# arXiv Information Theory

*URL:*http://arxiv.org/

*Updated:*hace 17 horas 47 mins

### Covert Wireless Communication with Artificial Noise Generation. (arXiv:1709.07096v1 [cs.IT])

Covert communication conceals the transmission of the message from an attentive adversary. Recent work on the limits of covert communication in additive white Gaussian noise (AWGN) channels has demonstrated that a covert transmitter (Alice) can reliably transmit a maximum of $\mathcal{O}\left(\sqrt{n}\right)$ bits to a covert receiver (Bob) without being detected by an adversary (Warden Willie) in $n$ channel uses. This paper focuses on the scenario where other friendly nodes distributed according to a two-dimensional Poisson point process with density $m$ are present in the environment. We propose a strategy where the friendly node closest to the adversary, without close coordination with Alice, produces artificial noise. We show that this method allows Alice to reliably and covertly send $\mathcal{O}(\min\{{n,m^{\gamma/2}\sqrt{n}}\})$ bits to Bob in $n$ channel uses, where $\gamma$ is the path-loss exponent. Moreover, we also consider a setting where there are $N_{\mathrm{w}}$ collaborating adversaries uniformly and randomly located in the environment and show that in $n$ channel uses, Alice can reliably and covertly send $\mathcal{O}\left(\min\left\{n,\frac{m^{\gamma/2} \sqrt{n}}{N_{\mathrm{w}}^{\gamma}}\right\}\right)$ bits to Bob when $\gamma >2$, and $\mathcal{O}\left(\min\left\{n,\frac{m \sqrt{n}}{N_{\mathrm{w}}^{2}\log^2 {N_{\mathrm{w}}}}\right\}\right)$ when $\gamma = 2$. Conversely, under mild restrictions on the communication strategy, we demonstrate that no higher covert throughput is possible for $\gamma>2$.

### Hypergraph Theory: Applications in 5G Heterogeneous Ultra-Dense Networks. (arXiv:1709.07129v1 [cs.IT])

Heterogeneous ultra-dense network (HUDN) can significantly increase the spectral efficiency of cellular networks and cater for the explosive growth of data traffic in the fifth-generation (5G) communications. Due to the dense deployment of small cells (SCs), interference among neighboring cells becomes severe. As a result, the effective resource allocation and user association algorithms are essential to minimize inter-cell interference and optimize network performance. However, optimizing network resources in HUDN is extremely complicated as resource allocation and user association are coupled. Therefore, HUDN requires low-complexity but effective resource allocation schemes to address these issues. Hypergraph theory has been recognized as a useful mathematical tool to model the complex relations among multiple entities. In this article, we show how the hypergraph models can be used to effectively tackle resource allocation problems in HUDN. We also discuss several potential research issues in this field.

### Analysis of Wireless-Powered Device-to-Device Communications with Ambient Backscattering. (arXiv:1709.07182v1 [cs.NI])

Self-sustainable communications based on advanced energy harvesting technologies have been under rapid development, which facilitate autonomous operation and energy-efficient transmission. Recently, ambient backscattering that leverages existing RF signal resources in the air has been invented to empower data communication among low-power devices. In this paper, we introduce hybrid device-to-device (D2D) communications by integrating ambient backscattering and wireless-powered communications. The hybrid D2D communications are self-sustainable, as no dedicated external power supply is required. However, since the radio signals for energy harvesting and backscattering come from external RF sources, the performance of the hybrid D2D communications needs to be optimized efficiently. As such, we design two mode selection protocols for the hybrid D2D transmitter, allowing a more flexible adaptation to the environment. We then introduce analytical models to characterize the impacts of the considered environment factors, e.g., distribution, spatial density, and transmission load of the ambient transmitters, on the hybrid D2D communications performance. Extensive simulations show that the repulsion factor among the ambient transmitters has a non-trivial impact on the communication performance. Additionally, we reveal how different mode selection protocols affect the performance metrics.

### Self-Dual Codes better than the Gilbert--Varshamov bound. (arXiv:1709.07221v1 [cs.IT])

We show that every self-orthogonal code over $\mathbb F_q$ of length $n$ can be extended to a self-dual code, if there exists self-dual codes of length $n$. Using a family of Galois towers of algebraic function fields we show that over any nonprime field $\mathbb F_q$, with $q\geq 64$, except possibly $q=125$, there are self-dual codes better than the asymptotic Gilbert--Varshamov bound.

### On Composite Quantum Hypothesis Testing. (arXiv:1709.07268v1 [quant-ph])

We extend quantum Stein's lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states $\rho^{\otimes n}$ against convex combinations of quantum states $\sigma^{\otimes n}$ is given by a regularized quantum relative entropy distance formula. We prove that in general such a regularization is needed but also discuss various settings where our formula as well as extensions thereof become single-letter. This includes a novel operational interpretation of the relative entropy of coherence in terms of hypothesis testing. For our proof, we start from the composite Stein's lemma for classical probability distributions and lift the result to the non-commutative setting by only using elementary properties of quantum entropy. Finally, our findings also imply an improved Markov type lower bound on the quantum conditional mutual information in terms of the regularized quantum relative entropy - featuring an explicit and universal recovery map.

### Hybrid Beamforming Based on Implicit Channel State Information for Millimeter Wave Links. (arXiv:1709.07273v1 [cs.IT])

Hybrid beamforming provides a promising solution to achieve high data rate transmission at millimeter waves. To implement the hybrid beamforming at the transceiver, a common solution is to decouple the transmitter and receiver functions and then optimize them separately based on given channel state information. However, many references ignore the complexity of the high-dimensional channel estimation problem or the effort for the subsequent step of computing the singular value decomposition of a large channel matrix. To this end, we present a low-complexity scheme that exploits implicit channel knowledge to facilitate the design of hybrid beamforming for frequency-selective fading channels. The implicit channel knowledge can be interpreted as a coupling of the channel and all pairs of possible analog beamforming vectors at the transmitter and receiver, and it is obtained by receiving the transmitted pilots. Based on the received pilots, different effective channel matrices are constructed in the sense that the matrix elements are essentially the coupling coefficients. Instead of calculating mutual information, we use the Frobenius norm of the effective channel as a key parameter of the hybrid beamforming gain. As a result, the complicated hybrid beamforming problem becomes a much simpler one: it amounts to trying different sets of the large-power received pilots to construct multiple alternatives for the effective channel matrix. Then, the set yielding the largest Frobenius norm provides the solution to the hybrid beamforming problem.

### Secure Energy Efficiency Optimization for MISO Cognitive Radio Network with Energy Harvesting. (arXiv:1709.07278v1 [cs.IT])

This paper investigates a secure energy efficiency (SEE) optimization problem in a multiple-input single-output (MISO) underlay cognitive radio (CR) network. In particular, a multi-antenna secondary transmitter (SU-Tx) simultaneously sends secured information and energy to a secondary receiver (SU-Rx) and an energy receiver (ER), respectively, in the presence of a primary receiver (PU-Rx). It is assumed that the SU-Rx, ER and PU-Rx are each equipped with a single antenna. In addition, the SU-Tx should satisfy constraints on maximum interference leakage to the PU-Rx and minimum harvested energy at the ER. In this CR network, we consider the transmit covariance matrix design with the assumption of perfect channel state information (CSI) at the SU-Tx. In addition, it is assumed that the ER is a potential passive eavesdropper due to broadcast nature of wireless transmission. On the other hand, we consider the worst-case scenario that ER's energy harvesting requirement is only satisfied when it performs only energy harvesting without intercepting or eavesdropping information intended for the SU-Rx. We formulate this transmit covariance matrix design as a SEE maximization problem which is a non-convex problem due the non-linear fractional objective function. To realize the solution for this non-convex problem, we utilize the non-linear fractional programming and difference of concave (DC) functions approaches to reformulate into a tractable form. Based on these techniques and the Dinkelbach's method, we propose iterative algorithms to determine the solution for the original SEE maximization problem. Numerical simulation results are provided to demonstrate the performance of the proposed transmit covariance matrix design and convergence of the proposed algorithms.

### Extended-Alphabet Finite-Context Models. (arXiv:1709.07346v1 [cs.IT])

The Normalized Relative Compression is a recent dissimilarity metric, related to the Kolmogorov Complexity. It has been successfully used in different applications, like DNA sequences, images or even ECG (electrocardiographic) signal. It uses a reference based compressor to represent a string and compresses a target string using that reference. One possible approach is to use finite-context models (\textrm{FCM}s) to represent the strings.

A finite-context model (\textrm{FCM}) calculates the probability distribution of the next symbol, given the previous $k$ symbols. In this paper, we introduce a generalization of the \textrm{FCM}s, called extended finite-context models (\textrm{xaFCM}), that calculate the probability of occurrence of the next $d$ symbols, given the previous $k$ symbols.

As a testbed application, we show the results for performing ECG biometric identification, using an ECG database previously used in other studies for ECG biometric identification. The results show that often \textrm{xaFCM}s outperform \textrm{FCM}s in accuracy ratios, using less memory, to represent the models, and less computational time.

### ComSens: Exploiting Pilot Diversity for Pervasive Integration of Communication and Sensing in MIMO-TDD-Frameworks. (arXiv:1709.07407v1 [cs.IT])

In this paper, we propose a fully-integrated radar and communication system -- named ComSens. We utilize two different pilot sequences (one for uplink and one for downlink) with the condition that they must be uncorrelated to each other. Within such a framework, the signal received from end-user and the back-scattered signal from the desired objects have uncorrelated pilots. Thus, the base-station is able to distinguish data signal from user and back-scattered signal from object. We assume a time division duplex (TDD) framework. The pilot sequences are designed for MIMO channels. We evaluate channel MSE as a figure of merit for communication system. We also show that the designed pilots are uncorrelated for a range of time lags. Moreover, designed uplink pilot has negligible autocorrelation for a range of time lags leading to an impulse-like autocorrelation for radar sensing.

### Barriers to Integration: Physical Boundaries and the Spatial Structure of Residential Segregation. (arXiv:1509.02574v3 [physics.soc-ph] UPDATED)

Despite modest declines in residential segregation levels since the Civil Rights Era, segregation remains a defining feature of the U.S. landscape. This study highlights the importance of considering physical barriers--features of the urban environment that disconnect locations--when measuring segregation. We use population and geographic data for 20 U.S. Rustbelt cities from the 2010 decennial census and a novel approach for measuring and analyzing segregation that incorporates the connectivity of roads and the excess distance imposed by physical barriers, such as highways, railroad tracks, and dead-end streets. We find that physical barriers divide urban space in ways that reinforce or exacerbate segregation, but there is substantial variation in the extent to which they increase segregation both within and across these cities and for different ethnoracial groups. By uncovering a new source of variation in the segregation experienced by city residents, the findings have implications for understanding the mechanisms that contribute to the persistence of segregation and the consequences of segregation.

### Wireless Information and Power Transfer: Nonlinearity, Waveform Design and Rate-Energy Tradeoff. (arXiv:1607.05602v3 [cs.IT] UPDATED)

The design of Wireless Information and Power Transfer (WIPT) has so far relied on an oversimplified and inaccurate linear model of the energy harvester. In this paper, we depart from this linear model and design WIPT considering the rectifier nonlinearity. We develop a tractable model of the rectifier nonlinearity that is flexible enough to cope with general multicarrier modulated input waveforms. Leveraging that model, we motivate and introduce a novel WIPT architecture relying on the superposition of multi-carrier unmodulated and modulated waveforms at the transmitter. The superposed WIPT waveforms are optimized as a function of the channel state information so as to characterize the rate-energy region of the whole system. Analysis and numerical results illustrate the performance of the derived waveforms and WIPT architecture and highlight that nonlinearity radically changes the design of WIPT. We make key and refreshing observations. First, analysis (confirmed by circuit simulations) shows that modulated and unmodulated waveforms are not equally suitable for wireless power delivery, namely modulation being beneficial in single-carrier transmissions but detrimental in multi-carrier transmissions. Second, a multicarrier unmodulated waveform (superposed to a multi-carrier modulated waveform) is useful to enlarge the rate-energy region of WIPT. Third, a combination of power splitting and time sharing is in general the best strategy. Fourth, a non-zero mean Gaussian input distribution outperforms the conventional capacity-achieving zero-mean Gaussian input distribution in multi-carrier transmissions. Fifth, the rectifier nonlinearity is beneficial to system performance and is essential to efficient WIPT design.

### A Constituent Codes Oriented Code Construction Scheme for Polar Code-Aim to Reduce the Decoding Latency. (arXiv:1612.02545v3 [cs.IT] UPDATED)

This paper proposes a polar code construction scheme that reduces constituent-code supplemented decoding latency. Constituent codes are the sub-codewords with specific patterns. They are used to accelerate the successive cancellation decoding process of polar code without any performance degradation. We modify the traditional construction approach to yield increased number of desirable constituent codes that speeds the decoding process. For (n,k) polar code, instead of directly setting the k best and (n-k) worst bits to the information bits and frozen bits, respectively, we swap the locations of some information and frozen bits carefully according to the qualities of their equivalent channels. We conducted the simulation of 1024 and 2048 bits length polar codes with multiple rates and analyzed the decoding latency for various length codes. The numerical results show that the proposed construction scheme generally is able to achieve at least around 20% latency deduction with an negligible loss in gain with carefully selected optimization threshold.

### Signaling on the Continuous Spectrum of Nonlinear Optical fiber. (arXiv:1704.05537v2 [cs.IT] UPDATED)

This paper studies different signaling techniques on the continuous spectrum (CS) of nonlinear optical fiber defined by nonlinear Fourier transform. Three different signaling techniques are proposed and analyzed based on the statistics of the noise added to CS after propagation along the nonlinear optical fiber. The proposed methods are compared in terms of error performance, distance reach, and complexity. Furthermore, the effect of chromatic dispersion on the data rate and noise in nonlinear spectral domain is investigated. It is demonstrated that, for a given sequence of CS symbols, an optimal bandwidth (or symbol rate) can be determined so that the temporal duration of the propagated signal at the end of the fiber is minimized. In effect, the required guard interval between the subsequently transmitted data packets in time is minimized and the effective data rate is significantly enhanced. Moreover, by selecting the proper signaling method and design criteria a reach distance of 7100 km is reported by only singling on the CS at a rate of 9.6 Gbps.

### Cooperative Network Synchronization: Asymptotic Analysis. (arXiv:1709.05476v2 [cs.IT] UPDATED)

Accurate clock synchronization is required for collaborative operations among nodes across wireless networks. Compared with traditional layer-by-layer methods, cooperative network synchronization techniques lead to significant improvement in performance, efficiency, and robustness. This paper develops a framework for the performance analysis of cooperative network synchronization. We introduce the concepts of cooperative dilution intensity (CDI) and relative CDI to characterize the interaction between agents, which can be interpreted as properties of a random walk over the network. Our approach enables us to derive closed-form asymptotic expressions of performance limits, relating them to the quality of observations as well as network topology.

### MacWilliams' extension theorem for infinite rings. (arXiv:1709.06070v2 [math.RA] UPDATED)

Finite Frobenius rings have been characterized as precisely those finite rings satisfying the MacWilliams extension property, by work of Wood. In the present note we offer a generalization of this remarkable result to the realm of Artinian rings. Namely, we prove that a left Artinian ring has the left MacWilliams property if and only if it is left pseudo-injective and its finitary left socle embeds into the semisimple quotient. Providing a topological perspective on the MacWilliams property, we also show that the finitary left socle of a left Artinian ring embeds into the semisimple quotient if and only if it admits a finitarily left torsion-free character, if and only if the Pontryagin dual of the regular left module is almost monothetic. In conclusion, an Artinian ring has the MacWilliams property if and only if it is finitarily Frobenius, i.e., it is quasi-Frobenius and its finitary socle embeds into the semisimple quotient.

### Achievable Rates for Probabilistic Shaping. (arXiv:1707.01134v3 [cs.IT] UPDATED)

For a layered probabilistic shaping (PS) scheme with a general decoding metric, an achievable rate is derived using Gallager's error exponent approach and the concept of achievable code rates is introduced. Several instances for specific decoding metrics are discussed, including bit-metric decoding, interleaved coded modulation, and hard-decision decoding. It is shown that important previously known achievable rates can also be achieved by layered PS. A practical instance of layered PS is the recently proposed probabilistic amplitude shaping (PAS).

### On Collaborative Compressive Sensing Systems: The Framework, Design and Algorithm. (arXiv:1709.06616v1 [cs.IT])

We propose a collaborative compressive sensing (CCS) framework consisting of a bank of $K$ compressive sensing (CS) systems that share the same sensing matrix but have different sparsifying dictionaries. This CCS system is guaranteed to yield better performance than each individual CS system in a statistical sense, while with the parallel computing strategy, it requires the same time as that needed for each individual CS system to conduct compression and signal recovery. We then provide an approach to designing optimal CCS systems by utilizing a measure that involves both the sensing matrix and dictionaries and hence allows us to simultaneously optimize the sensing matrix and all the $K$ dictionaries under the same scheme. An alternating minimization-based algorithm is derived for solving the corresponding optimal design problem. We provide a rigorous convergence analysis to show that the proposed algorithm is convergent. Experiments with real images are carried out and show that the proposed CCS system significantly improves on existing CS systems in terms of the signal recovery accuracy.

### Secure Beamforming in Full-Duplex SWIPT Systems. (arXiv:1709.06623v1 [cs.IT])

Physical layer security is a key issue in the full duplex (FD) communication systems due to the broadcast nature of wireless channels. In this paper, the joint design of information and artificial noise beamforming vectors is proposed for the FD simultaneous wireless information and power transferring (FD-SWIPT) systems. To guarantee high security and energy harvesting performance of the FD-SWIPT system, the proposed design is formulated as a sum information transmission rate (SITR) maximization problem under information-leakage and energy constraints. In addition, we consider the fairness issue between the uplink and downlink information transmission rates by formulating a \mbox{fairness-aware} SITR-maximization problem. Although the formulated \mbox{SITR-maximization} and \mbox{fairness-aware} \mbox{SITR-maximization} problems are non-convex, we solve them via semidefinite relaxation and one-dimensional search. The optimality of our proposed algorithms is theoretically proved, and the computation complexities are established. Moreover, we propose two suboptimal solutions to the formulated optimization problems. In terms of the SITR-maximization problem, numerical results show that the performance achieved by one of the two suboptimal algorithms is close to the performance of the optimal algorithm with increasing maximum transmission power of the FD-BST.

### Dynamic Cross-Layer Beamforming in Hybrid Powered Communication Systems With Harvest-Use-Trade Strategy. (arXiv:1709.06625v1 [cs.IT])

The application of renewable energy is a promising solution to realize the Green Communications. However, if the cellular systems are solely powered by the renewable energy, the weather dependence of the renewable energy arrival makes the systems unstable. On the other hand, the proliferation of the smart grid facilitates the loads with two-way energy trading capability. Hence, a hybrid powered cellular system, which combines the smart grid with the base stations, can reduce the grid energy expenditure and improve the utilization efficiency of the renewable energy. In this paper, the long-term grid energy expenditure minimization problem is formulated as a stochastic optimization model. By leveraging the stochastic optimization theory, we reformulate the stochastic optimization problem as a \mbox{per-frame} grid energy plus weighted penalized packet rate minimization problem, which is NP-hard. As a result, two suboptimal algorithms, which jointly consider the effects of the channel quality and the packet reception failure, are proposed based on the successive approximation beamforming (SABF) technique and the \mbox{zero-forcing} beamforming (ZFBF) technique. The convergence properties of the proposed suboptimal algorithms are established, and the corresponding computational complexities are analyzed. Simulation results show that the proposed SABF algorithm outperforms the ZFBF algorithm in both grid energy expenditure and packet delay. By tuning a control parameter, the grid energy expenditure can be traded for the packet delay under the proposed stochastic optimization model.

### Construction C*: an improved version of Construction C. (arXiv:1709.06640v1 [cs.IT])

Besides all the attention given to lattice contructions, it is common to find some very interesting nonlattice constellations, as Construction C, for example, which also has relevant applications in communication problems (multi-stage decoding, good quantization efficieny). In this work we present a generalization of Construction C, based on inter-level coding, which we call Construction C*. The generalized construction has better immunity to noise and also provides a simple way of describing the Leech lattice. We give necessary and sufficient condition under which Construction C* is a lattice constellation.