arXiv subjects

Holger Boche

Publications and source records attributed to Holger Boche.

At least 127 records · Page 7Linked to original sources

arXiv2023

Communication with Unreliable Entanglement Assistance

Entanglement resources can increase transmission rates substantially. Unfortunately, entanglement is a fragile resource that is quickly degraded by decoherence effects. In order to generate entanglement for optical communication, the transmitter and the receiver first prepare entangled spin-photon pairs locally, and then the photon at the transmitter is sent to the receiver through an optical fiber or free space. Without feedback, the transmitter does not know whether the entangled photon has reached the receiver. The present work introduces a new model of unreliable entanglement assistance, whereby the communication system operates whether entanglement assistance is present or not. While the sender is ignorant, the receiver knows whether the entanglement generation was successful. In the case of a failure, the receiver decodes less information. In this manner, the effective transmission rate is adapted according to the assistance status. Regularized formulas are derived for the classical and quantum capacity regions with unreliable entanglement assistance, characterizing the tradeoff between the unassisted rate and the excess rate that can be obtained from entanglement assistance. It is further established that time division between entanglement-assisted and unassisted coding strategies is optimal for the noiseless qubit channel, but can be strictly suboptimal for a noisy channel.

quant-ph↗

arXiv2023

Sensing-Assisted Receivers for Resilient-By-Design 6G MU-MIMO Uplink

We address the resilience of future 6G MIMO communications by considering an uplink scenario where multiple legitimate transmitters try to communicate with a base station in the presence of an adversarial jammer. The jammer possesses full knowledge about the system and the physical parameters of the legitimate link, while the base station only knows the UL-channels and the angle-of-arrival (AoA) of the jamming signals. Furthermore, the legitimate transmitters are oblivious to the fact that jamming takes place, thus the burden of guaranteeing resilience falls on the receiver. For this case we derive one optimal jamming strategy that aims to minimize the rate of the strongest user and multiple receive strategies, one based on a lower bound on the achievable signal-to-interference-to-noise-ratio (SINR), one based on a zero-forcing (ZF) design, and one based on a minimum SINR constraint. Numerical studies show that the proposed anti-jamming approaches ensure that the sum rate of the system is much higher than without protection, even when the jammer has considerably more transmit power and even if the jamming signals come from the same direction as those of the legitimate users.

eess.SP↗

arXiv2023

Optimal and Robust Waveform Design for MIMO-OFDM Channel Sensing: A Cramér-Rao Bound Perspective

Wireless channel sensing is one of the key enablers for integrated sensing and communication (ISAC) which helps communication networks understand the surrounding environment. In this work, we consider MIMO-OFDM systems and aim to design optimal and robust waveforms for accurate channel parameter estimation given allocated OFDM resources. The Fisher information matrix (FIM) is derived first, and the waveform design problem is formulated by maximizing the log determinant of the FIM. We then consider the uncertainty in the parameters and state the stochastic optimization problem for a robust design. We propose the Riemannian Exact Penalty Method via Smoothing (REPMS) and its stochastic version SREPMS to solve the constrained non-convex problems. In simulations, we show that the REPMS yields comparable results to the semidefinite relaxation (SDR) but with a much shorter running time. Finally, the designed robust waveforms using SREMPS are investigated, and are shown to have a good performance under channel perturbations.

cs.IT↗

arXiv2023

Computability of Optimizers

Optimization problems are a staple of today's scientific and technical landscape. However, at present, solvers of such problems are almost exclusively run on digital hardware. Using Turing machines as a mathematical model for any type of digital hardware, in this paper, we analyze fundamental limitations of this conceptual approach of solving optimization problems. Since in most applications, the optimizer itself is of significantly more interest than the optimal value of the corresponding function, we will focus on computability of the optimizer. In fact, we will show that in various situations the optimizer is unattainable on Turing machines and consequently on digital computers. Moreover, even worse, there does not exist a Turing machine, which approximates the optimizer itself up to a certain constant error. We prove such results for a variety of well-known problems from very different areas, including artificial intelligence, financial mathematics, and information theory, often deriving the even stronger result that such problems are not Banach-Mazur computable, also not even in an approximate sense.

math.OC↗

arXiv2022

Deterministic Identification For MC ISI-Poisson Channel

Several applications of molecular communications (MC) feature an alarm-prompt behavior for which the prevalent Shannon capacity may not be the appropriate performance metric. The identification capacity as an alternative measure for such systems has been motivated and established in the literature. In this paper, we study deterministic identification (DI) for the discrete-time \emph{Poisson} channel (DTPC) with inter-symbol interference (ISI) where the transmitter is restricted to an average and a peak molecule release rate constraint. Such a channel serves as a model for diffusive MC systems featuring long channel impulse responses and employing molecule counting receivers. We derive lower and upper bounds on the DI capacity of the DTPC with ISI when the number of ISI channel taps $K$ may grow with the codeword length $n$ (e.g., due to increasing symbol rate). As a key finding, we establish that for deterministic encoding, the codebook size scales as $2^{(n\log n)R}$ assuming that the number of ISI channel taps scales as $K = 2^{κ\log n}$, where $R$ is the coding rate and $κ$ is the ISI rate. Moreover, we show that optimizing $κ$ leads to an effective identification rate [bits/s] that scales linearly with $n$, which is in contrast to the typical transmission rate [bits/s] that is independent of $n$.

cs.IT↗

arXiv2022

Semantic Security for Quantum Wiretap Channels

We consider the problem of semantic security via classical-quantum and quantum wiretap channels and use explicit constructions to transform a non-secure code into a semantically secure code, achieving capacity by means of biregular irreducible functions. Explicit parameters in finite regimes can be extracted from theorems. We also generalize the semantic security capacity theorem, which shows that a strongly secure code guarantees a semantically secure code with the same secrecy rate, to any quantum channel, including the infinite-dimensional and non-Gaussian ones.

quant-ph↗

arXiv2022

Secure and Private Source Coding with Private Key and Decoder Side Information

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.

cs.IT↗

arXiv2022

Neuromorphic Twins for Networked Control and Decision-Making

We consider the problem of remotely tracking the state of and unstable linear time-invariant plant by means of data transmitted through a noisy communication channel from an algorithmic point of view. Assuming the dynamics of the plant are known, does there exist an algorithm that accepts a description of the channel's characteristics as input, and returns 'Yes' if the transmission capabilities permit the remote tracking of the plant's state, 'No' otherwise? Does there exist an algorithm that, in case of a positive answer, computes a suitable encoder/decoder-pair for the channel? Questions of this kind are becoming increasingly important with regards to future communication technologies that aim to solve control engineering tasks in a distributed manner. In particular, they play an essential role in digital twinning, an emerging information processing approach originally considered in the context of Industry 4.0. Yet, the abovementioned questions have been answered in the negative with respect to algorithms that can be implemented on idealized digital hardware, i.e., Turing machines. In this article, we investigate the remote state estimation problem in view of the Blum-Shub-Smale computability framework. In the broadest sense, the latter can be interpreted as a model for idealized analog computation. Especially in the context of neuromorphic computing, analog hardware has experienced a revival in the past view years. Hence, the contribution of this work may serve as a motivation for a theory of neuromorphic twins as a counterpart to digital twins for analog hardware.

cs.IT↗

arXiv2022

On the Need of Neuromorphic Twins to Detect Denial-of-Service Attacks on Communication Networks

As we are more and more dependent on the communication technologies, resilience against any attacks on communication networks is important to guarantee the digital sovereignty of our society. New developments of communication networks tackle the problem of resilience by 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 the 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.

cs.IT↗

arXiv2022

Message Transmission and Common Randomness Generation over MIMO Slow Fading Channels with Arbitrary Channel State Distribution

We investigate the problem of message transmission and the problem of common randomness (CR) generation over single-user multiple-input multiple-output (MIMO) slow fading channels with average input power constraint, additive white Gaussian noise (AWGN), arbitrary state distribution and with complete channel state information available at the receiver side (CSIR). First, we derive a lower and an upper bound on the outage transmission capacity of MIMO slow fading channels for arbitrary state distribution and show that the bounds coincide except possibly at the points of discontinuity of the outage transmission capacity, of which there are, at most, countably many. To prove the lower bound on the outage transmission capacity, we also establish the capacity of a specific compound MIMO Gaussian channel. Second, we define the outage CR capacity for a two-source model with unidirectional communication over a MIMO slow fading channel with arbitrary state distribution and establish a lower and an upper bound on it using our bounds on the outage transmission capacity of the MIMO slow fading channel.

cs.IT↗

arXiv2022

Common Randomness Generation from Sources with Countable Alphabet

We study a standard two-source model for common randomness (CR) generation in which Alice and Bob generate a common random variable with high probability of agreement by observing independent and identically distributed (i.i.d.) samples of correlated sources on countably infinite alphabets. The two parties are additionally allowed to communicate as little as possible over a noisy memoryless channel. In our work, we give a single-letter formula for the CR capacity for the proposed model and provide a rigorous proof of it. This is a challenging scenario because some of the finite alphabet properties, namely of the entropy can not be extended to the countably infinite case. Notably, it is known that the Shannon entropy is in fact discontinuous at all probability distributions with countably infinite support.

cs.IT↗

arXiv2022

On the Need of Analog Signals and Systems for Digital-Twin Representations

We consider the task of converting different digital descriptions of analog bandlimited signals and systems into each other, with a rigorous application of mathematical computability theory. Albeit very fundamental, the problem appears in the scope of digital twinning, an emerging concept in the field of digital processing of analog information that is regularly mentioned as one of the key enablers for next-generation cyber-physical systems and their areas of application. In this context, we prove that essential quantities such as the peak-to-average power ratio and the bounded-input/bounded-output norm, which determine the behavior of the real-world analog system, cannot generally be determined from the system's digital twin, depending on which of the above-mentioned descriptions is chosen. As a main result, we characterize the algorithmic strength of Shannon's sampling type representation as digital twin implementation and also introduce a new digital twin implementation of analog signals and systems. We show there exist two digital descriptions, both of which uniquely characterize a certain analog system, such that one description can be algorithmically converted into the other, but not vice versa.

cs.IT↗

arXiv2022

A General Formula for Uniform Common Randomness Capacity

We generalize the uniform common randomness capacity formula, initially established by Ahslwede and Csiszár for a two-source model for common randomness generation from independent and identically distributed (i.i.d.) discrete sources with unidirectional communication over rate-limited discrete noiseless channels to the case when the one-way communication is over arbitrary single-user channels. In our proof, we will make use of the transmission capacity formula established by Verdú and Han for arbitrary point-to-point channels.

cs.IT↗

arXiv2022

A Single-Letter Capacity Formula for MIMO Gauss-Markov Rayleigh Fading Channels

Over the past decades, the problem of communication over finite-state Markov channels (FSMCs) has been investigated in many researches and the capacity of FSMCs has been studied in closed form under the assumption of the availability of partial/complete channel state information at the sender and/or the receiver. In our work, we focus on infinite-state Markov channels by investigating the problem of message transmission over time-varying single-user multiple-input multiple-output (MIMO) Gauss-Markov Rayleigh fading channels with average power constraint and with complete channel state information available at the receiver side (CSIR). We completely solve the problem by giving a single-letter characterization of the channel capacity in closed form and by providing a proof of it.

cs.IT↗

arXiv2022

On non-detectability of non-computability and the degree of non-computability of solutions of circuit and wave equations on digital computers

It is known that there exist mathematical problems of practical relevance which cannot be computed on a Turing machine. An important example is the calculation of the first derivative of continuously differentiable functions. This paper precisely classifies the non-computability of the first derivative, and of the maximum-norm of the first derivative in the Zheng-Weihrauch hierarchy. Based on this classification, the paper investigates whether it is possible that a Turing machine detects this non-computability of the first derivative by observing the data of the problem, and whether it is possible to detect upper bounds for the peak value of the first derivative of continuously differentiable functions. So from a practical point of view, the question is whether it is possible to implement an exit-flag functionality for observing non-computability of the first derivative. This paper even studies two different types of exit-flag functionality. A strong one, where the Turing machine always has to stop, and a weak one, where the Turing machine stops if and only if the input lies within the corresponding set of interest. It will be shown that non-computability of the first derivative is not detectable by a Turing machine for two concrete examples, namely for the problem of computing the input--output behavior of simple analog circuits and for solutions of the three-dimensional wave equation. In addition, it is shown that it is even impossible to detect an upper bound for the maximum norm of the first derivative. In particular, it is shown that all three problems are not even semidecidable. Finally, we briefly discuss implications of these results for analog and quantum computing.

cs.IT↗

arXiv2022

Arbitrarily Varying Wiretap Channels with Non-Causal Side Information at the Jammer

Secure communication in a potentially malicious environment becomes more and more important. The arbitrarily varying wiretap channel (AVWC) provides information theoretical bounds on how much information can be exchanged even in the presence of an active attacker. If the active attacker has non-causal side information, situations in which a legitimate communication system has been hacked, can be modeled. We investigate the AVWC with non-causal side information at the jammer for the case that there exists a best channel to the eavesdropper. Non-causal side information means that the transmitted codeword is known to an active adversary before it is transmitted. By considering the maximum error criterion, we allow also messages to be known at the jammer before the corresponding codeword is transmitted. A single letter formula for the common randomness secrecy capacity is derived. Additionally, we provide a single letter formula for the common randomness secrecy capacity, for the cases that the channel to the eavesdropper is strongly degraded, strongly noisier, or strongly less capable with respect to the main channel. Furthermore, we compare our results to the random code secrecy capacity for the cases of maximum error criterion but without non-causal side information at the jammer, maximum error criterion with non-causal side information of the messages at the jammer, and the case of average error criterion without non-causal side information at the jammer.

cs.IT↗

arXiv2022

A Rigorous Proof of the Capacity of MIMO Gauss-Markov Rayleigh Fading Channels

We investigate the problem of message transmission over time-varying single-user multiple-input multiple-output (MIMO) Rayleigh fading channels with average power constraint and with complete channel state information available at the receiver side (CSIR). To describe the channel variations over the time, we consider a first-order Gauss-Markov model. We completely solve the problem by giving a single-letter characterization of the channel capacity in closed form and by providing a rigorous proof of it.

cs.IT↗

arXiv2022

Deterministic Identification for Molecular Communications over the Poisson Channel

Various applications of molecular communications (MC) are event-triggered, and, as a consequence, the prevalent Shannon capacity may not be the right measure for performance assessment. Thus, in this paper, we motivate and establish the identification capacity as an alternative metric. In particular, we study deterministic identification (DI) for the discrete-time Poisson channel (DTPC), subject to an average and a peak power constraint, which serves as a model for MC systems employing molecule counting receivers. It is established that the codebook size for this channel scales as $2^{(n\log n)R}$, where $n$ and $R$ are the codeword length and coding rate, respectively. Lower and upper bounds on the DI capacity of the DTPC are developed. The obtained large capacity of the DI channel sheds light on the performance of natural DI systems such as natural olfaction, which are known for their extremely large chemical discriminatory power in biology. Furthermore, numerical simulations for the empirical miss-identification and false identification error rates are provided for finite length codes. This allows us to quantify the scale of error reduction in terms of the codeword length.

cs.IT↗