This paper investigates two distinct types of block errors - undetected errors (confusions) and erasures - in additive white Gaussian noise (AWGN) channels with error-bounded block decoders operating in the finite blocklength (FBL) regime. While block error rate (BLER) is a common metric, it does not distinguish between confusions and erasures, which can have significantly different impacts in cross-layer protocol design, despite upper-layer protocols universally assuming physical (PHY) errors manifest as packet erasures rather than undetected corruptions - an assumption lacking rigorous PHY-layer validation. We present a systematic analysis of confusions and erasures under BLER-constrained maximum likelihood (ML) decoding. Through sphere-packing analysis, we provide analytical bounds for both block confusion and erasure probabilities, and derive the sensitivities of these bounds to blocklength and signal-to-noise ratio (SNR). To the best of our knowledge, this is the first study on this topic in the FBL regime. Our findings provide theoretical validation for the block erasure channel abstraction commonly assumed in medium access control (MAC) and network layer protocols, confirming that, for practical FBL codes, block confusions are negligible compared to block erasures, especially at large blocklengths and high SNR.

This paper presents a novel framework for enhancing the security, data rate, and sensing performance of integrated sensing and communications (ISAC) systems. We employ a random frequency and pulse repetition interval (PRI) agility (RFPA) method for the waveform design, where the necessary random sequences are governed by shared secrets. These secrets, which can be pre-shared or generated via channel reciprocity, obfuscate critical radar parameters like Doppler frequency and pulse start times, thereby significantly impeding the ability to perform reconnaissance from a passive adversary without the secret key. To further introduce enhanced data throughput, we also introduce a hybrid information embedding scheme that integrates amplitude shift keying (ASK), phase shift keying (PSK), index modulation (IM), and spatial modulation (SM), for which a low-complexity sparse-matched filter receiver is proposed for accurate decoding with practical complexity. Finally, the excellent range-velocity resolution and clutter suppression of the proposed waveform are analyzed via the ambiguity function (AF).

Semantic communication has emerged as a promising paradigm to address the challenges of next-generation communication networks. While some progress has been made in its conceptualization, fundamental questions remain unresolved. In this paper, we propose a probabilistic model for semantic communication that, unlike prior works primarily rooted in intuitions from human language, is grounded in a rigorous philosophical conception of information and its relationship with data as Constraining Affordances, mediated by Levels of Abstraction (LoA). This foundation not only enables the modeling of linguistic semantic communication but also provides a domain-independent definition of semantic content, extending its applicability beyond linguistic contexts. As the semantic communication problem involves a complex interplay of various factors, making it difficult to tackle in its entirety, we propose to orthogonalize it by classifying it into simpler sub-problems and approach the general problem step by step. Notably, we show that Shannon's framework constitutes a special case of semantic communication, in which each message conveys a single, unambiguous meaning. Consequently, the capacity in Shannon's model-defined as the maximum rate of reliably transmissible messages-coincides with the semantic capacity under this constrained scenario. In this paper, we specifically focus on the sub-problem where semantic ambiguity arises solely from physical channel noise and derive a lower bound for its semantic capacity, which reduces to Shannon's capacity in the corresponding special case. We also demonstrate that the achievable rate of all transmissible messages for reliable semantic communication, exceeds Shannon's capacity by the added term H(X|S).

We introduce a comprehensive approach to enhance the security, privacy, and sensing capabilities of integrated sensing and communications (ISAC) systems by leveraging random frequency agility (RFA) and random pulse repetition interval agility (RPA) techniques. The combination of these techniques, which we collectively refer to as random frequency and pulse repetition interval agility (RFPA), with channel reciprocity-based key generation (CRKG) obfuscates both Doppler frequency and pulse repetition intervals (PRIs), significantly hindering passive adversaries’ ability to estimate radar parameters. In addition, a hybrid information embedding method integrating amplitude shift keying (ASK), phase shift keying (PSK), index modulation (IM), and spatial modulation (SM) is incorporated to significantly increase the system’s achievable bit rate. Next, a sparse-matched filter receiver design is proposed to efficiently decode the embedded information with a low bit error rate (BER). Finally, a novel RFPA-based secret generation scheme using CRKG enables secure code creation without a coordinating authority. The improved range and velocity estimation, and the reduced clutter effects achieved by the method, are demonstrated through the evaluation of the ambiguity function (AF) of the proposed waveforms.

In this paper, we investigate the pertinence of the angle of arrival (AoA) as a feature for robust physical layer authentication (PLA). While most of the existing approaches to PLA focus on amplitude-dependent features of the physical layer of communication channels, such as channel frequency response, channel impulse response, or received signal strength, the use of AoA in this domain has not yet been studied in depth, particularly regarding the ability to thwart spoofing (impersonation) attacks. In this work, we demonstrate that an impersonation attack targeting AoA-based PLA is only feasible under strict conditions on the attackers location, which highlights the AoA’s role as a strong feature for unspoofable PLA, especially when 2D AoA is employed.We extend previous works considering a single-antenna attacker to the case of a multiple-antenna attacker, and we develop a theoretical characterization of the conditions under which a successful impersonation attack can be mounted. Furthermore, we have performed extensive simulations in support of theoretical analyses, to validate the robustness of AoA-based PLA.

This work addresses the problem of integrated sensing and communications (ISAC) involving a massive number of unsourced and uncoordinated users. In the proposed model, known as the unsourced ISAC system (UNISAC), all active communication and sensing users simultaneously share a short frame to transmit their signals without requiring scheduling by the base station or the need to announce their identities. Consequently, the received signal from each user is heavily affected by interference from numerous other users, making it challenging to extract individual transmissions. UNISAC is designed to decode the message sequences from communication users while simultaneously detecting active sensing users and estimating their angles of arrival, regardless of the senders’ identities. We establish a second-order achievable bound for UNISAC that explicitly quantifies performance deviations due to finite resources, and we show that it outperforms ISAC approaches built on traditional multiple access methods, including ALOHA, time-division multiple access (TDMA), treating interference as noise (TIN), and a TDMA-based scheme combined with multiple signal classification for sensing. Additionally, we propose a practical model that validates the feasibility of the achievable result, showing comparable or even superior performance in scenarios with a small number of users. Through numerical simulations, we demonstrate the effectiveness of both the practical UNISAC model and the achievable result.

Recent studies have explored the synergy between reconfigurable intelligent surfaces (RIS) and multiple-input multiple-output (MIMO) systems to overcome limitations in spectral efficiency and coverage. While RIS-aided MIMO systems promise transformative gains, their real-world deployment faces critical challenges rooted in hardware imperfections, in particular, the nonlinearity of power amplifiers (PAs) in the MIMO transmitters. To bridge this gap, this paper investigates a holistic design that jointly optimizes RIS phase shifts and base station transmit precoder for the RIS-aided MIMO systems with a practical PA model in real life. We propose a hardware-aware joint design framework that co-optimizes the base station precoder and RIS phase shifts to balance beamforming gain with PA distortion suppression. A closed-form solution for the optimal RIS phase-shifting matrix is derived as a function of the precoder, reducing the joint optimization to an equivalent precoder optimization problem. A low-complexity successive convex approximation-based algorithm is developed for efficient precoder design. Simulations demonstrate that the proposed method achieves up to 30.6% spectral efficiency improvement over benchmarks under PA nonlinearity, highlighting its practical significance in RIS-aided systems.

We consider a superdense coding based quantum communication system utilizing entangled qubits. These qubits are added to and retrieved from a pool of available entangled qubits. In this work, we examine the reliability of such a system with respect to probability of depletion of the entangled qubit budget. Furthermore, we analyze the latency ahead of resuming transmission. Our model and analysis includes specific effects, such as quantum decoherence. Additionally, we compare different approaches for transmission after exhaustion of the entangled qubit budget. Since reliability and latency are essential metrics for quantum communication systems, joint analysis of these in relation to the system parameters is of significant interest. The results presented in this work will help guide quantum communication system designers in making modifications to meet reliability and latency specifications.

This paper studies the capacity of fast-fading channels from an algorithmic perspective, examining whether the channel capacity can be computed algorithmically or not. To address this question, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that certain computable continuous fading probability distribution functions yield capacities that are non-computable. Furthermore, the implications of this non-computability in information theory and coding are discussed, particularly the impossibility of designing universal algorithms that, given the fast-fading channel parameters and a predefined decoding error$\epsilon$, can compute codes operating at the maximum rate with a decoding error probability no higher than$\epsilon$.

As we advance towards 6G networks, the concept of ultra-reliability takes center stage. For ensuring ultra-reliabile communication the outage requirement is crucial. In this paper, the outage capacity of slow fading channels with additive white Gaussian noise is studied from a fundamental algorithmic point of view by addressing the question of whether or not the outage capacity can be algorithmically computed. For this purpose, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that there are fading channels having a computable continuous and differentiable probability density function whose outage capacity yields a non-computable number. Moreover, it is demonstrated that for these channels, it is impossible to algorithmically determine the minimum blocklength for transmission codes needed to operate at a certain precision relative to their outage capacity.

In this paper, we focus on the nonlinear distortion in a massive MIMO system with nonlinear power amplifiers. It is known that the distortion generated by nonlinear power amplifiers is beamformed in the line-of-sight (LoS) channel. In particular, spurious emissions are caused by beamformed intermodulation (IM) distortion and form as IM beams. We propose a precoder for IM beam suppression in the MIMO system, which aims to suppress the intermodulation beams while maintaining beamforming for the intended receivers. First, we derive the direction of the IM beams under the free-space LoS channel condition. Then, the intermodulation suppression (IMS) precoder is proposed by maximizing the signal-to-leakage ratio. Moreover, we propose a generalized IMS precoder to achieve the trade-off between the intended signal coherent combination and IM beam suppression. Adjusting the weights of the precoder can suppress the IM beams while ensuring a coherent combination of signals at intended receivers. Simulation results show that the proposed IMS precoder can suppress the IM beams and reduce the power leakage in spurious directions. The power gain obtained by the proposed IMS precoder can approach to the maximum ratio transmission while achieving substantial suppression gain for the IM beams.

This paper studies the computability of the secrecy capacity of fast-fading wiretap channels from an algorithmic perspective, examining whether it can be computed algorithmically. To address this question, the concept of Turing machines is used, providing the fundamental performance limits of digital computers. It is shown that certain computable continuous fading probability distribution functions yield secrecy capacities that are non-computable numbers. Additionally, we assess the secrecy capacity's classification within the arithmetic hierarchy, revealing absence of computable achievability and converse bounds.

The wiretap channel is a well-studied problem in the physical layer security literature. Although it is proven that the decoding error probability and information leakage can be made arbitrarily small in the asymptotic regime, further research on finite-blocklength codes is required on the path towards practical, secure communication systems. This work provides the first experimental characterization of a deep learning-based, finite-blocklength code construction for multi-tap fading wiretap channels without channel state information. In addition to the evaluation of the average probability of error and information leakage, we examine the designed codes in the presence of fading in terms of the equivocation rate and illustrate the influence of (i) the number of fading taps, (ii) differing variances of the fading coefficients, and (iii) the seed selection for the hash function-based security layer.

In this paper, we study the performance of a practical secret key generation method under low-mobility scenarios. Instead of relying on traditional cryptographic methods or leveraging spatial diversity and reconfigurable intelligent surfaces to increase channel variations, we utilize locally generated pilots to add randomness to the system, thus in turn helping to increase the secret key rate. The results demonstrate significant improvements over the original channels, whose entropy source mainly relies on mobility and channel variations. More importantly, this scheme works well without extra helpers or multiple antennas, thus providing a potential for developing reliable, lightweight security solutions for resource-constrained devices in practice.

Resilience and power consumption are two important performance metrics for many modern communication systems, and it is therefore important to define, analyze, and optimize them. In this work, we consider a wireless communication system with secret-key generation, in which the secret-key bits are added to and used from a pool of available key bits. We propose novel physical layer resilience metrics for the survivability of such systems. In addition, we propose multiple power allocation schemes and analyze their trade-off between resilience and power consumption. In particular, we investigate and compare constant power allocation, an adaptive analytical algorithm, and a reinforcement learning-based solution. It is shown how the transmit power can be minimized such that a specified resilience is guaranteed. These results can be used directly by designers of such systems to optimize the system parameters for the desired performance in terms of reliability, security, and resilience.

Designing capacity-achieving coding schemes for the band-limited additive colored Gaussian noise (ACGN) channel has been and is still a challenge. In this paper, the capacity of the band-limited ACGN channel is studied from a fundamental algorithmic point of view by addressing the question of whether or not the capacity can be algorithmically computed. To this aim, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that there are band-limited ACGN channels having computable continuous spectral densities whose capacity are non-computable numbers. Moreover, it is demonstrated that for those channels, it is impossible to find computable sequences of asymptotically sharp upper bounds for their capacities. Furthermore, the implications of the non-computability of the ACGN channel capacity in information theory and coding are discussed, particularly regarding the impossibility of computing achievable rates in the finite blocklength regime and the challenges of finding universal algorithms that compute capacity-achieving power spectral densities for the ACGN channel.

This work considers the problem of integrated sensing and communications (ISAC) with a massive number of unsourced and uncoordinated users. In the proposed model, known as the unsourced ISAC system (UNISAC), all active communication and sensing users simultaneously share a short frame to transmit their signals, without requiring scheduling with the base station (BS). Hence, the signal received from each user is affected by significant interference from numerous interfering users, making it challenging to extract the transmitted signals. UNISAC aims to decode the transmitted message sequences from communication users while simultaneously detecting active sensing users and estimating their angles of arrival, regardless of the identity of the senders. In this paper, we derive an approximate achievable result for UNISAC and demonstrate its superiority over conventional approaches such as ALOHA, time-division multiple access, treating interference as noise, and multiple signal classification. Through numerical simulations, we validate the effectiveness of UNISAC’s sensing and communication capabilities for a large number of users.

In this paper, we investigate the secret key generation (SKG) for static scenarios utilizing the pilot randomization method. In fact, the majority have studied SKG under dynamic scenarios in which a high secret key rate is achievable due to sufficiently high randomness. In this study, we instead consider the static scenario which, though important, is not well-studied. More specifically, we utilize the pilot randomization method, which is known to prevent injection attacks effectively, to randomize the associated channels. More importantly, we derive the secret key rate of the system and demonstrate that the secret key rate of a static system can increase significantly due to the added randomness. The proposed approach is demonstrated against known methods to show its effectiveness in increasing the secret key rate in static environments.

This paper considers an information theoretic model for secure integrated sensing and communication (ISAC) with the goal of establishing fundamental limits in low-latency scenarios. In this secure ISAC model, a message is transmitted through a state-dependent wiretap channel with decoder-side state availability. The model is studied under a strong secrecy constraint when only a part of the transmitted message should be kept secret. First, the secrecy-distortion rate region is established for a degraded channel by treating the model as a special case of a feed-backed secure ISAC model. Finite-length inner bounds are then proved by applying nonasymptotic random binning techniques. Bounds on the rates have a similar form to common finite-length bounds, and the distortion bound follows from a bound for letter-typical sequences.

We consider a wireless communication system with a passive eavesdropper, in which a transmitter and legitimate receiver generate and use key bits to secure the transmission of their data. These bits are added to and used from a pool of available key bits. In this work, we analyze the reliability of the system in terms of the probability that the budget of available key bits will be exhausted. In addition, we investigate the latency before a transmission can take place. Since security, reliability, and latency are three important metrics for modern communication systems, it is of great interest to jointly analyze them in relation to the system parameters. The results presented in this work will allow system designers to adjust the system parameters in such a way that the requirements of the application in terms of both reliability and latency are met.

This paper examines the computability of optimal power allocation strategies for utility maximization and maxmin fairness. It is demonstrated that a computable constraint power function exists. However, when both total and individual power constraints are taken into account, it is determined that the optimal power allocation for maximizing network utility is not computable since every single power value is a non-computable number. Furthermore, it is established that within the same constraint context, both the max-min fairness level and its corresponding power values are non-computable numbers.

This paper investigates the computational complexity involved in determining the capacity of the band-limited additive colored Gaussian noise (ACGN) channel and its capacity-achieving input power spectral density (p.s.d.). A band-limited polynomial time computable continuous and strictly positive noise p.s.d. is constructed for the ACGN channel such that the computation of its corresponding capacity is$\# \mathrm{P}_{1}$-complete. This means that it is even more complex than problems that are$\text{NP}_{1}$-complete. Additionally, it is shown that computing the capacity-achieving input p.s.d. is also$\# \mathrm{P}_{1}$-complete. Furthermore, under the widely accepted assumption that$\text{FP}_{1}\neq\# \mathrm{P}_{1}$, there are two significant implications for the ACGN channel. First, there exists a polynomial time computable noise p.s.d. for which computing its capacity is not polynomial-time feasible, meaning the number of computational steps on a Turing Machine grows faster than any polynomial. Second, there is a polynomial time computable noise p.s.d. where determining its capacity-achieving input p.s.d. is also not achievable in polynomial time.

Training neural encoders requires a differentiable channel model for backpropagation. This can be bypassed by approximating the channel distribution using pilot signals. A common method for this is the use of generative adversarial networks (GANs). In this paper, we introduce diffusion models (DMs) for channel generation and propose an efficient training algorithm. Our DMs provide a solution that achieves near-optimal end-to-end symbol error rates (SERs). Importantly, DMs outperform GANs in high signal-to-noise ratio regions. Here, in particular, we explore the trade-off between sample quality and speed. We also show that the right noise scheduling can significantly reduce sampling time with a minor increase in SER.

Integrated sensing and communications (ISAC) is envisioned to be a key to advanced applications in future wireless networks. In this paper, we study the coded modulation designs for ISAC transmissions with short block lengths over correlated Rayleigh fading channels. In line with the short block length transmission, we consider the non-coherent communication detection and coherent radar sensing, where a neural network (NN)-assisted frame-wise constellation design is proposed. Specifically, we first derive the optimal communication and radar receivers. Then, we present some heuristic understandings of the code designs by considering special cases, based on which a conjecture on the optimal codes for the considered ISAC transmissions is developed. The constellation obtained from the proposed NN agrees with our conjecture and shows an important conclusion that the optimal codes of the considered problem may be a combination of the “on-off keying” and phase-shifted keying signalings. Our numerical results show that the proposed code exhibits promising communication and sensing performance simultaneously and outperforms the transmissions with a standard channel code and symbol-wise modulation.

This paper explores the computability of the optimal point in convex problems with inequality constraints. It is shown that feasible sets, defined by computable convex functions, can yield non-computable optimal points for strictly convex and computable objective functions. Additionally, the optimal point of the Lagrangian dual problem associated with such convex constraints is also proven to be non-computable. Despite converging sequences of computable numbers towards the Lagrangian's optimal point, algorithmic control of the approximation error is shown to be impossible.

Resilience and power consumption are important performance metrics for many modern communication systems, and it is therefore important to define, analyze, and optimize them. In this work, we consider a wireless communication system with secret-key generation, in which the secret-key bits are added to and used from a pool of available key bits. We propose novel resilience metrics for the survivability of such a system and analyze them. In addition, we investigate the problem of minimizing the transmit power such that a specified resilience is guaranteed. These results can be used directly by designers of such systems to optimize the system parameters for the desired performance in terms of reliability and resilience.

We consider a wireless communication system with a passive eavesdropper, in which a transmitter and legitimate receiver generate and use key bits to secure the transmission of their data. These bits are added to and used from a pool of available key bits. In this work, we analyze the reliability of the system in terms of the probability that the budget of available key bits will be exhausted. In addition, we investigate the latency before a transmission can take place. Since security, reliability, and latency are three important metrics for modern communication systems, it is of great interest to jointly analyze them in relation to the system parameters. In particular, we show under what conditions the system may remain in an active state indefinitely, i.e., never run out of available secret-key bits. The results presented in this work will allow system designers to adjust the system parameters in such a way that the requirements of the application in terms of both reliability and latency are met.

This paper explores the computational complexity involved in determining the capacity of the band-limited additive colored Gaussian noise (ACGN) channel and its capacity-achieving power spectral density (p.s.d.). The study reveals that when the noise p.s.d. is a strictly positive computable continuous function, computing the capacity of the band-limited ACGN channel becomes a #P1-complete problem within the set of polynomial time computable noise p.s.d.s. Meaning that it is even more complex than problems that are NP1-complete. Additionally, it is shown that computing the capacity-achieving distribution is also #P1-complete. Furthermore, under the widely accepted assumption that FP1≠ #P1, it has two significant implications for the ACGN channel. The first implication is the existence of a polynomial time computable noise p.s.d. for which the computation of its capacity cannot be performed in polynomial time, i.e., the number of computational steps on a Turing Machine grows faster than all polynomials. The second one is the existence of a polynomial time computable noise p.s.d. for which determining its capacity-achieving p.s.d. cannot be done within polynomial time. This implies that either the sequence of achievable rates with guaranteed distance to capacity is not polynomial time computable, or the corresponding blocklength sequence is not polynomial time computable.

The capacity of finite state channels (FSCs) with feedback has been expressed by a limit of a sequence of multi-letter expressions. Despite many efforts, a closed-form single-letter capacity characterization remains unknown to date. In this paper, the feedback capacity is studied from a fundamental algorithmic point of view by addressing the question of whether or not the capacity can be algorithmically computed. To this aim, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that the feedback capacity of FSCs is not Banach-Mazur computable and therefore also not Borel-Turing computable. It is further shown that it is even impossible to approximate the feedback capacity function of FSCs by a computable function. As a consequence, it is shown that computable achievability and converse can never be tight, which means that there are FSCs for which it is impossible to find computable tight upper and lower bounds. Furthermore, it is shown that the feedback capacity cannot be characterized as the maximization of a finite-letter formula of entropic quantities.

As we become more and more dependent on communication technologies, resilience against any attacks on communication networks is important to guarantee the digital sovereignty of our society. New developments of communication networks approach the problem of resilience through in-network computing approaches for higher protocol layers, while the physical layer remains an open problem. This is particularly true for wireless communication systems which are inherently vulnerable to adversarial attacks due to the open nature of the wireless medium. In denial-of-service (DoS) attacks, an active adversary is able to completely disrupt the communication and it has been shown that Turing machines are incapable of detecting such attacks. As Turing machines provide the fundamental limits of digital information processing and therewith of digital twins, this implies that even the most powerful digital twins that preserve all information of the physical network error-free are not capable of detecting such attacks. This stimulates the question of how powerful the information processing hardware must be to enable the detection of DoS attacks. Therefore, in this paper the need of neuromorphic twins is advocated and by the use of Blum-Shub-Smale machines a first implementation that enables the detection of DoS attacks is shown. This result holds for both cases of with and without constraints on the input and jamming sequences of the adversary.

Designing capacity-achieving coding schemes for the band-limited additive colored Gaussian noise (ACGN) channel has been and is still a challenge. In this paper, the capacity of the band-limited ACGN channel is studied from a fundamental algorithmic point of view by addressing the question of whether or not the capacity can be algorithmically computed. For this purpose, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that there are band-limited ACGN channels having a computable continuous spectral density whose capacity is a non-computable number. Moreover, it is demonstrated that for these channels, it is impossible to find a computable sequence of asymptotically sharp upper bounds for their capacity.

Data security is one of the key concerns in the next generation of ultra-reliable and low-latency networks, especially with machine-type communications. In this work, we propose a novel metric, leakage-failure probability, to represent the reliable-secure performance of the considered system. We discover that the system performance can be enhanced by counter-intuitively trading the reliability for security, i.e., allocating less blocklength in the short-packet transmission. In order to solve the corresponding blocklength allocation problem, we propose a novel optimization framework, for which a lower-bounded approximation of the decoding error probability in the finite blocklength regime is provided. Based on that, we reformulate the optimization problem into a convex one and propose an iterative searching method. We show the efficiency and the convergence of such a method analytically. Furthermore, we discuss the extendability of the proposed framework with an example of the effective secure throughput as the metric. Via numerical results, we verify the performance of the optimization problem and demonstrate the reliability-security tradeoff under various setups.

Small neural networks (NNs) used for error correction were shown to improve on classic channel codes and to address channel model changes. We extend the code dimension of any such structure by using the same NN under one-hot encoding multiple times, then serially-concatenated with an outer classic code. We design NNs with the same network parameters, where each Reed-Solomon codeword symbol is an input to a different NN. Significant improvements in block error probabilities for an additive Gaussian noise channel as compared to the small neural code are illustrated, as well as robustness to channel model changes.

It is widely believed that large IRS-aided MIMO settings maintain the fundamental features of massive MIMO systems. This work gives a rigorous proof that confirms this belief. We show that using a large passive IRS, the end-to-end MIMO channel between the transmitter and the receiver always hardens, even if the IRS elements are strongly correlated. For fading direct and reflection links between the transmitter and the receiver, our derivations demonstrate that for a large number of reflecting elements on the IRS, the capacity of the end-to-end channel is accurately approximated by a real-valued Gaussian random variable whose variance goes to zero as the number of IRS elements grows unboundedly large. The order of this drop depends on how the physical dimensions of the IRS grow. We derive this order explicitly. Numerical experiments show that the closed-form approximation very closely matches the histogram of the capacity term, even in practical scenarios. As a sample application of the results, we characterize the dimensional trade-off between the transmitter and the IRS. The result is intuitive: For a target performance, the larger the IRS is, the fewer transmit antennas are required.

How to provide information security while fulfilling ultra reliability and low-latency requirements is one of the major concerns for enabling the next generation of ultra-reliable and low-latency communications service (xURLLC), specially in machine-type communications. In this work, we investigate the reliability-security tradeoff by defining the leakage-failure probability, a metric that jointly characterizes both reliability and security performances for short-packet transmissions. We discover that the system performance can be enhanced, counter-intuitively, by allocating fewer resources for the transmission with finite blocklength (FBL) codes. In order to solve the corresponding optimization problem for the joint resource allocation, we propose an optimization framework, that leverages lower-bounded approximations for the decoding error probability in the FBL regime. We characterize the convexity of the reformulated problem and establish an efficient iterative searching method, the convergence of which is guaranteed. To show the extendability of the framework, we further discuss the blocklength allocation schemes with practical requirements of reliable-secure performance, as well as the transmissions with the statistical channel state information (CSI). Numerical results verify the accuracy of the proposed approach and demonstrate the reliability-security tradeoff under various setups.

The distributed source coding problem is extended by positing that noisy measurements of a remote source are the correlated random variables that should be reconstructed at another terminal. We consider a secure and private distributed lossy source coding problem with two encoders and one decoder such that (i) all terminals noncausally observe a noisy measurement of the remote source; (ii) a private key is available to each legitimate encoder and all private keys are available to the decoder; (iii) rate-limited noiseless communication links are available between each encoder and the decoder; (iv) the amount of information leakage to an eavesdropper about the correlated random variables is defined assecrecyleakage, andprivacyleakage is measured with respect to the remote source; and (v) two passive attack scenarios are considered, where a strong eavesdropper can access both communication links and a weak eavesdropper can choose only one of the links to access. Inner and outer bounds on the rate regions defined under secrecy, privacy, communication, and distortion constraints are derived for both passive attack scenarios. When one or both sources should be reconstructed reliably, the rate region bounds are simplified.

The capacity of a channel can usually be characterized as a maximization of certain entropic quantities. From a practical point of view it is of primary interest to not only compute the capacity value, but also to find the corresponding optimizer, i.e., the capacity-achieving input distribution. This paper addresses the general question of whether or not it is possible to find algorithms that can compute the optimal input distribution depending on the channel. For this purpose, the concept of Turing machines is used which provides the fundamental performance limits of digital computers and therewith fully specifies which tasks are algorithmically feasible in principle. It is shown for discrete memoryless channels that it is impossible to algorithmically compute the capacity-achieving input distribution, where the channel is given as an input to the algorithm (or Turing machine). Finally, it is further shown that it is even impossible to algorithmically approximate these input distributions.

Federated learning (FL) enables large-scale machine learning with user data privacy due to its decentralized structure. However, the user data can still be inferred via the shared model updates. To strengthen the privacy, we consider FL with local differential privacy (LDP). One of the challenges in FL is its huge communication cost caused by iterative transmissions of model updates. It has been relieved by quantization in the literature, however, there have been not many works that consider its effect on LDP and the unboundedness of the randomized model updates. We propose a communication-efficient FL algorithm with LDP that uses a Gaussian mechanism followed by quantization and the Elias-gamma coding. A novel design of the algorithm guarantees LDP even after the quantization. Under the proposed algorithm, we provide a trade-off analysis of privacy and communication costs theoretically: quantization reduces the communication costs but requires a larger perturbation to enable LDP. Experimental results show that the accuracy is mostly affected by the noise from LDP mechanisms, and it becomes enhanced when the quantization error is larger. Nonetheless, our experimental results enabled LDP with a significant compression ratio and only a slight reduction of accuracy in return. Furthermore, the proposed algorithm outperforms another algorithm with a discrete Gaussian mechanism under the same privacy budget and communication costs constraints in the experiments.

Trustworthiness verification and integrity testing have been identified as key challenges for the sixth generation (6G) of mobile networks and its variety of envisioned features. In this paper, these issues are addressed from a fundamental, algorithmic point of view. For this purpose, the concept of Turing machines is used which provides the fundamental performance limits of digital computers. It is shown that, in general, trustworthiness and integrity cannot be verified by Turing machines and therewith by today’s digital computers. In addition, the trustworthiness problem is further shown to be non-Banach-Mazur computable which is the weakest form of computability. Neuromorphic computing has an enormous potential to overcome the limitations of today’s digital hardware and, accordingly, it is interesting to study the issues of trustworthiness verification and integrity testing also for such powerful computing models. In particular, as considerable progress in the hardware design for neuromorphic computing has been achieved.

The capacity of a channel can usually be characterized as a maximization of certain entropic quantities. From a practical point of view it is of crucial interest to not only compute the capacity value, but also to find the corresponding optimizer, i.e., the capacity-achieving input distribution. This paper addresses the general question of whether or not it is possible to find algorithms that can compute the optimal input distribution depending on the channel. For this purpose, the concept of Turing machines is used which provides the fundamental performance limits of digital computers and therewith fully specifies which tasks are algorithmically feasible in principle. It is shown that it is impossible to algorithmically compute the capacity-achieving input distribution, where the channel is given as an input to the algorithm or Turing machine. Finally, it is further shown that it is also impossible to algorithmically approximate these input distributions.

The capacity of finite state channels (FSCs) with feedback has been expressed by a limit of a sequence of multi-letter expressions. Despite many efforts, a closed-form single-letter capacity characterization remains unknown to date. In this paper, the feedback capacity is studied from a fundamental algorithmic point of view by addressing the question of whether or not the capacity can be algorithmically computed. To this aim, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that the feedback capacity of FSCs is not Banach-Mazur computable and therefore also not Borel-Turing computable. As a consequence, it is shown that either achievability or converse (or both) is not Banach-Mazur computable, which means that there are FSCs for which it is impossible to find computable tight upper and lower bounds. Furthermore, it is shown that the feedback capacity cannot be characterized as the maximization of a finite-letter formula of entropic quantities.

This work considers mitigation of information leakage between communication and sensing operations in joint communication and sensing systems. Specifically, a discrete memoryless state-dependent broadcast channel model is studied in which (i) the presence of feedback enables a transmitter to simultaneously achieve reliable communication and channel state estimation; (ii) one of the receivers is treated as an eavesdropper whose state should be estimated but which should remain oblivious to a part of the transmitted information. The model abstracts the challenges behind security for joint communication and sensing if one views the channel state as a characteristic of the receiver, e.g., its location. For independent and identically distributed (i.i.d.) states, perfect output feedback, and when part of the transmitted message should be kept secret, a partial characterization of the secrecy-distortion region is developed. The characterization is exact when the broadcast channel is either physically-degraded or reversely-physically-degraded. The characterization is also extended to the situation in which the entire transmitted message should be kept secret. The benefits of a joint approach compared to separation-based secure communication and state-sensing methods are illustrated with a binary joint communication and sensing model.

We extend a previous framework for designing differentially private (DP) mechanisms via randomized graph colorings that was restricted to binary functions, corresponding to colorings in a graph, to multi-valued functions. As before, datasets are nodes in the graph and any two neighboring datasets are connected by an edge. In our setting, we assume that each dataset has a preferential ordering for the possible outputs of the mechanism, each of which we refer to as a rainbow. Different rainbows partition the graph of datasets into different regions. We show that if the DP mechanism is pre-specified at the boundary of such regions and behaves identically for all same-rainbow boundary datasets, at most one optimal such mechanism can exist and the problem can be solved by means of a morphism to a line graph. We then show closed form expressions for the line graph in the case of ternary functions. Treatment of ternary queries in this paper displays enough richness to be extended to higher-dimensional query spaces with preferential query ordering, but the optimality proof does not seem to follow directly from the ternary proof.

The problem of secure source coding with multiple terminals is extended by considering a remote source whose noisy measurements are the correlated random variables used for secure source reconstruction. The main additions to the problem include 1) all terminals noncausally observe a noisy measurement of the remote source; 2) a private key is available to all legitimate terminals; 3) the public communication link between the encoder and decoder is rate-limited; and 4) the secrecy leakage to the eavesdropper is measured with respect to the encoder input, whereas the privacy leakage is measured with respect to the remote source. Exact rate regions are characterized for a lossy source coding problem with a private key, remote source, and decoder side information under security, privacy, communication, and distortion constraints. By replacing the distortion constraint with a reliability constraint, we obtain the exact rate region also for the lossless case. Furthermore, the lossy rate region for scalar discrete-time Gaussian sources and measurement channels is established.

A capacity result involves two parts: achievability and converse. The achievability proof is usually non-constructive and only the existence of capacity-achieving codes is shown invoking probabilistic techniques. Recently, capacity-achieving codes have been found for several channels demonstrating that such codes can actually be constructed algorithmically. To this end, each construction is designed for a pre-specified channel so that the corresponding algorithm is specifically tailored to it. This paper addresses the general question of whether or not it is possible to find algorithms that can construct capacity-achieving codes for a whole class of channels. To do so, the concept of Turing machines is used which provides the fundamental performance limits of digital computers and therewith fully specifies which tasks are algorithmically feasible in principle. It is shown that there exists no Turing machine that is able to construct capacity-achieving codes for a whole class of channels, where the channel realization from this class is given as an input to the Turing machine. It is further shown that such an algorithmic construction remains impossible when the optimality condition is dropped and codes only need to achieve a fraction of the capacity. Finally, implications on channel-aware transmission, link adaptation, and cross-layer optimization are discussed.

Consider the identification (ID) via channels problem, where a receiver decides whether the transmitted identifier is its identifier, rather than decoding it. This model allows to transmit identifiers whose size scales doubly-exponentially in the blocklength, unlike common transmission codes with exponential scaling. Binary constant-weight codes (CWCs) suffice to achieve the ID capacity. Relating parameters of a binary CWC to the minimum distance of a code and using higher-order correlation moments, two upper bounds on binary CWC sizes are proposed. These bounds are also upper bounds on identifier sizes for ID codes constructed by using binary CWCs. We propose two constructions based on optical orthogonal codes (OOCs), which are used in optical multiple access schemes, have constant-weight codewords, and satisfy cyclic cross-correlation and auto-correlation constraints. These constructions are modified and concatenated with outer Reed-Solomon codes to propose new binary CWCs being optimal for ID. Improvements to the finite-parameter performance are shown by using outer codes with larger minimum distance vs. blocklength ratios. We illustrate ID regimes for which our ID code constructions perform significantly better than existing constructions.

We consider a set of security and privacy problems under reliability and storage constraints that can be tackled by using codes and particularly focus on the secret-key agreement problem. Polar subcodes (PSCs) are polar codes (PCs) with dynamically-frozen symbols and have a larger code minimum distance than PCs with only statically-frozen symbols. A randomized nested PSC construction, where the low-rate code is a PSC and the high-rate code is a PC, is proposed for successive cancellation list (SCL) and sequential decoders. This code construction aims to perform lossy compression with side information, i.e., Wyner-Ziv (WZ) coding. Nested PSCs are used in the key agreement problem with physical identifiers and two terminals since WZ-coding constructions significantly improve on Slepian-Wolf coding constructions such as fuzzy extractors. Significant gains in terms of the secret-key vs. storage rate ratio as compared to nested PCs with the same list sizes are illustrated to show that nested PSCs significantly improve on all existing code constructions. The performance of the nested PSCs is shown to improve with larger list sizes, unlike the nested PCs considered. A design procedure to efficiently construct nested PSCs and possible improvements to the nested PSC designs are also provided.

In intelligent reflecting surface (IRS)-aided multiple-input multiple-output (MIMO) systems, the IRS can be utilized to suppress the information leakage towards malicious terminals. This can lead to significant secrecy gains. This work exploits these gains via a tractablejointdesign of downlink beamformers and IRS phase-shifts. In this respect, we consider a generic IRS-aided MIMO wiretap setting and invoke fractional programming and alternating optimization to iteratively find the beamformers and phase-shifts that maximize the achievable weighted secrecy sum-rate. Our design is comprised of two low-complexity algorithms. Performance of the proposed algorithms are numerically evaluated and compared to the benchmark. The results reveal that integrating IRSs into MIMO systems not only boosts the secrecy performance, but also improves the robustness against passive eavesdropping.

We consider a distributed function computation problem in which parties observing noisy versions of a remote source facilitate the computation of a function of their observations at a fusion center through public communication. The distributed function computation is subject to constraints, including not only reliability and storage but also secrecy and privacy. Specifically, 1) the function computed should remainsecretfrom an eavesdropper observing the public communication and correlated observations, measured in terms of the information leaked about the arguments of the function, to ensure secrecy regardless of the exact function used; 2) the remote source should remainprivatefrom the eavesdropper and the fusion center, measured in terms of the information leaked about the remote source itself. We derive the exact rate regions for lossless and lossy single-function computation and illustrate the lossy single-function computation rate region for an information bottleneck example, in which the optimal auxiliary random variables are characterized for binary-input symmetric-output channels. We extend the approach to lossless and lossy asynchronous multiple-function computations with joint secrecy and privacy constraints, in which case inner and outer bounds for the rate regions that differ only in the Markov chain conditions imposed are characterized.

Using intelligent reflecting surfaces (IRSs), wireless propagation channels can be manipulated such that information leakage to eavesdropping terminals in a multiple-input multiple-output (MIMO) setting is significantly suppressed. This observation illustrates the potential secrecy gains of IRS-aided MIMO systems. This work develops a novel low-complexity algorithm by which these potential gains are exploited. Invoking methods from fractional programming, the algorithm iteratively designs the digital precoder at the transmitter and tunes the IRS elements, such that the weighted secrecy sum-rate is maximized. It is shown that as the algorithm iterates, the weighted secrecy sum-rate evolves in a non-decreasing way. Numerical investigations confirm the efficiency of the proposed algorithm.

Wireless channels are considered that change over time but remain constant for a certain (coherence) period. This behavior is perfectly captured by block fading channels and affects the performance of the corresponding wireless communication systems. Desired closed-form characterizations of optimal transmission schemes remain unknown in many cases. This paper approaches this issue from a fundamental, algorithmic point of view by studying whether or not it is in principle possible to construct or find such optimal transmission schemes algorithmically (without putting any constraints on the computational complexity of such algorithms). To this end, the concept of averaged channels is considered as a model for block fading and it is shown that, although the averaged channel itself is computable, the corresponding capacity need not be computable, i.e., there exists no (universal) algorithm that takes the channel as an input and computes the corresponding capacity expression. Subsequently, examples of block fading channels are presented for which it is even impossible to find an algorithm that computes for every blocklength the corresponding optimal transmission scheme.

Wireless communication systems are inherently vulnerable to adversarial attacks since malevolent jammers might jam and disrupt the legitimate transmission intentionally. Of particular interest are so- called denial-of-service (DoS) attacks in which the jammer is able to completely disrupt the communication. Accordingly, it is of crucial interest for the legitimate users to detect such DoS attacks. Turing machines provide the fundamental limits of today’s digital computers and therewith of the traditional signal processing. It has been shown that these are incapable of detecting DoS attacks. This stimulates the question of how powerful the signal processing must be to enable the detection of DoS attacks. This paper investigates the general computation framework of Blum-Shub-Smale machines which allows the processing and storage of arbitrary reals. It is shown that such real number signal processing then enables the detection of DoS attacks.

Federated learning (FL) allows to train a massive amount of data privately due to its decentralized structure. Stochastic gradient descent (SGD) is commonly used for FL due to its good empirical performance, but sensitive user information can still be inferred from weight updates shared during FL iterations. We consider Gaussian mechanisms to preserve local differential privacy (LDP) of user data in the FL model with SGD. The trade-offs between user privacy, global utility, and transmission rate are proved by defining appropriate metrics for FL with LDP. Compared to existing results, the query sensitivity used in LDP is defined as a variable, and a tighter privacy accounting method is applied. The proposed utility bound allows heterogeneous parameters over all users. Our bounds characterize how much utility decreases and transmission rate increases if a stronger privacy regime is targeted. Furthermore, given a target privacy level, our results guarantee a significantly larger utility and a smaller transmission rate as compared to existing privacy accounting methods.

For communication systems there is a recent trend towards shifting functionalities from the physical layer to higher layers by enabling software-focused solutions. Having obtained a (physical layer-based) description of the communication channel, such approaches exploit this knowledge to enable various services by subsequently processing it on higher layers. For this it is a crucial task to first find out in which state the underlying communication channel is. This paper develops a framework based on Turing machines and studies whether or not it is in principle possible to algorithmically decide in which state the communication system is. It is shown that there exists no Turing machine that takes the physical description of the communication channel as an input and solves a non-trivial classification task. Subsequently, this general result is used to study communication under adversarial attacks and it is shown that it is impossible to algorithmically detect denial-of-service (DoS) attacks on the transmission. Jamming attacks on ACK/NACK feedback cannot be detected as well and, in addition, ACK/NACK feedback is shown to be useless for the detection of DoS attacks on the actual message transmission.

Proving a capacity result usually involves two parts: achievability and converse which establish matching lower and upper bounds on the capacity. For achievability, only the existence of good (capacity-achieving) codes is usually shown. Although the existence of such optimal codes is known, constructing such capacity-achieving codes has been open for a long time. Recently, significant progress has been made and optimal code constructions have been found including for example polar codes. A crucial observation is that all these constructions are done for a fixed and given channel and this paper addresses the question whether or not it is possible to find universal algorithms that can construct optimal codes for a whole class of channels. For this purpose, the concept of Turing machines is used which provides the fundamental performance limits of digital computers. It is shown that there exists no universal Turing machine that takes the channel from the class of interest as an input and outputs optimal codes. Finally, implications on channel-aware transmission schemes are discussed.

The use of deep learning-based techniques for approximating secure encoding functions has attracted considerable interest in wireless communications due to impressive results obtained for general coding and decoding tasks for wireless communication systems. Of particular importance is the development of model-free techniques that work without knowledge about the underlying channel. Such techniques utilize for example generative adversarial networks to estimate and model the conditional channel distribution, mutual information estimation as a reward function, or reinforcement learning. In this paper, the approach of reinforcement learning is studied and, in particular, the policy gradient method for a model-free approach of neural network-based secure encoding is investigated. Previously developed techniques for enforcing a certain co-set structure on the encoding process can be combined with recent reinforcement learning approaches. This new approach is evaluated by extensive simulations, and it is demonstrated that the resulting decoding performance of an eavesdropper is capped at a certain error level.

Communication systems are subject to adversarial attacks since malevolent adversaries might harm and disrupt legitimate transmissions intentionally. Of particular interest in this paper are so-called denial-of-service (DoS) attacks in which the jammer completely prevents any transmission. Arbitrarily varying classical-quantum channels, providing a suitable model to capture the jamming attacks of interest, are studied. Algorithmic detection frameworks are developed based on Turing machines and also Blum-Shub-Smale (BSS) machines, where the latter can process and store arbitrary real numbers. It is shown that Turing machines are not capable of detecting DoS attacks. However, BSS machines are capable thereof implying that real number signal processing enables the algorithmic detection of DoS attacks.

We consider a distributed function computation problem in which parties observing noisy versions of a remote source facilitate the computation of a function of their observations at a fusion center through public communication. The distributed function computation is subject to constraints, including not only reliability and storage but also privacy and secrecy. Specifically, 1) the remote source should remain private from an eavesdropper and the fusion center, measured in terms of the information leaked about the remote source; 2) the function computed should remain secret from the eavesdropper, measured in terms of the information leaked about the arguments of the function, to ensure secrecy regardless of the exact function used. We derive the exact rate regions for lossless and lossy single-function computation and illustrate the lossy single-function computation rate region for an information bottleneck example, in which the optimal auxiliary random variables are characterized for binary input symmetric output channels. We extend the approach to lossless and lossy asynchronous multiple-function computations with joint secrecy and privacy constraints, in which case inner and outer bounds for the rate regions differing only in the Markov chain conditions imposed are characterized.

Consider the identification (ID) via channels problem, where a receiver wants to decide whether the transmitted identifier is its identifier, rather than decoding the identifier. This model allows to transmit identifiers whose size scales doubly-exponentially in the blocklength, unlike common transmission (or channel) codes whose size scales exponentially. It suffices to use binary constant-weight codes (CWCs) to achieve the ID capacity. By relating the parameters of a binary CWC to the minimum distance of a code and using higher-order correlation moments, two upper bounds on the binary CWC size are proposed. These bounds are shown to be upper bounds also on the identifier sizes for ID codes constructed by using binary CWCs. We propose two code constructions based on optical orthogonal codes, which are used in optical multiple access schemes, have constant-weight codewords, and satisfy cyclic cross-correlation and autocorrelation constraints. These constructions are modified and concatenated with outer Reed-Solomon codes to propose new binary CWCs optimal for ID. Improvements to the finite-parameter performance of both our and existing code constructions are shown by using outer codes with larger minimum distance vs. blocklength ratios. We also illustrate ID performance regimes for which our ID code constructions perform significantly better than existing constructions.

The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric means or the Hölder inequality. In a probabilistic setting, the Jensen inequality describes the relationship between a convex function and the expected value. In this work, we want to look at the probabilistic setting from the reverse direction of the inequality. We show that under minimal constraints and with a proper scaling, the Jensen inequality can be reversed. We believe that the resulting tool can be helpful for many applications and provide a variational estimation of mutual information, where the reverse inequality leads to a new estimator with superior training behavior compared to current estimators.

For communication systems there is a recent trend towards shifting functionalities from the physical layer to higher layers by enabling software-focused solutions. Having obtained a (physical layer-based) description of the communication channel, such approaches exploit this knowledge to enable various services by subsequently processing it on higher layers. For this it is a crucial task to first find out in which state the underlying communication channel is. This paper develops a framework based on Turing machines and studies whether or not it is in principle possible to algorithmically solve such classification tasks, i.e., to decide in which state the communication system is. Turing machines have no limitations on computational complexity, computing capacity and storage, and can simulate any given algorithm and therewith are a simple but very powerful model of computation. They characterize the fundamental performance limits for today's digital computers. It is shown that there exists no Turing machine that takes the physical description of the communication channel as an input and solves a non-trivial classification task. Subsequently, this general result is used to study communication under adversarial attacks and it is shown that it is impossible to algorithmically detect denial-of-service (DoS) attacks on the transmission. Jamming attacks on ACK/NACK feedback cannot be detected as well and, in addition, ACK/NACK feedback is shown to be useless for the detection of DoS on the actual message transmission. Further applications are discussed including DoS attacks on the Post Shannon task of identification, and on physical layer security and resilience by design.

Passively overheard massive multiple-input multiple-output (MIMO) settings are capable of suppressing eavesdroppers via narrow beamforming towards legitimate receivers. This implies that secrecy is obtained almost for free in these settings. This study shows that this is a valid property for a large class of low-complexity massive MIMO transmitters. The investigations consider two dominant approaches for complexity reduction, namely antenna selection and hybrid analog-digital precoding. It is shown that using either approach, the information leakage per achievable sum-rate vanishes as the number of transmit antennas grows large. The results demonstrate that, as the transmit array size grows large, the normalized information leakage obtained by antenna selection and hybrid analog-digital precoding converges to zero double-logarithmically and logarithmically, respectively. The analytical results are confirmed for various benchmark architectures via numerical simulations.

Recently, a hybrid analog-digital architecture has been proposed for multiuser MIMO transmission in the millimeter-wave spectrum using reflect-arrays. The architecture exhibits scalability and high energy-efficiency while keeping the transmitter cost-efficient. Inspired by this architecture, we design a secure multiuser hybrid analog-digital precoding scheme. This scheme utilizes the method of regularized least-squares to shape the downlink beamformers, such that the signal received via malicious terminals is effectively suppressed. Numerical investigations depict high robustness of this scheme against the density of malicious terminals, as well as the quality of overhearing channels. Such properties along with high efficiency of the transmitter imply that the proposed scheme is an effective candidate for secure communication in multiuser millimeter-wave massive MIMO systems.

The availability and quality of channel state information heavily influences the performance of wireless communication systems. For perfect channel knowledge, optimal signal processing and coding schemes are well studied and often closed-form solutions are known. On the other hand, the case of imperfect channel information is much less understood and closed-form solutions remain unknown in general. This paper approaches this question from a fundamental, algorithmic point of view to study whether or not such optimal schemes can be found algorithmically in principle (without putting any constraints on the computational complexity of such algorithms). To this end, the compound channel is considered as a model for channel uncertainty and it is shown that although the compound channel itself is a computable channel, the corresponding capacity is not computable in general, i.e., there exists no algorithm or Turing machine that takes the channel as an input and computes the corresponding capacity. As an implication of this, it is then shown that for such compound channels, there are no effectively constructible optimal signal processing and coding schemes that achieve the capacity. This is particularly noteworthy as such schemes must exist (since the capacity is known), but they cannot be effectively, i.e., algorithmically, constructed.

Noisy measurements of a physical unclonable function (PUF) are used to store secret keys with reliability, security, privacy, and complexity constraints. A new set of low-complexity and orthogonal transforms with no multiplication is proposed to obtain bit-error probability results significantly better than all methods previously proposed for key binding with PUFs. The uniqueness and security performance of a transform selected from the proposed set is shown to be close to optimal. An error-correction code with a low-complexity decoder and a high code rate is shown to provide a block-error probability significantly smaller than provided by previously proposed codes with the same or smaller code rates.

A coding theorem consists of two parts: achievability and converse which establish lower and upper bounds on the capacity. This paper analyzes these bounds from a fundamental, algorithmic point of view by studying whether or not such bounds can be computed algorithmically in principle (without putting any constraints on the computational complexity of such algorithms). For this purpose, the concept of Turing machines is used which provides the fundamental performance limits of digital computers. To this end, computable continuous functions are studied and properties of computable sequences of such functions are identified. Subsequently, these findings are exemplarily applied to two different open problems. The first one is the ϵ-capacity of compound channels which is unknown to date. It is studied whether or not the ϵ-capacity can be algorithmically computed and it is shown that there is no computable characterization of the difference between computable upper and lower bounds possible. Thus, computable sharp lower and upper bounds on the ϵ-capacity of computable compound channels cannot exist. The crucial consequence is that the ϵ-capacity cannot be characterized by a finite-letter entropic expression. The second application involves asymptotic bounds for error-correcting codes which is a long-standing open problem in coding theory. Only lower and upper bounds are known which are not sharp. It is conjectured that the asymptotic bound is indeed a non-computable function which would then imply with the previous findings that it is impossible to find computable lower and upper bounds that are asymptotically tight.

The problem of secret-key based authentication under privacy and storage constraints on the source sequence is considered. The identifier measurement channels during authentication are assumed to be controllable via a cost-constrained action sequence. Single-letter inner and outer bounds for the keyleakage-storage-cost regions are derived for a generalization of a classic two-terminal key agreement model with an eavesdropper that observes a sequence that is correlated with the sequences observed by the legitimate terminals. The additions to the model are that the encoder observes a noisy version of a remote source, and the noisy output and the remote source output together with an action sequence are given as inputs to the measurement channel at the decoder. Thus, correlation is introduced between the noise components on the encoder and decoder measurements. The model with a secret key generated by an encoder is extended to the randomized models, where a secret-key is embedded to the encoder. The results are relevant for several user and device authentication scenarios including physical and biometric identifiers with multiple measurements that provide diversity and multiplexing gains. To illustrate the behavior of the rate region, achievable (secret-key rate, storage-rate, cost) tuples are given for binary identifiers and measurement channels that can be represented as a mixture of binary symmetric subchannels. The gains from using an action sequence such as a large secret-key rate at a significantly small hardware cost, are illustrated to motivate the use of low-complexity transform-coding algorithms with cost-constrained actions.

In this paper, fast fading Gaussian multiuser channels are considered. If the channel state information (CSI) is perfectly known to the transmitter, capacities have been derived for many cases in which the channels satisfy certain information-theoretic orders such as degradedness, or strong/very strong interference. We study the case when only the statistics of the CSI are known at the transmitter, which is an open problem in general. The main contributions of this paper are the following: First, we derive a sufficient condition to construct equivalent (having the same capacity region as the original channel) degraded Gaussian broadcast channels, which is based on the marginal distributions of the channel gains. To achieve this goal, we leverage three schemes: coupling, maximal coupling, and copulas, in addition to the same marginal property. The underlying idea of all schemes is to obtain an equivalent channel by changing the joint distribution in such a way that it satisfies a certain information-theoretic order while ensuring that the marginal distributions of the channels to different users are not changed. The construction of this equivalent multiuser channel allows us to directly apply existing capacity results. We then further derive the capacity regions of Gaussian interference channels with strong and very strong interferences, and also the secrecy capacity of Gaussian wiretap channels, while in all cases, the transmitters know only the statistics of the channels. Several practical examples such as Rayleigh fading and Nakagami-m fading illustrate the applicability of the derived results.

The source model for secret key generation with one way public communication refers to a setting in which a secret key should be agreed upon at two terminals. At both terminals correlated components of a common source are available. In addition, a message can be sent from one terminal to the other via a public channel. In this paper, a related scenario is considered where instead of secret key generation, the goal is to securely store data in a public database. The database allows for error-free storing of the data, but is constrained in its size which imposes a rate constraint on storing. The corresponding capacity for secure storage is known and it has been shown that the capacity-achieving strategy satisfies the strong secrecy criterion. Here, the case when the storage in the public database is subject to errors is considered and the corresponding capacity is characterized. In addition, the continuity properties of the two capacity functions are analyzed. These capacity functions are continuous as opposed to the discontinuous secret key capacity with rate constraint. It is shown that for secure storage the phenomenon of super activation can occur. Finally, it is discussed how the results in this paper differ from previous results on super activation.

Modern communication systems need to satisfy pre-specified requirements on spectral efficiency and security. Physical layer security is a concept that unifies both and connects them with entropic quantities. In this paper, a framework based on Turing machines is developed to address the question of deciding whether or not a communication system meets these requirements. It is known that the class of Turing solvable problems coincides with the class of algorithmically solvable problems so that this framework provides the theoretical basis for effective verification of such performance requirements. A key issue here is to decide whether or not the performance functions, i.e., capacities, of relevant communication scenarios, particularly those with secrecy requirements and active adversaries, are Turing computable. This is a necessary condition for the corresponding communication protocols to be effectively verifiable. Within this framework, it is then shown that for certain scenarios including the wiretap channel the corresponding capacities are Turing computable. Next, a general necessary condition on the performance function for Turing computability is established. With this, it is shown that for certain scenarios, including the wiretap channel with an active jammer, the performance functions are not computable when deterministic codes are used. As a consequence, such performance functions are also not computable on all other computer architectures such as the von Neumann-architecture or the register machines.

The problem of identification is considered, in which it is of interest for the receiver to decide only whether a certain message has been sent or not, and the identification-feedback (IDF) capacity of channels with feedback is studied. The IDF capacity is shown to be discontinuous and super-additive for both deterministic and randomized encoding. For the deterministic IDF capacity the phenomenon of super-activation occurs, which is the strongest form of super-additivity. This is the first time that super-activation is observed for discrete memoryless channels. On the other hand, for the randomized IDF capacity, super-activation is not possible. Finally, the developed theory is studied from an algorithmic point of view by using the framework of Turing computability. The problem of computing the IDF capacity on a Turing machine is connected to problems in pure mathematics and it is shown that if the IDF capacity would be Turing computable, it would provide solutions to other problems in mathematics including Goldbach's conjecture and the Riemann Hypothesis. However, it is shown that the deterministic and randomized IDF capacities are not Banach-Mazur computable. This is the weakest form of computability implying that the IDF capacity is not computable even for universal Turing machines. On the other hand, the identification capacity without feedback is Turing computable revealing the impact of the feedback: It transforms the identification capacity from being computable to non-computable.

Secret key generation refers to the problem of generating a common secret key without revealing any information about it to an eaves-dropper. All users observe correlated components of a common source and can further use a rate-limited public channel for discussion which is open to eavesdroppers. This paper studies the Turing computability of the secret key capacity with a single rate-limited public forward transmission. Turing computability provides fundamental performance limits for today’s digital computers. It is shown that the secret key capacity under rate constraints is not Turing computable, and consequently there is no algorithm that can simulate or compute the secret key capacity, even if there are no limitations on computational complexity and computing power. On the other hand, if there are no rate constraints on the forward transmission, the secret key capacity is Turing computable. This shows that restricting the communication rate over the public channel transforms a Turing computable problem into a non-computable problem. To the best of our knowledge, this is the first time that such a phenomenon has been observed.

Wireless communication systems are inherently vulnerable to adversarial attacks since malevolent jammers might jam and disrupt the legitimate transmission intentionally. Accordingly it is of crucial interest for the legitimate users to detect such adversarial attacks. This paper develops a detection framework based on Turing machines and studies the detectability of adversarial attacks. Of particular interest are so-called denial-of-service attacks in which the jammer is able to completely prevent any transmission. It is shown that there exists no Turing machine which can detect such an attack and consequently there is no algorithm that can decide whether or not such a denialof-service attack takes place, even if there are no limitations on computational complexity and computing capacity of the hardware.

End-to-end learning of communication systems with neural networks and particularly autoencoders is an emerging research direction which gained popularity in the last year. In this approach, neural networks learn to simultaneously optimize encoding and decoding functions to establish reliable message transmission. In this paper, this line of thinking is extended to communication scenarios in which an eavesdropper must further be kept ignorant about the communication. The secrecy of the transmission is achieved by utilizing a modified secure loss function based on cross-entropy which can be implemented with state-of-the-art machine-learning libraries. This secure loss function approach is applied in a Gaussian wiretap channel setup, for which it is shown that the neural network learns a trade-off between reliable communication and information secrecy by clustering learned constellations. As a result, an eavesdropper with higher noise cannot distinguish between the symbols anymore.

We investigate the application of copulas for characterizing channel orders, e.g., degradedness or strong/very strong interference, of Gaussian multiuser channels with statistical channel state information at the transmitter (CSIT). When there is solely statistical CSIT, identifying such channel orders is much more involved and, thus, the capacity remains unknown in general. We use the maximum copula to construct equivalent channels by modifying the joint distributions such that these newly constructed channels possess certain channel orders. We also derive sufficient conditions to attain these equivalent channels. We further discuss the meaning of achieving the maximum copula with respect to the concordance between the fading channels. We illustrate the theoretical results by numerical simulations, which visualize the joint probability distributions.

The problem of identification is considered, in which it is of interest for the receiver to decide only whether a certain message has been sent or not. Identification via correlation-assisted discrete memoryless channels is studied, where the transmitter and the receiver further have access to correlated source observations. Analytical properties and representations of the corresponding identification capacity are studied. In this paper, it is shown that the identification capacity cannot be represented as a maximization of a single-letter (or multi-letter with fixed length) expression of entropic quantities. Further, it is shown that the identification capacity is not Banach-Mazur computable and therewith not Turing computable. Consequently, there is no algorithm that can simulate or compute the identification capacity, even if there are no limitations on computational complexity and computing power.

In this paper, ergodic capacities of fading Gaussian multi-user channels with only statistical channel state information at the transmitter are considered. The main contributions are twofold: First, we introduce a framework to classify random fading channels solely based on their joint distributions, such that we can construct equivalent channels in order to directly make use of existing capacity results. To attain this goal, we leverage three schemes: maximal coupling, coupling, and copulas in addition to the usual stochastic order with the same marginal property. Second, we apply the developed framework to Gaussian broadcast channels, Gaussian interference channels, and Gaussian wiretap channels to obtain novel capacity (region) results.

Finite state channels (FSCs) model discrete channels with memory where the channel output depends on the channel input and the actual channel state. The capacity of general FSCs has been established as the limit of a sequence of multi-letter expressions; a corresponding finite-letter characterization is not known to date. In this paper, it is shown that it is indeed not possible to find such a finite-letter entropic characterization for FSCs whose input, output, and state alphabets satisfy |X| ≥2, |Y| ≥2, and |S| ≥q2. Further, the algorithmic computability of the capacity of FSCs is studied. To account for this, the concept of a Turing machine is adopted as it provides fundamental performance limits for today's digital computers. It is shown that the capacity of a FSC is not Banach-Mazur computable and therewith not Turing computable for |X| ≥2, |Y| ≥2, |S| ≥2.

The theory of Verdú and Han provides a powerful framework to analyze and study general non-independent and identically distributed (non-i.i. d.) sources and channels. Already for simple non-i.i. d. sources and channels, this framework can result in complicated general capacity formulas. Ahlswede asked in his Shannon lecture if these general capacity formulas can be effectively, i.e., algorithmically, computed. In this paper, it is shown that there exist computable non-i.i. d. sources and channels, for which the capacity is a non-computable number. Even worse, it is shown that there are non-i.i. d. sources and channels for which the capacity is a computable number, i.e., the limit of the corresponding sequence of multi-letter capacity expressions is computable, but the convergence of this sequence is not effective. This answers Ahlswede's question in a strong form, since in this case, the multi-letter capacity expressions for these sources and channels cannot be used to approximate the optimal performance algorithmically.

A basic model for key agreement with biometric or physical identifiers is extended to include measurements of a hidden source through a general broadcast channel (BC). An inner bound for strong secrecy, maximum key rate, and minimum privacy-leakage and database-storage rates is proposed. The inner bound is shown to be tight for physically-degraded and less-noisy BCs.

Joint user selection and precoding in multiuser MIMO settings can be interpreted as group sparse recovery in linear models. In this problem, a signal with group sparsity is to be reconstructed from an underdetermined system of equations. This paper utilizes this equivalent interpretation and develops a computationally tractable algorithm based on the method of group LASSO. Compared to the state of the art, the proposed scheme shows performance enhancements in two different respects: higher achievable sum-rate and lower interference at the non-selected user terminals.

We consider a cache-aided wireless device-to-device (D2D) network of the type introduced by Ji et al., where the placement phase is orchestrated by a central server. We assume that the devices' caches are filled with uncoded data, and the whole content database is contained in the collection of caches. After the cache placement phase, the files requested by the users are serviced by inter-device multicast communication. For such a system setting, we provide the exact characterization of the optimal load-memory trade-off under the assumptions of uncoded placement and one-shot delivery. In particular, we derive both the minimum average (under uniformly distributed demands) and the minimum worst-case sum-load of the D2D transmissions, for given individual cache memory size at disposal of each user. Furthermore, we show that the performance of the proposed scheme is within factor 4 of the information-theoretic optimum. Capitalizing on the one-shot delivery property, we also propose an extension of the presented scheme that provides robustness against random user inactivity.

This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second-order coding rate for discrete memoryless and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal tradeoff between reliability and secrecy in the finite-blocklength regime. Underlying our achievability bounds are two new privacy amplification results, which not only refine the classic privacy amplification results, but also achieve secrecy under the stronger semantic-security metric.

In massive MIMO wiretap settings, the base station can significantly suppress eavesdroppers by narrow beamforming toward legitimate terminals. Numerical investigations show that by this approach, secrecy is obtained at no significant cost. We call this property of massive MIMO systems "secrecy for free" and show that it not only holds when all the transmit antennas at the base station are employed, but also when only a single antenna is set active. Using linear precoding, the information leakage to the eavesdroppers can be sufficiently diminished, when the total number of available transmit antennas at the base station grows large, even when only a fixed number of them are selected. This result indicates that passive eavesdropping has no significant impact on massive MIMO systems, regardless of the number of active transmit antennas.

We investigate secure communication over a channel that undergoes two different classes of attacks at the same time: passive eavesdropping and active jamming. This scenario is perfectly modeled by the concept of arbitrarily varying wiretap channels (AVWCs). We derive a full characterization of the secrecy capacity of AVWCs under list decoding. We show that the list secrecy capacity is either equivalent to the correlated random secrecy capacity or zero depending on the order of symmetrizability of the legitimate AVC. Differently from correlated random codes, our coding scheme does not assume any restrictions on the communication between the eavesdropper and the jammer.

The problem of identification is considered, in which it is of interest for the receiver to decide only whether a certain message has been sent or not, and the identification-feedback (IDF) capacity of channels with feedback is studied. The IDF capacity is shown to be discontinuous and super-additive for both deterministic and randomized encoding. For the deterministic IDF capacity the phenomenon of super-activation occurs, which is the strongest form of super-additivity. For the randomized IDF capacity, super-activation is not possible. These findings imply that the IDF capacity is not Turing computable.

In this invited paper, the concept of privacy amplification is reviewed and recent developments are discussed. Its applications in information-theoretic security problems are considered including semantic security and polar coding for privacy amplification.

In this paper, we study the impacts of transmit antenna selection on the secrecy performance of massive MIMO systems. We consider a wiretap setting in which a fixed number of transmit antennas are selected and then confidential messages are transmitted over them to a multi-antenna legitimate receiver while being overheard by a multi-antenna eavesdropper. For this setup, we derive an accurate approximation of the instantaneous secrecy rate. Using this approximation, it is shown that in some wiretap settings under antenna selection the growth in the number of active antennas enhances the secrecy performance of the system up to some optimal number and degrades it when this optimal number is surpassed. This observation demonstrates that antenna selection in some massive MIMO settings not only reduces the RF-complexity, but also enhances the secrecy performance. We then consider various scenarios and derive the optimal number of active antennas analytically using our large-system approximation. Numerical investigations show an accurate match between simulations and the analytic results.

We study the potential employment of improper Gaussian signaling (IGS) in full-duplex relaying (FDR) with non-negligible residual self-interference (RSI) under Nakagami-m fading. IGS is recently shown to outperform traditional proper Gaussian signaling (PGS) in several interference-limited settings. In this paper, IGS is employed as an attempt to alleviate RSI. We use two performance metrics, namely, the outage probability and the ergodic rate. First, we provide upper and lower bounds for the system performance in terms of the relay transmit power and circularity coefficient, a measure of the signal impropriety. Then, we numerically optimize the relay signal parameters based only on the channel statistics to improve the system performance. Based on the analysis, IGS allows FDR to operate even with high RSI. The results show that IGS can leverage higher power budgets to enhance the performance, meanwhile it relieves RSI impact via tuning the signal impropriety. Interestingly, 1-D optimization of the circularity coefficient, with maximum relay power, offers a similar performance as the joint optimization, which reduces the optimization complexity. From a throughput standpoint, it is shown that IGS-FDR can outperform not only PGS-FDR, but also half-duplex relaying with/without maximum ratio combining over certain regions of the target source rate.

The problem of secure broadcasting with independent secret keys is studied. The particular scenario is analyzed in which a common message has to be broadcast to two legitimate receivers, while keeping an external eavesdropper ignorant of it. The transmitter shares independent secret keys of sufficiently high rates with both legitimate receivers, which can be used in different ways: they can be used as one-time pads to encrypt the common message, as fictitious messages for wiretap coding, or as a hybrid of these. In this paper, capacity results are established when the broadcast channels involving the three receivers are degraded. If both legitimate channels are degraded versions of the eavesdropper's channel, it is shown that the one-time pad approach is optimal for several cases, yielding corresponding capacity expressions. Alternatively, the wiretap coding approach is shown to be optimal if the eavesdropper's channel is degraded with respect to both legitimate channels, establishing capacity in this case as well. If the eavesdropper's channel is neither the strongest nor the weakest, an intricate scheme that carefully combines both concepts of one-time pad and wiretap coding with fictitious messages turns out to be capacity-achieving. Finally we also obtain some results for the general non-degraded broadcast channel.

The problem of secret-key based authentication under a privacy constraint on the source sequence is considered. The identifier measurements during authentication are assumed to be controllable via a cost-constrained “action” sequence. Single-letter characterizations of the optimal trade-off among the secret-key rate, storage rate, privacy-leakage rate, and action cost are given for the four problems where noisy or noiseless measurements of the source are enrolled to generate or embed secret keys. The results are relevant for several user-authentication scenarios, including physical and biometric authentications with multiple measurements. Our results include, as special cases, new results for secret-key generation and embedding with action-dependent side information without any privacy constraint on the enrolled source sequence.

In secret-key generation using a compound source, the actual statistics of the source are unknown to the participants. It is assumed rather that the actual source belongs to a set (compound set) which is known to the participants. The secret-key generation protocol should guarantee in this case reliability and security of the generated secret-key simultaneously for all elements of the compound set. In this paper, secret-key generation based on a three-party compound source is studied in which an eavesdropper's side information is also taken into account and strong secrecy is guaranteed. At the same time, the public communication rate constraint between the legitimate users is part of the secret-key generation protocol. In this setting, the achievable secret-key rates for finite compound sources are first reformulated as a region of secret-key rate versus communication rate constraint pairs. It is shown that this region is in general convex, even if the compound set is infinite. Based on this, the secret-key capacity results are extended to be valid for arbitrary (possibly infinite) compound sources with a finite set of marginals. In this case, the secret-key capacity is completely characterized as a function of the forward communication rate parameter between the legitimate users.

Interference channels with confidential messages are studied under strong secrecy constraints, based on the framework of channel resolvability theory. It is shown that if the random binning rate for securing a confidential message is above the resolution of its corresponding wiretapped channel, strong secrecy can be guaranteed. The information-spectrum method introduced by Han and Verdú is generalized to an arbitrary interference channel to obtain a direct channel resolvability result as a first step. For stationary and memoryless channels with discrete output alphabets, the results show that the achievable rates under weak and strong secrecy constraints are the same. This result is then generalized to channels with continuous output alphabets by deriving a reverse direction of Pinsker's inequality to bound the secrecy measure from above by a function of the variational distance of relevant distributions. As an application, Gaussian interference channels are studied in which the agreement between the best known weak and strong secrecy rate regions also appear. Following the footsteps of Csiszár, Hayashi and of Bloch and Laneman, these results provide further evidence that channel resolvability is a powerful and general framework for strong secrecy analysis in multiuser networks.

In this paper, the detrimental effects of intra-cell pilot contamination for physical layer secure communication in cognitive multi-user massive multiple-input multiple-output (MIMO) systems with underlay spectrum sharing are investigated. The channel estimates at the primary base-station (PBS) and secondary base-station are obtained by using non-orthogonal pilot sequences transmitted by the primary user nodes and secondary user nodes, respectively. Hence, these channel estimates are affected by intra-cell pilot contamination. Furthermore, a passive multi-antenna eavesdropper is assumed to be eavesdropping upon either the primary or secondary confidential transmissions. In this context, a physical layer security strategy is provisioned for the primary and secondary transmissions via artificial noise generation at the PBS and zero-forcing precoders. For this system set-up, the average and asymptotic achievable secrecy rate expressions are derived in closed-form, and thereby, the secrecy rate degradation due to intra-cell pilot contamination is quantified. Our analysis reveals that a physical layer secure communication can be provisioned for both primary and secondary massive MIMO systems even with channel estimation errors and pilot contamination.

This paper studies the impact of transmit antenna selection on the secrecy performance of massive MIMO wiretap channels. We consider a scenario in which a multi-antenna transmitter selects a subset of transmit antennas with the strongest channel gains. Confidential messages are then transmitted to a multi-antenna legitimate receiver while the channel is being overheard by a multi-antenna eavesdropper. For this setup, we approximate the distribution of the instantaneous secrecy rate in the large-system limit. The approximation enables us to investigate the optimal number of selected antennas which maximizes the asymptotic secrecy throughput of the system. We show that increasing the number of selected antennas enhances the secrecy performance of the system up to some optimal value, and that further growth in the number of selected antennas has a destructive effect. Using the large-system approximation, we obtain the optimal number of selected antennas analytically for various scenarios. Our numerical investigations show an accurate match between simulations and the analytic results even for not so large dimensions.

For secret-key generation by using a compound source, the actual statistics of the source are unknown to the participants. It is assumed that the probability distribution of the source belongs to a set which is known to the participants. The secret-key generation protocol should guarantee in this case the reliability and security of the generated secret-key simultaneously for all possible source statistics which belong to this set. At the same time, the communication rate between the legitimate users should not exceed a given communication rate parameter. In this work, this problem is studied for the case where the set of source states is arbitrary (possibly infinite) and the set of marginals (transmitter's states) is finite. The secret-key capacity is completely characterized as a function of the forward communication rate parameter between the legitimate users.

This paper studies the maximum secrecy rate for a semi-deterministic wiretap channel, in which the channel between the transmitter and the legitimate receiver is deterministic, while that between the transmitter and the eavesdropper is a discrete memoryless channel. For a given decoding error probability and information leakage (measured by the total variation distance), the optimal second-order secrecy rate is derived. Unlike the secrecy capacity, the second-order secrecy rate characterizes the optimal tradeoff between secrecy and reliability at finite blocklength.

The arbitrarily varying channel (AVC) models communication over a channel that varies in an arbitrary and unknown manner from channel use to channel use. This paper considers the AVC under list decoding and studies the corresponding list capacity. In particular, the list capacity function is shown to be discontinuous and the corresponding discontinuity points are characterized for all possible list sizes. For orthogonal AVCs it is then shown that the list capacity is super-additive, implying that joint encoding and decoding for two orthogonal AVCs can yield a larger list capacity than independent processing of both channels. This discrepancy is shown to be arbitrary large.

In the classical secret-key generation model, common randomness is generated by two terminals based on the observation of correlated components of a common source, while keeping it secret from a non-legitimate observer. It is assumed that the statistics of the source are known to all participants. In this paper, the secret-key generation based on a compound source is studied where the realization of the source statistic is unknown. The protocol should guarantee the security and reliability of the generated secret-key, simultaneously for all possible realizations of the compound source. A single-letter lower-bound of the secret-key capacity for a finite compound source is derived as a function of the public communication rate constraint. A multi-letter capacity formula is further computed for a finite compound source for the case in which the public communication is unconstrained. Finally, a single-letter capacity formula is derived for a degraded compound source with an arbitrary (possibly infinite) set of source states and a finite set of marginal states.

The capacity regions of Gaussian broadcast channels depends on the knowledge of channel state information (CSI). When there is only statistical CSI at the transmitter and full CSI at the receiver, the ergodic capacity region is unknown in general. In this paper we investigate the relation between the degradedness and stochastic orders among channels from the transmitter to different receivers. We derive criteria to identify the degradedness for single and multiple-antenna cases when the channels belong to the usual stochastic order or the increasing convex order. Examples illustrate the usage of the derived criteria. We also show a case in which the channel enhancement technique can be applied even when there is only statistical CSIT.

The question of additivity of the capacity of a channel goes back to Shannon who asked this for the zero error capacity function. Despite the common sense that the capacity is usually additive, there is surprisingly little known for non-trivial channels. This paper addresses this question for the arbitrarily varying wiretap channel (AVWC) which models secure communication in the presence of arbitrarily varying channel (AVC) conditions. For orthogonal AVWCs it has been shown that the non-additivity phenomenon of super-activation occurs; that is, there are orthogonal AVWCs, each having zero secrecy capacity, which allow for transmission with positive secrecy rate if they are used together. It is shown that for such orthogonal AVWCs super-activation is generic in the sense that whenever super-activation is possible, it is possible for all AVWCs in a certain neighborhood as well. Moreover, it is shown that the issue of super-activation and the continuity of the secrecy capacity solely depend on the legitimate link. Accordingly, the single-user AVC is studied and it is shown that in this case, super-activation for non-secure message transmission is not possible, making it a unique feature of secure communication over AVWCs. However, the capacity for message transmission of the single-user AVC is shown to be super-additive including a complete characterization.

This paper investigates the maximal secrecy rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are shown to be tighter than existing bounds. The bounds also lead to the tightest second-order coding rate for discrete memoryless and Gaussian wiretap channels.

We consider problems of two-user secret key generation through an intermediate relay. In the untrusted relay setting, the goal is to establish key agreement between the two users at the highest key rate without leaking information about the key to the relay. We characterize inner and outer bounds to the optimal tradeoff between communication and key rates. The inner bound is based on the scheme which involves a combination of binning, network coding, and key aggregation techniques. For the trusted relay setting with a public broadcast link, the optimal communication-key rate tradeoff is provided for a special case where the two sources are available losslessly at the relay.

This paper studies sub-classes of two-user fast fading Gaussian interference channels (GIC) with ergodic strong/very strong interference, for which channel state information (CSI) is only available at the receivers. Under this setting, the ergodic capacity region is open. In this work we derive a sufficient condition for ergodic strong/very strong GIC to achieve the ergodic capacity regions by stochastic ordering with same marginal property. We also illustrate examples to show the usage scenarios of the derived conditions.

In this paper, secure communication over a broadcast channel with multiple legitimate receivers and an external eavesdropper is investigated. Two different secrecy measures are considered. The first criterion is a conservative one known as joint secrecy, where the mutual leakage of all confidential messages must be small. The second criterion is a less conservative constraint known as individual secrecy, where the individual leakage of each confidential message must be small. At first, we consider the degraded multi-receiver wiretap broadcast channel and manage to establish the individual secrecy capacity region. Our encoding scheme applies a careful combination of the standard techniques of wiretap random coding and Shannon's one time pad encoding, where the confidential messages of the weak receivers are used as secret keys for the stronger ones. The validity of this technique is due to the properties of the degraded broadcast channel and the secrecy requirements of the individual secrecy criterion. Our result indicates that the individual secrecy capacity region is in fact larger than the joint one established in earlier literature. The established capacity region is then used to derive the individual secrecy capacity regions of the Gaussian single-input single-output and degraded Gaussian multiple-input multiple-output multi-receiver wiretap broadcast channels. Furthermore, we present an achievable rate region for the general two-receiver wiretap broadcast channel under both the joint and the individual secrecy criterion. Comparing these two rate regions suggests that even for the general case, the individual secrecy criterion might be able to provide a larger rate region compared with the joint one.

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.

The performance of a secure communication system such as the wiretap channel is usually characterized by its secrecy capacity. In this paper, the issue of whether or not the secrecy capacity is a continuous function of the system parameters is examined. In particular, this is done for channel uncertainty modeled via compound channels and arbitrarily varying channels, in which the legitimate users know only that the true channel realization is from a pre-specified uncertainty set. In the former model, this realization remains constant for the entire duration of transmission, while in the latter the realization varies from channel use to channel use in an unknown and arbitrary manner. The secrecy capacity of the compound wiretap channel is shown to be robust in the sense that it is a continuous function of the uncertainty set. Thus, small variations in the uncertainty set lead to small variations in secrecy capacity. However, the secrecy capacity of the arbitrarily varying wiretap channel is shown to be discontinuous in the uncertainty set meaning that small variations can lead to dramatic losses in capacity.

We consider multiple-input single-output (MISO) Gaussian channels with joint sum and per-antenna power constraints. A closed-form solution of the optimal beamforming vector is derived which achieves the maximal transmission rate. The result shows that if the sum power constraint only optimal power allocation violates a per-antenna power constraint then the joint power constraint optimal power allocation is at the intersection of the sum power constraint and the per-antenna power constraints.

We study secure communication over a degraded wiretap broadcast channel with multiple receivers and an eavesdropper. We consider two different secrecy measures: the traditional joint secrecy where the mutual information leakage of all messages must be small; and individual secrecy where the sum of the information leakage of each individual message must be small. At first, we investigate the joint secrecy criterion, where we present the capacity region established before and provide a simpler converse proof. We then consider the individual secrecy criterion and establish its capacity region, by combining the techniques of wiretap random coding and Shannon's one time pad principle. Our results indicate that the individual secrecy capacity region is bigger than the joint one. Further, we show that the established capacity regions are valid for any degraded wiretap broadcast channel, regardless of the degradedness order of the eavesdropper. Finally, we extend our results to Gaussian channels.

This work examines the properties of code sequences for the scalar Gaussian broadcast channel (BC). Specifically, the behavior in terms of the mutual information and minimum mean-square error (MMSE) functions for all signal-to-noise ratios (SNRs) is explored. It is shown that “good”, capacity achieving, code sequences must follow the behavior of a capacity achieving superposition code sequence, even if they use a different encoding-decoding scheme (such as “Dirty Paper Coding”). Necessary and sufficient conditions for reliable decoding in general and specifically for “good” code sequences for the scalar Gaussian BC, in terms of the MMSE and conditional MMSE functions, are derived. Finally, “bad” code sequences, that do not obtain the capacity of the scalar Gaussian BC, are examined. These codes are defined by an additional MMSE constraint at some other SNR. This constraint limits the amount of disturbance these codes may have on some unintended receiver at that SNR. The capacity region, given this constraint, is fully depicted.

The broadcast channel with independent secret keys is studied. In this scenario, a common message has to be securely broadcast to two legitimate receivers in the presence of an eavesdropper. The transmitter shares with each legitimate receiver an independent secret key of arbitrary rate. These keys can either be used as one-time pads to encrypt the common message or can be interpreted as fictitious messages used as randomization resources for wiretap coding. Both approaches are discussed and the secrecy capacity is derived for various cases. Depending on the qualities of the legitimate and eavesdropper channels, either a one-time pad, wiretap coding, or a combination of both turns out to be capacity-achieving.

This work examines the properties of “good” codes for the scalar Gaussian wiretap channel that achieve the maximum level of equivocation. Specifically, the minimum mean-square error (MMSE) behavior of these codes is explored as a function of the signal-to-noise ratio (SNR). It is first shown that reliable decoding of the codeword at the legitimate receiver and at the eavesdropper, conditioned on the transmitted message, is a necessary and sufficient condition for an optimally secure code sequence. Moreover, it is observed that a stochastic encoder is required for any code sequence with rate below the channel point-to-point capacity. Then, for code sequences attaining the maximum level of equivocation, it is shown that their codebook sequences must resemble “good” point-to-point, capacity achieving, code sequences. Finally, it is shown that the mapping over such “good” codebook sequences that produces a maximum equivocation code must saturate the eavesdropper. These results support several “rules of thumb” in the design of capacity achieving codes for the Gaussian wiretap.

The compound broadcast channel with confidential messages (BCC) generalizes the BCC by modeling the uncertainty of the channel. For the compound BCC, it is known only that the actual channel realization belongs to a pre-specified uncertainty set of channels and that it is constant during the entire transmission. For reliable and secure communication it is necessary to operate at a rate pair within the compound BCC capacity region. Therefore, the question of whether small variations of the uncertainty set lead to large losses of the compound BCC capacity region is of interest, and this problem is studied here. In particular, it is shown that the compound BCC model is robust, i.e., the capacity region depends continuously on the uncertainty set.

Information theoretic approaches to security have been examined as a promising complement to current cryptographic techniques. Such information theoretic approaches establish reliable communication and data confidentiality directly at the physical layer of a communication network by taking the properties of the noisy channel into account leading to unconditional security regardless of the computational capabilities of eavesdroppers. The provision of accurate channel state information is a major challenge particularly in wireless communication systems, especially information about the channels to eavesdroppers. In addition, there might be malevolent adversaries who jam or influence the channel of the legitimate users. This paper surveys different models for secure communication under channel uncertainty and adversarial attacks and reviews the corresponding secrecy capacity results, which characterize the maximum rate at which information can be sent to legitimate receivers while being kept perfectly security from eavesdroppers.

The wiretap channel models secure communication between two users in the presence of an eavesdropper who must be kept ignorant of transmitted messages. The performance of such a system is usually characterized by its secrecy capacity which determines the maximum transmission rate of secure communication. In this paper, the issue of whether or not the secrecy capacity is a continuous function of the system parameters is examined. In particular, this is done for channel uncertainty modeled via compound channels and arbitrarily varying channels, in which the legitimate users know only that the true channel realization is from a prespecified uncertainty set. In the former model, this realization remains constant for the entire duration of transmission, while in the latter the realization varies from channel use to channel use in an unknown and arbitrary manner. These models not only capture the case of channel uncertainty, but are also suitable for modeling scenarios in which a malicious adversary jams or otherwise influences the legitimate transmission. The secrecy capacity of the compound wiretap channel is shown to be robust in the sense that it is a continuous function of the uncertainty set. Thus, small variations in the uncertainty set lead to small variations in secrecy capacity. On the other hand, the deterministic secrecy capacity of the arbitrarily varying wiretap channel is shown to be discontinuous in the uncertainty set meaning that small variations can lead to dramatic losses in capacity.

Strong secrecy capacity of compound wiretap channels is studied. The known lower bounds for the secrecy capacity of compound finite-state memoryless channels under discrete alphabets are extended to arbitrary uncertainty sets and continuous alphabets under the strong secrecy criterion. The conditions under which these bounds are tight are given. Under the saddle-point condition, the compound secrecy capacity is shown to be equal to that of the worst-case channel. Based on this, the compound Gaussian multiple-input multiple-output wiretap channel is studied under the spectral norm constraint and without the degradedness assumption. First, it is assumed that only the eavesdropper channel is unknown, but is known to have a bounded spectral norm (maximum channel gain). The compound secrecy capacity is established in a closed form and the optimal signaling is identified. The compound capacity equals the worst-case channel capacity and thus establishing the saddlepoint property; the optimal signaling is Gaussian and on the eigenvectors of the legitimate channel and the worst-case eavesdropper is isotropic. The eigenmode power allocation somewhat resembles the standard water-filling but is not identical to it. More general uncertainty sets are considered and the existence of a maximum element is shown to be sufficient for a saddle-point to exist, so that signaling on the worst-case channel achieves the compound capacity of the whole class of channels. The case of rank-constrained eavesdropper is considered and the respective compound secrecy capacity is established. Subsequently, the case of additive uncertainty in the legitimate channel, in addition to the unknown eavesdropper channel, is studied. Its compound secrecy capacity and the optimal signaling are established in a closed form as well, revealing the same saddle-point property. When a saddle-point exists under strong secrecy, strong and weak secrecy compound capacities are equal.

The compound broadcast channel with confidential messages is studied, where the transmitter sends a common message to two receivers and, at the same time, a confidential message to one receiver which has to be kept secret from the other one. It is only known to the transmitter and receivers that the actual channel realization is fixed and from a pre-specified set of channels. The information theoretic criterion of strong secrecy is analyzed in detail and generalized in such a way that it completely captures the behavior and the abilities of the non-legitimate receiver. Its impact on the decoding performance of the non-legitimate receiver is characterized as well. In particular, it is shown that regardless of the computational capabilities and the applied decoding strategy of the non-legitimate receiver, his decoding error always tends to one. This gives a valuable signal processing implication of the generalized secrecy criterion and identifies desirable properties of an optimal code design.

The use of secret keys in broadcast channels with receiver side information is studied. The particular scenario is analyzed where a transmitter wants to send two confidential messages to two receivers, while keeping an external eavesdropper ignorant. Each receiver has one of the confidential messages as side information available for decoding. In addition to that, the transmitter shares independent secret keys of arbitrary rates with both receivers. The secret keys can be used in different ways: They can act as one-time pads to encrypt the confidential messages or they can be used as randomization resources for wiretap coding. Both approaches are discussed and an achievable rate region based on superposition coding is established for the one-time pad approach. For the wiretap coding approach, the secrecy capacity for degraded channels is derived. In the optimal coding scheme, the available secret keys are used as the randomization part of the wiretap code to keep the eavesdropper ignorant. In establishing the capacity region, a new upper bound on the sum-rate is derived. This bound shows that in an optimal coding scheme, in the degraded case, the total equivocation-rate of the (opposite) secret-keys at the legitimate receivers must equal the equivocation-rate of the secret-keys at the eavesdropper, when informed about the messages.

Research activities reveal a trend from an exclusive to a shared use of certain frequency bands. Then, uncoordinated interference will be unavoidable resulting in a channel that may vary in an arbitrary and unknown manner from channel use to channel use. This is the arbitrarily varying channel (AVC), for which it has been shown that the classical deterministic approaches with pre-specified encoder and decoder fail if the AVC is symmetrizable. This necessitates more sophisticated strategies such as common randomness (CR) assisted strategies or list decoding which are capable to resolve the ambiguity induced by symmetrizable AVCs. Here, we study the arbitrarily varying multiple access channel (AVMAC) with conferencing encoders, which is motivated by cooperating base stations or access points in future communication systems. The capacity region of the AVMAC with conferencing encoders is established and it is shown that list decoding allows for reliable communication also for symmetrizable AVMACs. The list capacity region equals the CR-assisted capacity region for large enough list size. Finally, for fixed probability of decoding error the amount of resources, i.e., CR or list size, is shown to be finite.

The paradigm shift from an exclusive to a shared use of frequencies comes along with the necessity of new concepts since interference will be ubiquitous. Resulting channels may vary in an arbitrary and unknown manner from channel use to channel use. This is the arbitrarily varying channel (AVC). Here, coordination resources such as common randomness or correlated sources have been shown to be important for reliable communication; especially for symmetrizable AVCs where deterministic approaches with pre-specified encoder and decoder fail. Here, we study the arbitrarily varying bidirectional broadcast channel (AVBBC), which is motivated by the broadcast phase of bidirectional relaying. Here, a relay establishes a bidirectional communication between two nodes while sharing resources with other coexisting networks. The question is asked how much coordination is needed for reliable communication. The capacity region of the AVBBC is established and it is shown that for a transmission of block length n no more than O(log n) outputs of the correlated source suffices to achieve the same as with the much stronger resource of common randomness. Such weak coordination resources of correlated sources can easily be realized by broadcasting a signal (e.g. via satellite) observed by all users only as correlated versions.

The wiretap channel models secure communication in the presence of an eavesdropper who must be kept ignorant of transmitted messages. In this paper, the arbitrarily varying wiretap channel (AVWC), in which the channel may vary in an unknown and arbitrary manner from channel use to channel use, is considered. For arbitrarily varying channels (AVCs) the capacity might differ depending on whether deterministic or common randomness (CR) assisted codes are used. The AVWC has been studied for both coding strategies and the relation between the corresponding secrecy capacities has been established. However, a characterization of the CR-assisted secrecy capacity itself or even a general CR-assisted achievable secrecy rate remain open in general for weak and strong secrecy. Here, the secrecy measure of high decoding error at the eavesdropper is considered, where the eavesdropper is further assumed to know channel states and to adapt its decoding strategy accordingly. For this secrecy measure a general CR-assisted achievable secrecy rate is established. The relation between secrecy capacities for different secrecy measures is discussed: The weak and strong secrecy capacities are smaller than or equal to the one for high decoding error. It is conjectured that this relation can be strict for certain channels.

We study the transmission of a common message and three confidential messages over a broadcast channel with two legitimate receivers and an eavesdropper. Each legitimate receiver is interested in decoding two of the three confidential messages, while having the third one as side information. In order to measure the ignorance of the eavesdropper about the confidential messages, we investigate two different secrecy criteria: joint secrecy and individual secrecy. For both criteria, we provide a general achievable rate region. We establish both the joint and individual secrecy capacity if the two legitimate receivers are less noisy than the eavesdropper. We further investigate the scenario where the eavesdropper is less noisy than the two legitimate receivers. It is known that the joint secrecy constraints can not be fulfilled under this scenario, however, we manage to establish a non vanishing capacity region for the individual secrecy case.

The broadcast channel with confidential messages (BCC) consists of one transmitter and two receivers, where the transmitter sends a common message to both receivers and, at the same time, a confidential message to one receiver which has to be kept secret from the other one. In this paper, this communication scenario is studied for compound channels, where it is only known to the transmitter and receivers that the actual channel realization is fixed and from a prespecified set of channels. The information theoretic criterion of strong secrecy is analyzed in detail and its impact on the decoding performance of the non-legitimate receiver is characterized. In particular, it is shown that regardless of the computational capabilities and the applied decoding strategy of the non-legitimate receiver, his decoding error always tends to one. This gives a valuable signal processing implication of the strong secrecy criterion and identifies desirable properties of an optimal code design. Further, an achievable strong secrecy rate region is derived and a multiletter outer bound is given. Both together yield a multiletter expression of the strong secrecy capacity region of the compound BCC.

In this paper, the discrete memoryless arbitrarily varying broadcast channel (AVBC) with receiver side information is studied and its random code and deterministic code capacity regions are derived for the average error criterion. In addition, it is analyzed for deterministic list codes and it is shown that the corresponding list capacity region displays a behavior, which is similar to Ahlswede's famous dichotomy result for the single-user arbitrarily varying channel: it either equals the random code capacity region or otherwise has an empty interior. This is characterized in terms of list sizes at the receivers and an appropriate concept of symmetrizability for the AVBC with receiver side information. The scenario studied here is motivated by the broadcast phase of bidirectional relaying, where a half-duplex relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. The relay decodes the messages both nodes have sent in the initial multiple access phase and broadcasts a re-encoded composition of them in the succeeding broadcast phase. Then, the broadcast phase corresponds to the AVBC with receiver side information, which differs from the classical broadcast channel, since both receivers can exploit their own messages from the previous phase as side information for decoding.

The wiretap channel models the communication scenario where two legitimate users want to communicate in such a way that an external wiretapper is kept ignorant. In this paper, the wiretap channel with side information is studied, where the wiretapper has additional side information about the transmitted message available for post-processing. The secrecy of the message is modeled by the decoding performance of the wiretapper. It is required for the wiretapper to have worst behavior of decoding performance regardless of the decoding strategy that is used. The secrecy capacity is derived and shown to be equal to the one of the classical wiretap channel without side information available at the wiretapper. Further, the corresponding optimal transceiver design is characterized.

The wiretap channel models the communication scenario where two legitimate users want to communicate in such a way that an external wiretapper is kept ignorant. In this paper the wiretap channel with side information is studied, where the wiretapper has additional side information about the transmitted message available for decoding. The corresponding secrecy capacity is derived and shown to be equal to the one of the classical wiretap channel without side information available at the wiretapper. Further, the capacity-achieving code structure is analyzed and properties are identified. Finally, channel uncertainty is taken into account and the results are extended to the compound wiretap channel with side information.

Availability of channel state information, especially to non-legitimate users, is one major challenge for secure communication in wireless systems. For arbitrarily varying channels (AVC), coordination resources such as common randomness have been shown to be important for reliable communication; especially for symmetrizable AVCs. In this paper, the arbitrarily varying wiretap channel (AVWC) with active wiretapper is studied. Such an wiretapper may or may not exploit his knowledge about the coordination resources to control the channel conditions. Secrecy capacity results are derived for different forms of coordination resources including common randomness and correlated sources. Finally, it is demonstrated how two orthogonal AVWCs, each with zero secrecy capacity, i.e., useless for secure transmission, can be super-activated to a useful channel allowing for secure communication at non-zero secrecy rates.

The compound MIMO Gaussian wiretap channel is studied, where the channel to the legitimate receiver is known and the eavesdropper channel is not known to the transmitter but is known to have a bounded spectral norm (channel gain). The compound secrecy capacity is established without the de-gradedness assumption and the optimal signaling is identified: the compound capacity equals the worst-case channel capacity thus establishing the saddle-point property, the optimal signaling is Gaussian and on the eigenvectors of the legitimate channel and the worst-case eavesdropper is isotropic. The eigenmode power allocation somewhat resembles the standard water-filling but is not identical to it.

The integration of multiple services such as the transmission of private, common, and confidential messages at the physical layer is becoming important for future wireless networks in order to increase spectral efficiency. In this paper, bidirectional relay networks are considered, in which a relay node establishes bidirectional communication between two other nodes using a decode-and-forward protocol. In the broadcast phase, the relay transmits additional common and confidential messages, which then requires the study of the bidirectional broadcast channel (BBC) with common and confidential messages. This channel generalizes the broadcast channel with receiver side information considered by Kramer and Shamai. Low complexity polar codes are constructed that achieve the capacity region of both the degraded symmetric BBC, and the BBC with common and confidential messages. The use of polar codes allows an intuitive interpretation of how to incorporate receiver side information and secrecy constraints as different sets of frozen bits at the different receivers for an optimal code design. In order to show that the constructed codes achieve capacity, a tighter bound on the cardinality of an auxiliary random variable used in the converse is found using a method by Salehi.

The wiretap channel models the communication scenario where two legitimate users want to communicate in such a way that a wiretapper is kept ignorant. In this paper, the wiretap channel with side information is studied, where the wiretapper has additional side information available. This side information allows the wiretapper to restrict the transmitted message to a certain subset of messages before further postprocessing. Two different criteria are employed to model the secrecy of the confidential message: the information theoretic criterion of strong secrecy and a signal-processing-inspired criterion based on the decoding performance of the wiretapper. For the latter, the wiretapper is required to have the worst decoding performance regardless of the specific decoding strategy that is used. It is shown that both criteria are equivalent in terms of secrecy capacity. Furthermore, the secrecy capacity equals the one of the classical wiretap channel without side information available at the wiretapper. In addition, the corresponding capacity-achieving code structure and optimal transceiver design are characterized and properties are identified. Finally, extensions to channel uncertainty and multiple wiretappers are discussed.

The classical wiretap channel models secure communication in the presence of a nonlegitimate wiretapper who has to be kept ignorant. Traditionally, the wiretapper is passive in the sense that he only tries to eavesdrop the communication using his received channel output. In this paper, more powerful active wiretappers are studied. In addition to eavesdropping, these wiretappers are able to influence the communication conditions of all users by controlling the corresponding channel states. Since legitimate transmitters and receivers do not know the actual channel realization or the wiretapper's strategy of influencing the channel states, they are confronted with arbitrarily varying channel (AVC) conditions. The corresponding secure communication scenario is, therefore, given by the arbitrarily varying wiretap channel (AVWC). In the context of AVCs, common randomness (CR) has been shown to be an important resource for establishing reliable communication, in particular, if the AVC is symmetrizable. But availability of CR also affects the strategy space of an active wiretapper as he may or may not exploit the common randomness for selecting the channel states. Several secrecy capacity results are derived for the AVWC. In particular, the CR-assisted secrecy capacity of the AVWC with an active wiretapper exploiting CR is established and analyzed in detail. Finally, it is demonstrated for active wiretappers how two orthogonal AVWCs, each useless for transmission of secure messages, can be super-activated to a useful channel allowing for secure communication at nonzero secrecy rates. To the best of our knowledge, this is not possible for passive wiretappers and, further, provides the first example of such super-activation, which has been expected to appear only in the area of quantum communication. Such knowledge is particularly important as it provides valuable insights for the design and the medium access control of future wireless communication systems.

To increase the spectral efficiency of future wireless networks, it is important to wisely integrate multiple services at the physical layer. Here the efficient integration of confidential services in the three-node bidirectional relay channel is studied. A relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol, which is also known as two-way relaying. In the broadcast phase, the relay transmits not only the two bidirectional messages it received in the previous multiple access phase, but also an additional confidential message to one node while keeping the other node completely ignorant of it. The concept of strong information theoretic secrecy is used to ensure that the nonlegitimate node cannot decode the confidential message no matter what its computational resources are. Moreover, this implies that the average decoding error at the nonlegitimate node goes exponentially fast to one for any decoding strategy it may use. This results in the study of the bidirectional broadcast channel with confidential messages for which the strong secrecy capacity region is established. Furthermore, it is shown that the efficient integration of confidential messages with strong secrecy extends to such scenarios, where the relay further transmits an additional common message to both nodes.

In this paper the compound broadcast channel with confidential messages is studied, where it is only known to the transmitter and receivers that the actual channel realization is fixed and from a pre-specified set of channels. An achievable rate region for the strong secrecy criterion is derived. Further, a multi-letter outer bound is given, which establishes, together with the achievable rate region, a multi-letter expression of the strong secrecy capacity region.

In this work, the bidirectional broadcast channel (BBC) with confidential messages is studied. The problem is motivated by the concept of bidirectional relaying in a three-node network, where a half-duplex relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol and thereby transmits additional confidential information to one of them in the broadcast phase. The corresponding confidential message is transmitted at a certain secrecy level which characterizes the amount of information that can be kept secret from the non-legitimate node. The capacity-equivocation and secrecy capacity regions of the BBC with confidential messages are established where the latter characterizes the communication scenario with perfect secrecy, which means that the confidential information is completely hidden from the non-legitimate node. Thereby, it is shown that the optimal processing exploits ideas and concepts of the BBC with common messages and of the classical broadcast channel with confidential messages.

In order to increase spectral efficiency, it is becoming more and more important that next generation wireless networks wisely integrate multiple services such as transmissions of private, common, and confidential messages at the physical layer. This is referred to as physical layer service integration, and in this paper is being studied for bidirectional relay networks. Here, a relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. This is also known as two-way relaying. In the broadcast phase, the relay efficiently integrates additional common and confidential services at the physical layer, which then requires the study of the bidirectional broadcast channel (BBC) with common and confidential messages. The entire secrecy capacity regions for discrete memoryless and MIMO Gaussian channels are established. These results further unify previous partial results such as the BBC with common messages or the classical broadcast channel with common and confidential messages, where the relay node provides only some of the services.

Recent research developments show that the concept of bidirectional relaying significantly improves the performance in wireless networks. This applies to three-node networks, where a half-duplex relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. In this work we consider the scenario when in the broadcast phase the relay transmits additional confidential information to one node, which should be kept as secret as possible from the other, non-intended node. This is the bidirectional broadcast channel with confidential messages for which we derive the capacity-equivocation region and the secrecy capacity region. The latter characterizes the communication scenario with perfect secrecy, where the confidential message is completely hidden from the non-legitimated node.

In this work, we study the bidirectional broadcast channel with common and confidential messages and establish the capacity-equivocation and secrecy capacity regions. This problem is motivated by the concept of bidirectional relaying in a three-node network, where a relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol and thereby efficiently integrates additional common and confidential services.

In this work, the MIMO Gaussian bidirectional broadcast channel (BBC) with common messages is studied. The problem is motivated by the concept of bidirectional relaying in a three-node network, where a half-duplex relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol and thereby adds an own multicast message to the communication. The capacity region of the broadcast phase is derived and the corresponding transmit covariance matrix optimization problem is analyzed in detail. Thereby, it is shown that the transmit covariance optimization problem is strongly connected to the corresponding one of the MIMO Gaussian BBC without common messages. In particular, this knowledge can be exploited to transfer results such as optimal transmit strategies from one scenario to the other one.

In this work, we study the MIMO Gaussian bidirectional broadcast channel (BBC) with common message and characterize the capacity region. Moreover, we show that the transmit covariance matrix optimization problem has the same structure as the corresponding optimization problem of the BBC without common message which leads to the comfortable position to transfer results from one scenario to the other. This problem is motivated by the concept of bidirectional relaying in a three-node network, where a half-duplex relay node establishes a bidirectional communication between two other nodes and thereby adds an own multicast message to the communication.

The concept of bidirectional relaying is a key technique to improve the performance in wireless networks such as sensor, ad-hoc, and even cellular systems. It applies to three-node networks, where a relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. We assume that the communication is disturbed by unknown varying interference and analyze the impact of the degree of coordination. We show that the unknown variation of the interference has a dramatic impact on the communication. For traditional interference coordination it can lead to channels which completely prohibit any reliable communication. Anyhow, by allowing a relay-to-receivers coordination, communication can also be established in such situations where the traditional approach fails.

The concept of bidirectional relaying shows the potential to improve the performance in wireless networks such as sensor, ad-hoc, and even cellular systems. It applies to three-node networks, where a relay node establishes a bidirectional communication between two other nodes. In the first phase of a decode-and-forward protocol, the two nodes transmit their messages to a relay node, which decodes them. In the succeeding bidirectional broadcast phase, the relay broadcasts a re-encoded composition of them so that both nodes can decode the other's message using their own message as side information. We assume that the transmission is affected by unknown varying channels. Unfortunately, the unknown variation of the channel can lead to channels which completely prohibit any reliable communication. In this work, we analyze the bidirectional broadcast phase under list decoding and show that this decoding technique can improve the performance significantly in the sense that it allows to transmit reliably in scenarios where usual decoding schemes fail.

The concept of bidirectional relaying is a key technique to improve the performance in future wireless networks. It applies to three-node networks, where a relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. It divides the whole communication into two phases, namely the multiple access and bidirectional broadcast phase. Here, we concentrate on the second phase, which is also known as the bidirectional broadcast channel, and assume that the transmission is affected by arbitrarily varying channels. We impose constraints on the permissible input and state sequences and derive the capacity regions for random and deterministic coding.

Bidirectional relaying is a promising approach to improve the performance in wireless networks such as sensor, ad-hoc, and even cellular systems. Bidirectional relaying applies to three-node networks, where a relay establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. First, the two nodes transmit their messages to the relay which decodes them. Then, the relay broadcasts a reencoded message in such a way that both nodes can decode their intended message using their own message as side information. We consider uncertainty in the channel state information (CSI) and assume that all nodes only know that the channel over which the transmission takes place is from a pre-specified set of channels. In this work, we concentrate on the second phase, which is called the compound bidirectional broadcast channel. We present a robust coding strategy which enables reliable communication under channel uncertainty and show that this strategy actually achieves the compound capacity. Further, we analyze scenarios where either the receivers or the transmitter have perfect CSI. We show that CSI at the receivers does not affect the maximal achievable rates, while CSI at the transmitter improves the capacity region. A numerical example and a game-theoretic interpretation complete this work.

In this work we study optimal coding strategies for bidirectional relaying under the condition of arbitrarily varying channels. We consider a three-node network where a relay node establishes a bidirectional communication between two nodes using a spectrally efficient decode-and-forward protocol. In the first phase the two nodes transmit their messages to the relay node, which decodes them. In the succeeding bidirectional broadcast phase the relay node broadcasts an optimal re-encoded composition of them so that both nodes can decode the intended message using their own message as side information. We assume that the whole communication is affected by channels which vary in an unknown and arbitrary manner during the transmission so that all nodes have only imperfect channel state information. For both phases of the bidirectional relaying protocol we present robust coding strategies, which mitigate the uncertainty in channel state information so that reliable communication can be guaranteed. Further, we characterize the corresponding capacity regions for random and deterministic coding strategies.

In this work the transmit covariance matrix optimization problem for the MIMO Gaussian bidirectional broadcast channel is studied. A half-duplex relay node establishes bidirectional communication between two nodes using a decode-and-forward protocol. In the initial multiple access phase both nodes transmit their messages to the relay node. In the succeeding phase the relay broadcasts an optimal re-encoded message so that both nodes can decode the other's message using their own message as side information. We show that if the channels are orthogonal then there exist equivalent transmit strategies with different ranks. The study of special cases reveals some of the difficult structure of the optimal solution. In particular a closed form procedure for the case of full rank transmission for invertible channels is derived. Moreover, for parallel channels the optimal solution is completely characterized and discussed.

We consider the broadcast phase of a spectrally efficient two-phase decode-and-forward protocol which is used by a relay node to establish a bidirectional communication between two nodes. In the first phase the two nodes transmit their message to the relay node which decodes the messages. In the succeeding phase the relay node broadcasts a re-encoded composition of them. We consider imperfect channel knowledge and assume that all nodes merely know that the channel used for the transmission belongs to a set of channels. This is called compound bidirectional broadcast channel. We derive a universal strategy which achieves capacity and show that perfect channel state information (CSI) at the receivers does not lead to an increased capacity region. Otherwise, perfect CSI at the transmitter can advantageously be used to enlarge the capacity region. Finally, we give a game-theoretic interpretation as a game against nature.

In this work the transmit covariance matrix optimization problem for the discrete memoryless MIMO Gaussian bidirectional broadcast channel is studied. A half-duplex relay node establishes bidirectional communication between two nodes using a decode-and-forward protocol. In the initial multiple access phase both nodes transmit their messages to the relay node. In the succeeding phase the relay broadcasts an optimal re-encoded message so that both nodes can decode the other's message using their own message as side information. The capacity region of the bidirectional broadcast channel is completely characterized by a weighted rate sum maximization problem, which can be solved by a simple iterative fixed point algorithm. If an efficient transmit covariance matrix is invariant with respect to the joint subspace spanned by the channels, then different combinations of the part transmitted on the orthogonal subspaces result in equivalent transmit strategies with different ranks. A closed-form procedure to obtain the optimal transmit covariance is derived for the case where the rank of the channels is equal to the number of antennas at the relay node and a full-rank transmission is optimal. It shows the complicated structure of the optimal eigenspace, which depends on the weights and the mean transmit power constraint. For parallel channels the optimal solution is completely characterized and discussed, which also solves the optimal power allocation problem for a single-antenna OFDM system.

We consider the broadcast phase of a three-node network, where a relay node establishes a bidirectional communication between two nodes using a spectrally efficient two-phase decode-and-forward protocol. In the first phase the two nodes transmit their messages to the relay node. Then the relay node decodes the messages and broadcasts a re-encoded composition of them in the second phase. We consider Gaussian MIMO channels and determine the capacity region for the second phase which we call the Gaussian MIMO bidirectional broadcast channel.

We consider a three-node network, where a relay node establishes a bidirectional communication between two nodes using a two-phase decode-and-forward protocol. In the first phase the two nodes transmit their messages to the relay node which decodes them. Then the relay broadcasts the information to both nodes in the succeeding phase which we call the bidirectional broadcast channel. In this work we first consider both phases separately and compare existing strategies especially for the second phase. We determine the capacity region of the bidirectional broadcast channel and discuss the impact of multiple antennas and the correlation between the channels on the capacity region. We show how the available spectral resources can be shared between the two phases and compare achievable rate regions for the whole bidirectional communication. Finally, we indicate how the bidirectional relay communication and the knowledge about the corresponding rate region can be advantageously used in cellular systems or cross-layer designs.