sparsity, the ambient dimension, the minimum signal-to-noise ratio, the number of measurement vectors, and the number of measurements. These bounds can be used to provide guidelines for determining the system parameters for various compressed sensing applications with noisy MMV with different sensing matrices. Based on the bounds, we develop necessary and sufficient conditions for reliable support set reconstruction. We interpret these conditions to provide theoretical explanations regarding the benefits of taking more measurement vectors. We then compare our sufficient condition with the existing results for noisy MMV with the same sensing matrix. As a result, we show that noisy MMV with different sensing matrices may require fewer measurements for reliable support set reconstruction, under a sublinear sparsity regime in a low noise-level scenario. [ABSTRACT FROM AUTHOR]

The best outer bound on the capacity region of the two-user Gaussian interference channel (GIC) is known to be the intersection of regions of various bounds, including genie-aided outer bounds, in which a genie provides noisy input signals to the intended receiver. The Han and Kobayashi (HK) scheme provides the best known inner bound. The rate difference between the best known lower and upper bounds on the sum capacity remains as large as 1 b/channel use, especially around g^2=P^-1/3 , where P is the symmetric power constraint and g is the symmetric real cross-channel coefficient. In this paper, we pay attention to the moderate interference regime where g^2\in ~(\max (0.086, P^-1/3),1) . We propose a new upper-bounding technique that utilizes noisy observation of interfering signals as genie signals and applies time sharing to the genie signals at the receivers. A conditional version of the worst additive noise lemma is also introduced to derive new capacity bounds. The resulting upper (outer) bounds on the sum capacity (capacity region) are shown to be tighter than the existing bounds in a certain range of the moderate interference regime. Using the new upper bounds and the HK lower bound, we show that R\text {sym}^{ }=\frac {1}2\log \big (|g|P+|g|^{-1}(P+1)\big ) characterizes the capacity of the symmetric real GIC to within 0.104 b/channel use in the moderate interference regime at any signal-to-noise ratio (SNR). We further establish a high-SNR characterization of the symmetric real GIC, where the proposed upper bound is at most 0.1 b far from a certain HK achievable scheme with Gaussian signalling and time sharing for g^2\in ~(0,1] . In particular, R\text {sym}^{ } is achievable at high SNR by the proposed HK scheme and turns out to be the high-SNR capacity at least at g^2=0.25, 0.5 . We finally point out that there are two subregimes at high SNR in the weak interference regime, where g^2\in (0,1] . [ABSTRACT FROM AUTHOR]