arXiv subjects

Holger Boche

Publications and source records attributed to Holger Boche.

At least 91 records · Page 5Linked to original sources

arXiv2024

Zero-entropy encoders and simultaneous decoders in identification via quantum channels

Motivated by deterministic identification via classical channels, where the encoder is not allowed to use randomization, we revisit the problem of identification via quantum channels but now with the additional restriction that the message encoding must use pure quantum states, rather than general mixed states. Together with the previously considered distinction between simultaneous and general decoders, this suggests a two-dimensional spectrum of different identification capacities, whose behaviour could a priori be very different. We demonstrate two new results as our main findings: first, we show that all four combinations (pure/mixed encoder, simultaneous/general decoder) have a double-exponentially growing code size, and that indeed the corresponding identification capacities are lower bounded by the classical transmission capacity for a general quantum channel, which is given by the Holevo-Schumacher-Westmoreland Theorem. Secondly, we show that the simultaneous identification capacity of a quantum channel equals the simultaneous identification capacity with pure state encodings, thus leaving three linearly ordered identification capacities. By considering some simple examples, we finally show that these three are all different: general identification capacity can be larger than pure-state-encoded identification capacity, which in turn can be larger than pure-state-encoded simultaneous identification capacity.

quant-ph↗

arXiv2024

Ning Cai: A Tribute to a Pioneering Scholar in Information Theory

It is with heavy hearts that we mourn the passing of Ning Cai, a luminary whose pioneering spirit illuminated the realms of network coding and beyond. On May 25, 2023, at the age of 75, Prof. Cai bid farewell, leaving behind a profound legacy that continues to resonate across generations of researchers. His contributions spanned a vast spectrum, from the groundbreaking explorations in network coding to the intricate realms of quantum information theory. Ning's indelible mark on the academic landscape is a testament to his unwavering dedication and relentless pursuit of knowledge. Among his many accolades, Ning's seminal works garnered widespread recognition, exemplified by the prestigious 2005 IEEE Information Theory Society Paper Award for his work "Linear Network Coding." Furthermore, his enduring impact was underscored by the 2018 ACM SIGMOBILE Test-of-Time Paper Award, bestowed upon his paper "Network Information Flow." In addition to his scholarly achievements, Ning's unwavering commitment to mentorship has left an indelible mark on countless aspiring scholars. His guidance and wisdom continue to inspire and guide future generations in their scholarly pursuits. As we bid farewell to a titan in the field, let us cherish the legacy of Ning Cai, whose brilliance and generosity of spirit will forever endure in the annals of academia.

cs.IT↗

arXiv2024

An Achievable Rate-Distortion Region for Joint State and Message Communication over Multiple Access Channels

This paper derives an achievable rate-distortion (R-D) region for the state-dependent discrete memoryless multiple access channel (SD-DMMAC), where the generalized feedback and causal side information are present at encoders, and the decoder performs the joint task of message decoding and state estimation. The Markov coding and backward-forward two-stage decoding schemes are adopted in the proof. This scenario is shown to be capable of modeling various integrated sensing and communication (ISAC) applications, including the monostatic-uplink system and multi-modal sensor networks, which are then studied as examples.

cs.IT↗

arXiv2024

Workshop on Information Theory and Related Fields -- In Memory of Ning Cai

Sadly, our esteemed colleague and friend Ning Cai passed away on 25th May, 2023. In his memory, Ingo Althöfer, Holger Boche, Christian Deppe, Jens Stoye, Ulrich Tamm, Andreas Winter, and Raymond Yeung have organized the "Workshop on Information Theory and Related Fields" at the Bielefeld ZiF (Center for Interdisciplinary Research). This special event will be held from 24th November to 26th November, 2023. The workshop aims to celebrate Ning Cai's remarkable contributions to the field of information theory and to provide a platform for discussing current research in related areas. Ning Cai's work has had a significant impact on many domains, and this gathering will bring together colleagues, collaborators, and young researchers who have been influenced by his pioneering efforts.

cs.IT↗

arXiv2024

On Effective Convergence in Fekete's Lemma and Related Combinatorial Problems in Information Theory

Fekete's lemma is a well known result from combinatorial mathematics that shows the existence of a limit value related to super- and subadditive sequences of real numbers. In this paper, we analyze Fekete's lemma in view of the arithmetical hierarchy of real numbers by Zheng and Weihrauch and fit the results into an information-theoretic context. We introduce special sets associated to super- and subadditive sequences and prove their effective equivalence to $Σ_1$ and $Π_1$. Using methods from the theory established by Zheng and Weihrauch, we then show that the limit value emerging from Fekete's lemma is, in general, not a computable number. Given a sequence that additionally satisfies non-negativity, we characterize under which conditions the associated limit value can be computed effectively and investigate the corresponding modulus of convergence. Subsidiarily, we prove a theorem concerning the structural differences between computable sequences of computable numbers and computable sequences of rational numbers. We close the paper by a discussion on how our findings affect common problems from information theory.

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arXiv2024

An Achievable Rate-Distortion Region of Joint Identification and Sensing for Multiple Access Channels

In contrast to Shannon transmission codes, the size of identification (ID) codes for discrete memoryless channels (DMCs) experiences doubly exponential growth with the block length when randomized encoding is used. Additional enhancements within the ID paradigm can be realized through supplementary resources such as quantum entanglement, common randomness (CR), and feedback. Joint transmission and sensing demonstrate significant benefits over separation-based methods. Inspired by the significant impact of feedback on the ID capacity, our work delves into the realm of joint ID and sensing (JIDAS) for state-dependent multiple access channels (SD-MACs) with noiseless strictly casual feedback. Here, the senders aim to convey ID messages to the receiver while simultaneously sensing the channel states. We establish a lower bound on the capacity-distortion region of the SD-MACs. An example shows that JIDAS outperforms the separation-based approach.

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arXiv2024

Identification via Gaussian Multiple Access Channels in the Presence of Feedback

We investigate message identification over a K-sender Gaussian multiple access channel (K-GMAC). Unlike conventional Shannon transmission codes, the size of randomized identification (ID) codes experiences a doubly exponential growth in the code length. Improvements in the ID approach can be attained through additional resources such as quantum entanglement, common randomness (CR), and feedback. It has been demonstrated that an infinite capacity can be attained for a single-user Gaussian channel with noiseless feedback, irrespective of the chosen rate scaling. We establish the capacity region of both the K-sender Gaussian multiple access channel (K-GMAC) and the K-sender state-dependent Gaussian multiple access channel (K-SD-GMAC) when strictly causal noiseless feedback is available.

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arXiv2024

Computability of Classification and Deep Learning: From Theoretical Limits to Practical Feasibility through Quantization

The unwavering success of deep learning in the past decade led to the increasing prevalence of deep learning methods in various application fields. However, the downsides of deep learning, most prominently its lack of trustworthiness, may not be compatible with safety-critical or high-responsibility applications requiring stricter performance guarantees. Recently, several instances of deep learning applications have been shown to be subject to theoretical limitations of computability, undermining the feasibility of performance guarantees when employed on real-world computers. We extend the findings by studying computability in the deep learning framework from two perspectives: From an application viewpoint in the context of classification problems and a general limitation viewpoint in the context of training neural networks. In particular, we show restrictions on the algorithmic solvability of classification problems that also render the algorithmic detection of failure in computations in a general setting infeasible. Subsequently, we prove algorithmic limitations in training deep neural networks even in cases where the underlying problem is well-behaved. Finally, we end with a positive observation, showing that in quantized versions of classification and deep network training, computability restrictions do not arise or can be overcome to a certain degree.

cs.LG↗

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

Distribution-Preserving Integrated Sensing and Communication with Secure Reconstruction

Distribution-preserving integrated sensing and communication with secure reconstruction is investigated in this paper. In addition to the distortion constraint, we impose another constraint on the distance between the reconstructed sequence distribution and the original state distribution to force the system to preserve the statistical property of the channel states. An inner bound of the distribution-preserving capacity-distortion region is provided with some capacity region results under special cases. A numerical example demonstrates the tradeoff between the communication rate, reconstruction distortion and distribution preservation. Furthermore, we consider the case that the reconstructed sequence should be kept secret from an eavesdropper who also observes the channel output. An inner bound of the tradeoff region and a capacity-achieving special case are presented.

cs.IT↗

arXiv2024

Optimal Signal Processing for Common Randomness Generation over MIMO Gaussian Channels with Applications in Identification

Common randomness (CR), as a resource, is not commonly exploited in existing practical communication systems. In the CR generation framework, both the sender and receiver aim to generate a common random variable observable to both, ideally with low error probability. The availability of this CR allows us to implement correlated random protocols that can lead to faster and more efficient algorithms. Previous work focused on CR generation over perfect channels with limited capacity. In our work, we consider the problem of CR generation from independent and identically distributed (i.i.d.) samples of a correlated finite source with one-way communication over a Gaussian channel. We first derive the CR capacity for single-input single-output (SISO) Gaussian channels. This result is then used for the derivation of the CR capacity in the multiple-input multiple-output (MIMO) case. CR plays a key role in the identification scheme since it may allow a significant increase in the identification capacity of channels. In the identification framework, the decoder is interested in knowing \emph{whether} a specific message of special interest to him has been sent or not, rather than knowing \emph{what} the received message is. In many new applications, such as several machine-to-machine and human-to-machine systems and the tactile internet, this post-Shannon scheme is more efficient than classical transmission. In our work, we also consider a CR-assisted secure identification scheme and develop a lower bound on the corresponding secure identification capacity.

eess.SP↗

arXiv2024

Secure Identification for Gaussian Channels and Identification for Multi-Antenna Gaussian Channels

New applications in modern communications are demanding robust and ultra-reliable low latency information exchange such as machine-to-machine and human-to-machine communications. For many of these applications, the identification approach of Ahlswede and Dueck is much more efficient than the classical message transmission scheme proposed by Shannon. Previous studies concentrate mainly on identification over discrete channels. For discrete channels, it was proved that identification is robust under channels uncertainty. Furthermore, optimal identification schemes that are secure and robust against jamming attacks have been considered. However, no results for continuous channels have yet been established. That is why we focus on the continuous case: the Gaussian channel for its known practical relevance. We deal with secure identification over Gaussian channels. Provable secure communication is of a high interest for future communication systems. A key technique for implementing secure communication is the physical layer security based on information theoretic security. We model this with the wiretap channel. In particular, we provide a suitable coding scheme for the Gaussian wiretap channel (GWC) and determine the corresponding secure identification capacity. We also consider Multiple-Input Multiple-Output (MIMO) Gaussian channels and provide an efficient signal-processing scheme. This scheme allows a separation of signal-processing and Gaussian coding.

eess.SP↗

arXiv2024

Computability of the Zero-Error Capacity of Noisy Channels

Zero-error capacity plays an important role in a whole range of operational tasks, in addition to the fact that it is necessary for practical applications. Due to the importance of zero-error capacity, it is necessary to investigate its algorithmic computability, as there has been no known closed formula for the zero-error capacity until now. We show that the zero-error capacity of noisy channels is not Banach-Mazur computable and therefore not Borel-Turing computable. We also investigate the relationship between the zero-error capacity of discrete memoryless channels, the Shannon capacity of graphs, and Ahlswede's characterization of the zero-error-capacity of noisy channels with respect to the maximum error capacity of 0-1-arbitrarily varying channels. We will show that important questions regarding semi-decidability are equivalent for all three capacities. So far, the Borel-Turing computability of the Shannon capacity of graphs is completely open. This is why the coupling with semi-decidability is interesting.

cs.IT↗

arXiv2024

Computability of the Channel Reliability Function and Related Bounds

The channel reliability function is an important tool that characterizes the reliable transmission of messages over communication channels. For many channels, only upper and lower bounds of the function are known. We analyze the computability of the reliability function and its related functions. We show that the reliability function is not a Turing computable performance function. The same also applies to the functions related to the sphere packing bound and the expurgation bound. Furthermore, we consider the $R_\infty$ function and the zero-error feedback capacity, since they play an important role in the context of the reliability function. Both the $R_\infty$ function and the zero-error feedback capacity are not Banach Mazur computable.

cs.IT↗

arXiv2024

Common Randomness Generation from Sources with Infinite Polish Alphabet

We investigate the problem of common randomness (CR) generation in the basic two-party communication setting in which a sender and a receiver aim to agree on a common random variable with high probability. The terminals observe independent and identically distributed (i.i.d.) samples of sources with an arbitrary distribution defined on a Polish alphabet and are allowed to communicate as little as possible over a noisy, memoryless channel. We establish single-letter upper and lower bounds on the CR capacity for the specified model. The derived bounds hold with equality except for at most countably many points where discontinuity issues might arise.

cs.IT↗

arXiv2024

Function Computation and Identification over Locally Homomorphic Multiple-Access Channels

We develop the notion of a locally homomorphic channel and prove an approximate equivalence between those and codes for computing functions. Further, we derive decomposition properties of locally homomorphic channels which we use to analyze and construct codes where two messages must be encoded independently. This leads to new results for identification and K-identification when all messages are sent over multiple-access channels, which yield surprising rate improvements compared to naive code constructions. In particular, we demonstrate that for the example of identification with deterministic encoders, both encoders can be constructed independently.

cs.IT↗

arXiv2024

Resilient-By-Design Framework for MIMO-OFDM Communications under Smart Jamming

Native jamming mitigation is essential for addressing security and resilience in future 6G wireless networks. In this paper a resilient-by-design framework for effective anti-jamming in MIMO-OFDM wireless communications is introduced. A novel approach that integrates information from wireless sensing services to develop anti-jamming strategies, which do not rely on any prior information or assumptions on the adversary's concrete setup, is explored. To this end, a method that replaces conventional approaches to noise covariance estimation in anti-jamming with a surrogate covariance model is proposed, which instead incorporates sensing information on the jamming signal's directions-of-arrival (DoAs) to provide an effective approximation of the true jamming strategy. The study further focuses on integrating this novel, sensing-assisted approach into the joint optimization of beamforming, user scheduling and power allocation for a multi-user MIMO-OFDM uplink setting. Despite the NP-hard nature of this optimization problem, it can be effectively solved using an iterative water-filling approach. In order to assess the effectiveness of the proposed sensing-assisted jamming mitigation, the corresponding worst-case jamming strategy is investigated, which aims to minimize the total user sum-rate. Experimental simulations eventually affirm the robustness of our approach against both worst-case and barrage jamming, demonstrating its potential to address a wide range of jamming scenarios. Since such an integration of sensing-assisted information is directly implemented on the physical layer, resilience is incorporated preemptively by-design.

cs.IT↗

arXiv2024

An Analysis of Capacity-Distortion Trade-Offs in Memoryless ISAC Systems

This manuscript investigates the information-theoretic limits of integrated sensing and communications (ISAC), aiming for simultaneous reliable communication and precise channel state estimation. We model such a system with a state-dependent discrete memoryless channel (SD-DMC) with present or absent channel feedback and generalized side information at the transmitter and the receiver, where the joint task of message decoding and state estimation is performed at the receiver. The relationship between the achievable communication rate and estimation error, the capacity-distortion (C-D) trade-off, is characterized across different causality levels of the side information. This framework is shown to be capable of modeling various practical scenarios by assigning the side information with different meanings, including monostatic and bistatic radar systems. The analysis is then extended to the two-user degraded broadcast channel, and we derive an achievable C-D region that is tight under certain conditions. To solve the optimization problem arising in the computation of C-D functions/regions, we propose a proximal block coordinate descent (BCD) method, prove its convergence to a stationary point, and derive a stopping criterion. Finally, several representative examples are studied to demonstrate the versatility of our framework and the effectiveness of the proposed algorithm.

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