arXiv subjects

Rafael F. Schaefer

Publications and source records attributed to Rafael F. Schaefer.

At least 37 records · Page 2Linked to original sources

arXiv2025

Semantic Communication: From Philosophical Conceptions Towards a Mathematical Framework

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).

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arXiv2025

Frequency Hopping Waveform Design for Secure Integrated Sensing and Communications

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 (PRI) agility (RPA) techniques. The combination of these techniques, which we refer to collectively as random frequency and PRI agility (RFPA), with channel reciprocity-based key generation (CRKG) obfuscates both Doppler frequency and PRIs, significantly hindering the chances that passive adversaries can successfully 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 increase the achievable bit rate of the system significantly. 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 ensures secure code creation without a coordinating authority. The improved range and velocity estimation and reduced clutter effects achieved with the method are demonstrated via the evaluation of the ambiguity function (AF) of the proposed waveforms.

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arXiv2025

Modular Neural Wiretap Codes for Fading Channels

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.

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arXiv2025

Leveraging Angle of Arrival Estimation against Impersonation Attacks in Physical Layer Authentication

In this paper, we investigate the utilization 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 common 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 impersonation attacks. In this work, we demonstrate that an impersonation attack targeting AoA based PLA is only feasible under strict conditions on the attacker's location and hardware capabilities, which highlights the AoA's potential as a strong feature for PLA. 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 in which a successful impersonation attack can be mounted. Furthermore, we leverage extensive simulations in support of theoretical analyses, to validate the robustness of AoA-based PLA.

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arXiv2025

MinGRU-Based Encoder for Turbo Autoencoder Frameworks

Early neural channel coding approaches leveraged dense neural networks with one-hot encodings to design adaptive encoder-decoder pairs, improving block error rate (BLER) and automating the design process. However, these methods struggled with scalability as the size of message sets and block lengths increased. TurboAE addressed this challenge by focusing on bit-sequence inputs rather than symbol-level representations, transforming the scalability issue associated with large message sets into a sequence modeling problem. While recurrent neural networks (RNNs) were a natural fit for sequence processing, their reliance on sequential computations made them computationally expensive and inefficient for long sequences. As a result, TurboAE adopted convolutional network blocks, which were faster to train and more scalable, but lacked the sequential modeling advantages of RNNs. Recent advances in efficient RNN architectures, such as minGRU and minLSTM, and structured state space models (SSMs) like S4 and S6, overcome these limitations by significantly reducing memory and computational overhead. These models enable scalable sequence processing, making RNNs competitive for long-sequence tasks. In this work, we revisit RNNs for Turbo autoencoders by integrating the lightweight minGRU model with a Mamba block from SSMs into a parallel Turbo autoencoder framework. Our results demonstrate that this hybrid design matches the performance of convolutional network-based Turbo autoencoder approaches for short sequences while significantly improving scalability and training efficiency for long block lengths. This highlights the potential of efficient RNNs in advancing neural channel coding for long-sequence scenarios.

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arXiv2025

Characterization of the Arithmetic Complexity of the Secrecy Capacity of Fast-Fading Gaussian Channels

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 or not. To address this question, the concept of Turing machines is used, which establishes 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 arithmetical hierarchy, revealing the absence of computable achievability and converse bounds.

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arXiv2024

Secure Integrated Sensing and Communication Under Correlated Rayleigh Fading

We consider a secure integrated sensing and communication (ISAC) scenario, in which a signal is transmitted through a state-dependent wiretap channel with one legitimate receiver with which the transmitter communicates and one honest-but-curious target that the transmitter wants to sense. The secure ISAC channel is modeled as two state-dependent fast-fading channels with correlated Rayleigh fading coefficients and independent additive Gaussian noise components. Delayed channel outputs are fed back to the transmitter to improve the communication performance and to estimate the channel state sequence. We establish and illustrate an achievable secrecy-distortion region for degraded secure ISAC channels under correlated Rayleigh fading. We also evaluate the inner bound for a large set of parameters to derive practical design insights for secure ISAC methods. The presented results include in particular parameter ranges for which the secrecy capacity of a classical wiretap channel setup is surpassed and for which the channel capacity is approached.

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arXiv2024

Finite Blocklength Performance of Capacity-achieving Codes in the Light of Complexity Theory

Since the work of Polyanskiy, Poor and Verdú on the finite blocklength performance of capacity-achieving codes for discrete memoryless channels, many papers have attempted to find further results for more practically relevant channels. However, it seems that the complexity of computing capacity-achieving codes has not been investigated until now. We study this question for the simplest non-trivial Gaussian channels, i.e., the additive colored Gaussian noise channel. To assess the computational complexity, we consider the classes $\mathrm{FP}_1$ and $\#\mathrm{P}_1$. $\mathrm{FP}_1$ includes functions computable by a deterministic Turing machine in polynomial time, whereas $\#\mathrm{P}_1$ encompasses functions that count the number of solutions verifiable in polynomial time. It is widely assumed that $\mathrm{FP}_1\neq\#\mathrm{P}_1$. It is of interest to determine the conditions under which, for a given $M \in \mathbb{N}$, where $M$ describes the precision of the deviation of $C(P,N)$, for a certain blocklength $n_M$ and a decoding error $ε> 0$ with $ε\in\mathbb{Q}$, the following holds: $R_{n_M}(ε)>C(P,N)-\frac{1}{2^M}$. It is shown that there is a polynomial-time computable $N_*$ such that for sufficiently large $P_*\in\mathbb{Q}$, the sequences $\{R_{n_M}(ε)\}_{{n_M}\in\mathbb{N}}$, where each $R_{n_M}(ε)$ satisfies the previous condition, cannot be computed in polynomial time if $\mathrm{FP}_1\neq\#\mathrm{P}_1$. Hence, the complexity of computing the sequence $\{R_{n_M}(ε)\}_{n_M\in\mathbb{N}}$ grows faster than any polynomial as $M$ increases. Consequently, it is shown that either the sequence of achievable rates $\{R_{n_M}(ε)\}_{n_M\in\mathbb{N}}$ as a function of the blocklength, or the sequence of blocklengths $\{n_M\}_{M\in\mathbb{N}}$ corresponding to the achievable rates, is not a polynomial-time computable sequence.

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arXiv2024

Diffusion Models for Accurate Channel Distribution Generation

Strong generative models can accurately learn channel distributions. This could save recurring costs for physical measurements of the channel. Moreover, the resulting differentiable channel model supports training neural encoders by enabling gradient-based optimization. The initial approach in the literature draws upon the modern advancements in image generation, utilizing generative adversarial networks (GANs) or their enhanced variants to generate channel distributions. In this paper, we address this channel approximation challenge with diffusion models (DMs), which have demonstrated high sample quality and mode coverage in image generation. In addition to testing the generative performance of the channel distributions, we use an end-to-end (E2E) coded-modulation framework underpinned by DMs and propose an efficient training algorithm. Our simulations with various channel models show that a DM can accurately learn channel distributions, enabling an E2E framework to achieve near-optimal symbol error rates (SERs). Furthermore, we examine the trade-off between mode coverage and sampling speed through skipped sampling using sliced Wasserstein distance (SWD) and the E2E SER. We investigate the effect of noise scheduling on this trade-off, demonstrating that with an appropriate choice of parameters and techniques, sampling time can be significantly reduced with a minor increase in SWD and SER. Finally, we show that the DM can generate a correlated fading channel, whereas a strong GAN variant fails to learn the covariance. This paper highlights the potential benefits of using DMs for learning channel distributions, which could be further investigated for various channels and advanced techniques of DMs.

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arXiv2024

Secret Key Generation Rates for Line of Sight Multipath Channels in the Presence of Eavesdroppers

In this paper, the feasibility of implementing a lightweight key distribution scheme using physical layer security for secret key generation (SKG) is explored. Specifically, we focus on examining SKG with the received signal strength (RSS) serving as the primary source of shared randomness. Our investigation centers on a frequency-selective line-of-sight (LoS) multipath channel, with a particular emphasis on assessing SKG rates derived from the distributions of RSS. We derive the received signal distributions based on how the multipath components resolve at the receiver. The mutual information (MI) is evaluated based on LoS 3GPP channel models using a numerical estimator. We study how the bandwidth, delay spread, and Rician K-factor impact the estimated MI. This MI then serves as a benchmark setting bounds for the SKG rates in our exploration.

eess.SP↗

arXiv2024

Generalized Rainbow Differential Privacy

We study a new framework for designing differentially private (DP) mechanisms via randomized graph colorings, called rainbow differential privacy. In this framework, datasets are nodes in a graph, and two neighboring datasets are connected by an edge. Each dataset in the graph has a preferential ordering for the possible outputs of the mechanism, and these orderings are called rainbows. Different rainbows partition the graph of connected datasets into different regions. We show that if a DP mechanism at the boundary of such regions is fixed and it behaves identically for all same-rainbow boundary datasets, then a unique optimal $(ε,δ)$-DP mechanism exists (as long as the boundary condition is valid) and can be expressed in closed-form. Our proof technique is based on an interesting relationship between dominance ordering and DP, which applies to any finite number of colors and for $(ε,δ)$-DP, improving upon previous results that only apply to at most three colors and for $ε$-DP. We justify the homogeneous boundary condition assumption by giving an example with non-homogeneous boundary condition, for which there exists no optimal DP mechanism.

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arXiv2024

Reliability and Latency Analysis for Wireless Communication Systems with a Secret-Key Budget

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.

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arXiv2023

Learning End-to-End Channel Coding with Diffusion Models

It is a known problem that deep-learning-based end-to-end (E2E) channel coding systems depend on a known and differentiable channel model, due to the learning process and based on the gradient-descent optimization methods. This places the challenge to approximate or generate the channel or its derivative from samples generated by pilot signaling in real-world scenarios. Currently, there are two prevalent methods to solve this problem. One is to generate the channel via a generative adversarial network (GAN), and the other is to, in essence, approximate the gradient via reinforcement learning methods. Other methods include using score-based methods, variational autoencoders, or mutual-information-based methods. In this paper, we focus on generative models and, in particular, on a new promising method called diffusion models, which have shown a higher quality of generation in image-based tasks. We will show that diffusion models can be used in wireless E2E scenarios and that they work as good as Wasserstein GANs while having a more stable training procedure and a better generalization ability in testing.

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arXiv2023

Characterization of the Complexity of Computing the Capacity of Colored Noise Gaussian Channels

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 $\#\mathrm{P}_1$-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 $\mathrm{NP}_1$-complete. Additionally, it is shown that the capacity-achieving distribution is also $\#\mathrm{P}_1$-complete. Furthermore, under the widely accepted assumption that $\mathrm{FP}_1 \neq \#\mathrm{P}_1$, 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.

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arXiv2023

Algorithmic Computability of the Capacity of Gaussian Channels with Colored Noise

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. t 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.

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arXiv2023

Algorithmic Computability and Approximability of Capacity-Achieving Input Distributions

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.

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arXiv2023

Concatenated Classic and Neural (CCN) Codes: ConcatenatedAE

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.

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arXiv2023

Secure Integrated Sensing and Communication

This work considers the problem of mitigating information leakage between communication and sensing in systems jointly performing both operations. Specifically, a discrete memoryless state-dependent broadcast channel model is studied in which (i) the presence of feedback enables a transmitter to convey information, while simultaneously performing channel state estimation; (ii) one of the receivers is treated as an eavesdropper whose state should be estimated but which should remain oblivious to 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 key attribute, e.g., location. For independent and identically distributed 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 partial 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 binary joint communication and sensing models.

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