Search

Quantization plays an important role in the physical layer (PHY) disaggregation which is fundamental to the Open Radio Access Network (O-RAN) architecture, since digitized signals must be transmitted over fronthaul connections. In this paper we explore the effect of quantization on PHY performance, drawing on the Bussgang decomposition and the implications of the Bussgang theorem and extending it to the case of non-Gaussian signals. We first prove several theorems regarding the signal to distortion plus noise ratio for a general non-linearity, applicable to both the Gaussian and the non-Gaussian case, showing that the decomposition can be applied to the non-Gaussian case, but that formulae previously introduced should be amended. We then apply these results to the non-linearity created by quantization, both for Gaussian and non-Gaussian signal distributions, and give numerical results derived from both theory and simulation.

This letter focuses on enhancing target detection performance for a multi-user integrated sensing and communication (ISAC) system using orthogonal time frequency space (OTFS)-aided cell-free multiple-input multiple-output (MIMO) technology in high-speed vehicular environments. We propose a sensing-centric (SC) approach for target detection using communication signals with or without sensing signals. Power allocation is optimized to maximize the sensing signal-to-noise ratio (SNR) of the proposed SC scheme while ensuring a required quality-of-service (QoS) for the communication user equipment (UEs), and adhering to each access points (APs) power budget. Numerical results show that the proposed SC scheme vastly outperforms a communication-centric method that minimizes the total power consumed at the APs subject to the same constraints., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

In this article, we study the fundamental limits in the design of fair and/or private representations achieving perfect demographic parity and/or perfect privacy through the lens of information theory. More precisely, given some useful data $X$ that we wish to employ to solve a task $T$, we consider the design of a representation $Y$ that has no information of some sensitive attribute or secret $S$, that is, such that $I(Y;S) = 0$. We consider two scenarios. First, we consider a design desiderata where we want to maximize the information $I(Y;T)$ that the representation contains about the task, while constraining the level of compression (or encoding rate), that is, ensuring that $I(Y;X) \leq r$. Second, inspired by the Conditional Fairness Bottleneck problem, we consider a design desiderata where we want to maximize the information $I(Y;T|S)$ that the representation contains about the task which is not shared by the sensitive attribute or secret, while constraining the amount of irrelevant information, that is, ensuring that $I(Y;X|T,S) \leq r$. In both cases, we employ extended versions of the Functional Representation Lemma and the Strong Functional Representation Lemma and study the tightness of the obtained bounds. Every result here can also be interpreted as a coding with perfect privacy problem by considering the sensitive attribute as a secret.

We consider a variant of the coded caching problem where users connect to two types of caches, called private caches and access caches. The problem setting consists of a server having a library of files and a set of access caches. Every user, equipped with a private cache, connects to $L$ neighboring access caches in a cyclic wrap-around fashion. The server populates the private and access caches with file contents in either coded or uncoded format. For this setting, we derive a lower bound on the optimal worst-case transmission rate using cut-set arguments. This lower bound applies to both coded and uncoded placements. We then provide an achievable scheme with uncoded placement and show that our scheme specializes to the well-known Maddah-Ali-Niesen scheme for the dedicated cache network in the absence of access caches. Finally, we show that the proposed scheme achieves optimality in large memory regimes and provide numerical plots comparing the rate of the proposed scheme with the derived lower bound, demonstrating the optimality of our scheme., Comment: 15 pages, 5 figures and one table. Some overlap of introductory and background materials with our earlier submission arXiv:2407.00677v1 dated 30 June 2024

This paper establishes the fundamental limits of a multi-access system where multiple users communicate to a legitimate receiver in presence of an external warden. Only a specific subset of the users, called covert users, needs their communication to remain undetected to the warden, while the remaining non-covert users have no such constraint. The fundamental limits show a tradeoff between the different rates that are simultaneously achievable at the various users in function of the secret-key rates that the different users share with the legitimate receiver. Interestingly, the presence of the non-covert users can enhance the capacities of the covert users, especially under stringent secret-key budgets. Our findings underscore the essential requirement of employing a multiplexing (coded time-sharing) strategy to exhaust the fundamental region of all rates that are simultaneously achievable at the covert and the non-covert users. As a side-product of our results, we also establish the covert-capacity secret-key tradeoff for standard single-user and multi-access covert communication systems (without non-covert users), i.e., the largest covert rates that are achievable under given secret-key rate budgets. Previous works had only established the minimum secret-key rates required at largest covert rates., Comment: Submitted for review to IEEE Transactions on Information Theory

We present a generalization of Bregman divergences in symplectic vector spaces called symplectic Bregman divergences. Symplectic Bregman divergences are derived from a symplectic generalization of the Fenchel-Young inequalities which rely on symplectic subdifferentials. The generic symplectic Fenchel-Young inequality is obtained using symplectic Fenchel transforms which are defined with respect to linear symplectic forms. Some potential appplications of symplectic divergences in geometric mechanics, information geometry, and learning dynamics in machine learning are discussed., Comment: 10 pages, 2 figures

The body morphology plays an important role in the way information is perceived and processed by an agent. We address an information theory (IT) account on how the precision of sensors, the accuracy of motors, their placement, the body geometry, shape the information structure in robots and computational codes. As an original idea, we envision the robot's body as a physical communication channel through which information is conveyed, in and out, despite intrinsic noise and material limitations. Following this, entropy, a measure of information and uncertainty, can be used to maximize the efficiency of robot design and of algorithmic codes per se. This is known as the principle of Entropy Maximization (PEM) introduced in biology by Barlow in 1969. The Shannon's source coding theorem provides then a framework to compare different types of bodies in terms of sensorimotor information. In line with PME, we introduce a special class of efficient codes used in IT that reached the Shannon limits in terms of information capacity for error correction and robustness against noise, and parsimony. These efficient codes, which exploit insightfully quantization and randomness, permit to deal with uncertainty, redundancy and compacity. These features can be used for perception and control in intelligent systems. In various examples and closing discussions, we reflect on the broader implications of our framework that we called Informational Embodiment to motor theory and bio-inspired robotics, touching upon concepts like motor synergies, reservoir computing, and morphological computation. These insights can contribute to a deeper understanding of how information theory intersects with the embodiment of intelligence in both natural and artificial systems.

The Plotkin construction combines two codes to a code of doubled length. It can be applied recursively. The class of Reed-Muller (RM) codes is a particular example. Also, a special class of generalized concatenated codes (GCC) can be described as recursive Plotkin construction. Exploiting a property of the code words constructed by the recursive Plotkin construction, we present novel soft-decision decoders. These are based on the decoding of hidden code words which are inherent contained in the constructed code words and can be uncovered by adding particular parts of the overall code word. The main idea is to use more than one decoding variant where each variant starts with the decoding of a different hidden code word. The final decoding decision selects the best of the decisions of the used variants. The more variants are used the closer the performance gets to the maximum-likelihood (ML) decoding performance. This is verified by an ML-bound for the cases where the ML performance is not known. The decoding algorithms use only additions, comparisons, and sign operations. Further, due to the recursive structure, only relatively short codes have to be decoded, thus, the decoding complexity is very low. In addition, we introduce two novel classes of half-rate codes based on recursive Plotkin constructions with RM codes.

Through the lens of average and peak age-of-information (AoI), this paper takes a fresh look into the uplink medium access solutions for mission-critical (MC) communication coexisting with enhanced mobile broadband (eMBB) service. Considering the stochastic packet arrivals from an MC user, we study three access schemes: orthogonal multiple access (OMA) with eMBB preemption (puncturing), non-orthogonal multiple access (NOMA), and rate-splitting multiple access (RSMA), the latter two both with concurrent eMBB transmissions. Puncturing is found to reduce both average AoI and peak AoI (PAoI) violation probability but at the expense of decreased eMBB user rates and increased signaling complexity. Conversely, NOMA and RSMA offer higher eMBB rates but may lead to MC packet loss and AoI degradation. The paper systematically investigates the conditions under which NOMA or RSMA can closely match the average AoI and PAoI violation performance of puncturing while maintaining data rate gains. Closed-form expressions for average AoI and PAoI violation probability are derived, and conditions on the eMBB and MC channel gain difference with respect to the base station are analyzed. Additionally, optimal power and rate splitting factors in RSMA are determined through an exhaustive search to minimize MC outage probability. Notably, our results indicate that with a small loss in the average AoI and PAoI violation probability the eMBB rate in NOMA and RSMA can be approximately five times higher than that achieved through puncturing., Comment: 14 pages, 9 figures, under review for possible publication in IEEE TVT

Received samples of a stochastic process are processed by a server for delivery as updates to a monitor. Each sample belongs to a class that specifies a distribution for its processing time and a function that describes how the value of the processed update decays with age at the monitor. The class of a sample is identified when the processed update is delivered. The server implements a form of M/G/1/1 blocking queue; samples arriving at a busy server are discarded and samples arriving at an idle server are subject to an admission policy that depends on the age and class of the prior delivered update. For the delivered updates, we characterize the average age of information (AoI) and average value of information (VoI). We derive the optimal stationary policy that minimizes the convex combination of the AoI and (negative) VoI. It is shown that the policy has a threshold structure, in which a new sample is allowed to arrive to the server only if the previous update's age and value difference surpasses a certain threshold that depends on the specifics of the value function and system statistics., Comment: Appeared in IEEE ICC 2024

We introduce a method for construction of identification codes based on prime number generation over the noiseless channels. The earliest method for such construction based on prime numbers was proposed by Ahlswede which relies on algorithms for generation of prime numbers. This method requires knowledge of $2^n$ first prime numbers for identification codes with block length $n,$ which is not computationally efficient. In this work, we revisit Ahlswede's scheme and propose a number of modifications. In particular, employing probabilistic prime generation algorithm, we guarantee that the prime keys generation is possible in polynomial time. Furthermore, additional improvements in terms of type II upper bound are derived and presented. Finally, we propose a method for identification coding based on hash functions which generalizes the Ahlswede's scheme., Comment: 27 Pages, 4 Figures

In this letter, we analyze the performance of mixed coherent and non-coherent transmissions approach, which can improve the performance of cell-free multiple-input multiple-output orthogonal frequency division multiplexing (CF mMIMO-OFDM) systems under asynchronous reception. To this end, we first obtain the achievable downlink sum-rate for the mixed coherent and non-coherent transmissions, and then provide a closed-form expression for the case with the maximum ratio precoding. Subsequently, an efficient clustering algorithm is proposed to group access points into different clusters with the same quantized phase shift in each cluster. Numerical results demonstrate that the mixed coherent and non-coherent transmissions can effectively improve the sum-rate of CF mMIMO-OFDM systems under asynchronous reception., Comment: This work is submitted to IEEE for possible publication

Extremely large aperture array (ELAA) is a promising multiple-input multiple-output (MIMO) technique for next generation mobile networks. In this paper, we propose two novel approaches to accelerate the convergence of current iterative MIMO detectors in ELAA channels. Our approaches exploit the static components of the ELAA channel, which include line of sight (LoS) paths and deterministic non-LoS (NLoS) components due to channel hardening effects. This paper proposes novel convergence acceleration techniques for fast iterative ELAA-MIMO detection by leveraging the static channel component, including the LoS paths and deterministic NLoS components that arise due to channel hardening. Specifically, these static channel components are utilized in two ways: as preconditioning matrices for general iterative algorithms, and as initialization for quasi-Newton (QN) methods. Simulation results show that the proposed approaches converge significantly faster compared to current iterative MIMO detectors, especially under strong LoS conditions with high Rician K-factor. Furthermore, QN methods with the proposed initialization matrix consistently achieve the best convergence performance while maintaining low complexity., Comment: This work has been accepted by the IEEE Information Theory Workshop (ITW) 2024. Copyright may be transferred without notice, after which this version may no longer be accessible

Over-the-air computation (AirComp) integrates analog communication with task-oriented computation, serving as a key enabling technique for communication-efficient federated learning (FL) over wireless networks. However, AirComp-enabled FL (AirFL) with a single global consensus model fails to address the data heterogeneity in real-life FL scenarios with non-independent and identically distributed local datasets. In this paper, we introduce reconfigurable intelligent surface (RIS) technology to enable efficient personalized AirFL, mitigating the data heterogeneity issue. First, we achieve statistical interference elimination across different clusters in the personalized AirFL framework via RIS phase shift configuration. Then, we propose two personalized aggregation schemes involving power control and denoising factor design from the perspectives of first- and second-order moments, respectively, to enhance the FL convergence. Numerical results validate the superior performance of our proposed schemes over existing baselines., Comment: Accepted by SCIENCE CHINA Information Sciences

In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices $W_{t,n,k}$, representing $t$-element subsets versus $k$-element subsets of an $n$-element set. We provide both lower and upper bounds on the minimum distances of these codes and determine the exact values for any $t\leq 3$ and sufficiently large $n$. Our study combines design and integer linear programming techniques. The codes we consider are connected to locally recoverable codes, LDPC codes and combinatorial designs.

Channel prediction compensates for outdated channel state information in multiple-input multiple-output (MIMO) systems. Machine learning (ML) techniques have recently been implemented to design channel predictors by leveraging the temporal correlation of wireless channels. However, most ML-based channel prediction techniques have only considered offline training when generating channel predictors, which can result in poor performance when encountering channel environments different from the ones they were trained on. To ensure prediction performance in varying channel conditions, we propose an online re-training framework that trains the channel predictor from scratch to effectively capture and respond to changes in the wireless environment. The training time includes data collection time and neural network training time, and should be minimized for practical channel predictors. To reduce the training time, especially data collection time, we propose a novel ML-based channel prediction technique called aggregated learning (AL) approach for wideband massive MIMO systems. In the proposed AL approach, the training data can be split and aggregated either in an array domain or frequency domain, which are the channel domains of MIMO-OFDM systems. This processing can significantly reduce the time for data collection. Our numerical results show that the AL approach even improves channel prediction performance in various scenarios with small training time overhead., Comment: 16 pages, 16 figures, 4 tables

Centralized baseband processing (CBP) is required to achieve the full potential of massive multiple-input multiple-output (MIMO) systems. However, due to the large number of antennas, CBP suffers from two major issues: 1) Tremendous data interconnection between radio frequency (RF) circuitry and processing fabrics; and 2) high-dimensional computation. To this end, decentralized baseband processing (DBP) has been proposed, where the antennas at the BS are partitioned into clusters connected to separate RF circuits and equipped with separate computing units. Unfortunately, due to the decentralized structure, the optimal fusion scheme and performance analysis for DBP with general spatial correlation between clusters and imperfect channel state information (CSI) are not available in the literature. In this paper, we consider a decentralized MIMO system where all clusters adopt linear minimum mean-square error (LMMSE) receivers with imperfect CSI. Specifically, we first establish the optimal linear fusion scheme which has high computational and data input/output (I/O) costs. To reduce the costs, we further propose two sub-optimal fusion schemes with reduced complexity. For all three schemes, we derive the closed-form expressions for the signal-to-interference-and-noise ratio (SINR) by leveraging random matrix theory (RMT) and demonstrate the conditions under which the sub-optimal schemes are optimal. Furthermore, we determine the optimal regularization parameter for decentralized LMMSE receivers, identify the best antenna partitioning strategy, and prove that the SINR will decrease as the number of clusters increases. Numerical simulations validate the accuracy of the theoretical results.

The non-local interactions in several quantum devices allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will soon be realizable, it is important to construct stabilizer codes that, for a given code distance, admit fault-tolerant implementations of logical gates with the fewest number of physical qubits. We extract high-distance doubly even codes from the quantum quadratic-residue code family that admit a transversal implementation of the single-qubit Clifford group. Applying a doubling procedure [arXiv:1509.03239] to such codes yields a family of high-distance triply even codes which admit a transversal implementation of the logical $\texttt{T}$-gate. To our knowledge, both code families require a lower qubit overhead than any other qubit stabilizer code of the same distance which can realize their respective gates., Comment: 1 table, 2 figures

We develop a framework for studying the problem of identifying roots of a noisy function. We revisit a previous logarithmic bound on the number of observations and propose a general problem for identification of roots with three errors. As a key finding, we establish a novel logarithmic lower bound on the number of observations which outperforms the previous result across certain regimes of error and accuracy of the identification test. Furthermore, we recover the previous results for root identification as a special case and draw a connection to the message identification problem of Ahlswede., Comment: 17 Pages, 6 Figures, 3 Tables

This paper studies quantum supervised learning for classical inference from quantum states. In this model, a learner has access to a set of labeled quantum samples as the training set. The objective is to find a quantum measurement that predicts the label of the unseen samples. The hardness of learning is measured via sample complexity under a quantum counterpart of the well-known probably approximately correct (PAC). Quantum sample complexity is expected to be higher than classical one, because of the measurement incompatibility and state collapse. Recent efforts showed that the sample complexity of learning a finite quantum concept class $\mathcal{C}$ scales as $O(|\mathcal{C}|)$. This is significantly higher than the classical sample complexity that grows logarithmically with the class size. This work improves the sample complexity bound to $O(V_{\mathcal{C}^*} \log |\mathcal{C}^*|)$, where $\mathcal{C}^*$ is the set of extreme points of the convex closure of $\mathcal{C}$ and $V_{\mathcal{C}^*}$ is the shadow-norm of this set. We show the tightness of our bound for the class of bounded Hilbert-Schmidt norm, scaling as $O(\log |\mathcal{C}^*|)$. Our approach is based on a new quantum empirical risk minimization (ERM) algorithm equipped with a shadow tomography method., Comment: ISIT 2025

With the emergence of data marketplaces, the demand for methods to assess the value of data has increased significantly. While numerous techniques have been proposed for this purpose, none have specifically addressed graphs as the main data modality. Graphs are widely used across various fields, ranging from chemical molecules to social networks. In this study, we break down graphs into two main components: structural and featural, and we focus on evaluating data without relying on specific task-related metrics, making it applicable in practical scenarios where validation requirements may be lacking. We introduce a novel framework called blind message passing, which aligns the seller's and buyer's graphs using a shared node permutation based on graph matching. This allows us to utilize the graph Wasserstein distance to quantify the differences in the structural distribution of graph datasets, called the structural disparities. We then consider featural aspects of buyers' and sellers' graphs for data valuation and capture their statistical similarities and differences, referred to as relevance and diversity, respectively. Our approach ensures that buyers and sellers remain unaware of each other's datasets. Our experiments on real datasets demonstrate the effectiveness of our approach in capturing the relevance, diversity, and structural disparities of seller data for buyers, particularly in graph-based data valuation scenarios.

The number of possible melodies is unfathomably large, yet despite this virtually unlimited potential for melodic variation, melodies from different societies can be surprisingly similar. The motor constraint hypothesis accounts for certain similarities, such as scalar motion and contour shape, but not for other major common features, such as repetition, song length, and scale size. Here we investigate the role of information constraints arising from limitations on human memory in shaping these hallmarks of melodies. We measure determinants of information rate in 62 corpora of Folk melodies spanning several continents, finding multiple trade-offs that all act to constrain the information rate across societies. By contrast, 39 corpora of Art music from Europe (including Turkey) show longer, more complex melodies, and increased complexity over time, suggesting different cultural-evolutionary selection pressures in Art and Folk music, possibly due to the use of written versus oral transmission. Our parameter-free model predicts the empirical scale degree distribution using information constraints on scalar motion, melody length, and, most importantly, information rate. This provides strong evidence that information constraints during cultural transmission of music limit the number of notes in a scale, and proposes that preference for intermediate melodic complexity is a fundamental constraint on the cultural evolution of melody.

We consider the problem of user equipment (UE) positioning based on radio signals via deep learning. As in most supervised-learning tasks, a critical aspect is the availability of a relevant dataset to train a model. However, in a cellular network, the data-collection step may induce a high communication overhead. As a result, to reduce the required size of the dataset, it may be interesting to carefully choose the positions to be labelled and to be used in the training. We therefore propose an active learning approach for efficient data collection. We first show that significant gains (both in terms of positioning accuracy and size of the required dataset) can be obtained for the considered positioning problem using a genie. This validates the interest of active learning for positioning. We then propose a \textcolor{blue}{practical} method to approximate this genie., Comment: Submitted to Electronics Letters

We consider the problem of robust dynamic coded distributed storage (RDCDS) that is associated with the coded distributed storage of a message with $N$ servers where 1) it suffices to recover the message from the storage at any $R_r$ servers; and 2) each of the servers stores a coded portion of the message that is at most $\frac{1}{K_c}$ the size of the message. The goal is to enable two main functionalities: the read operation and the update operation of the message. Specifically, at time slot $t$, the user may execute either the read operation or the update operation, where the read operation allows the user to recover the message from the servers, and the update operation allows the user to update the message to the servers in the form of an additive increment so that any up to $X^{(t)}$ colluding servers reveal nothing about the increment. The two functionalities are robust if at any time slot $t$ 1) they tolerate temporarily dropout servers up to certain thresholds (the read threshold is $R_r$ and the update threshold is denoted as $R_u^{(t)}$); and 2) the user may remain oblivious to prior server states. The communication efficiency is measured by the download cost $C_r^{(t)}$ of the read operation and the upload cost $C_u^{(t)}$ of the update operation. Given $K_c$ and $R_r$, we are curious about the optimal $(R_u^{(t)},C_r^{(t)},C_u^{(t)})$ tuple. In this work, we settle the fundamental limits of RDCDS. In particular, denoting the number of dropout servers at time slot $t$ as $|\mathcal{D}^{(t)}|$, we first show that 1) $R_u^{(t)}\geq N-R_r+\lceil K_c\rceil+X^{(t)}$; and 2) $C_r^{(t)}\geq \frac{N-|\mathcal{D}^{(t)}|}{N-R_r+\lceil K_c\rceil-|\mathcal{D}^{(t)}|}, C_u^{(t)}\geq \frac{N-|\mathcal{D}^{(t)}|}{R_r-X^{(t)}-|\mathcal{D}^{(t)}|}$. Then, inspired by the idea of staircase codes, we construct an RDCDS scheme that simultaneously achieves the above lower bounds., Comment: 40 pages, 3 figures

After nearly a century of specialized applications in optics, remote sensing, and acoustics, the near-field (NF) electromagnetic propagation zone is experiencing a resurgence in research interest. This renewed attention is fueled by the emergence of promising applications in various fields such as wireless communications, holography, medical imaging, and quantum-inspired systems. Signal processing within NF sensing and wireless communications environments entails addressing issues related to extended scatterers, range-dependent beampatterns, spherical wavefronts, mutual coupling effects, and the presence of both reactive and radiative fields. Recent investigations have focused on these aspects in the context of extremely large arrays and wide bandwidths, giving rise to novel challenges in channel estimation, beamforming, beam training, sensing, and localization. While NF optics has a longstanding history, advancements in NF phase retrieval techniques and their applications have lately garnered significant research attention. Similarly, utilizing NF localization with acoustic arrays represents a contemporary extension of established principles in NF acoustic array signal processing. This article aims to provide an overview of state-of-the-art signal processing techniques within the NF domain, offering a comprehensive perspective on recent advances in diverse applications., Comment: 12pages7figures, submitted to IEEE

The passive reconfigurable intelligent surface (RIS) requires numerous elements to achieve adequate array gain, which linearly increases power consumption (PC) with the number of reflection phases. To address this, this letter introduces a rotatable block-controlled RIS (BC-RIS) that preserves spectral efficiency (SE) while reducing power costs. Unlike the element-controlled RIS (EC-RIS), which necessitates independent phase control for each element, the BC-RIS uses a single phase control circuit for each block, substantially lowering power requirements. In the maximum ratio transmission, by customizing specular reflection channels through the rotation of blocks and coherently superimposing signals with optimized reflection phase of blocks, the BC-RIS achieves the same averaged SE as the EC-RIS. To counteract the added power demands from rotation, influenced by block size, we have developed a segmentation scheme to minimize overall PC. Furthermore, constraints for rotation power-related parameters have been established to enhance the energy efficiency of the BC-RIS compared to the EC-RIS. Numerical results confirm that this approach significantly improves energy efficiency while maintaining performance., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Maximum distance separable (MDS) codes have significant combinatorial and cryptographic applications due to their certain optimality. Generalized Reed-Solomon (GRS) codes are the most prominent MDS codes. Twisted generalized Reed-Solomon (TGRS) codes may not necessarily be MDS. It is meaningful to study the conditions under which TGRS codes are MDS. In this paper, we study a general class of TGRS (A-TGRS) codes which include all the known special ones. First, we obtain a new explicit expression of the inverse of the Vandermonde matrix. Based on this, we further derive an equivalent condition under which an A-TGRS code is MDS. According to this, the A-TGRS MDS codes include nearly all the known related results in the previous literatures. More importantly, we also obtain many other classes of MDS TGRS codes with new parameter matrices. In addition, we present a new method to compute the inverse of the lower triangular Toplitz matrix by a linear feedback shift register, which will be very useful in many research fields.

Deep neural networks (DNNs) were shown to facilitate the operation of uplink multiple-input multiple-output (MIMO) receivers, with emerging architectures augmenting modules of classic receiver processing. Current designs consider static DNNs, whose architecture is fixed and weights are pre-trained. This induces a notable challenge, as the resulting MIMO receiver is suitable for a given configuration, i.e., channel distribution and number of users, while in practice these parameters change frequently with network variations and users leaving and joining the network. In this work, we tackle this core challenge of DNN-aided MIMO receivers. We build upon the concept of hypernetworks, augmenting the receiver with a pre-trained deep model whose purpose is to update the weights of the DNN-aided receiver upon instantaneous channel variations. We design our hypernetwork to augment modular deep receivers, leveraging their modularity to have the hypernetwork adapt not only the weights, but also the architecture. Our modular hypernetwork leads to a DNN-aided receiver whose architecture and resulting complexity adapts to the number of users, in addition to channel variations, without retraining. Our numerical studies demonstrate superior error-rate performance of modular hypernetworks in time-varying channels compared to static pre-trained receivers, while providing rapid adaptivity and scalability to network variations.

We present an interpretation of Deepcode, a learned feedback code that showcases higher-order error correction relative to an earlier interpretable model. By interpretation, we mean succinct analytical encoder and decoder expressions (albeit with learned parameters) in which the role of feedback in achieving error correction is easy to understand. By higher-order, we mean that longer sequences of large noise values are acted upon by the encoder (which has access to these through the feedback) and used in error correction at the decoder in a two-stage decoding process., Comment: accepted to 60th Annual Allerton Conference

This paper characterizes the optimal capacity-distortion (C-D) tradeoff in an optical point-to-point (P2P) system with single-input single-output for communication and single-input multiple-output for sensing (SISO-COM and SIMO-SEN) within an integrated sensing and communication (ISAC) framework. We consider the optimal rate-distortion (R-D) region and explore several inner (IB) and outer (OB) bounds. We introduce practical, asymptotically optimal maximum a posteriori (MAP) and maximum likelihood estimators (MLE) for target distance, addressing nonlinear measurement-to-state relationships and non-conjugate priors. As the number of sensing antennas increases, these estimators converge to the Bayesian Cram\'er-Rao bound (BCRB). We also establish that the achievable rate-CRB (AR-CRB) serves as an OB for the optimal C-D region, valid for both unbiased estimators and asymptotically large numbers of receive antennas. To clarify that the input distribution determines the tradeoff across the Pareto boundary of the C-D region, we propose two algorithms: \textit{i}) an iterative Blahut-Arimoto algorithm (BAA)-type method, and \textit{ii}) a memory-efficient closed-form (CF) approach. The CF approach includes a CF optimal distribution for high optical signal-to-noise ratio (O-SNR) conditions. Additionally, we adapt and refine the Deterministic-Random Tradeoff (DRT) to this optical ISAC context., Comment: 8 pages, 3 figures

While previous researchers have performed an exhaustive search to determine an optimal Wordle strategy, that computation is very time consuming and produced a strategy using words that are unfamiliar to most people. With Wordle solutions being gradually eliminated (with a new puzzle each day and no reuse), an improved strategy could be generated each day, but the computation time makes a daily exhaustive search impractical. This paper shows that simple heuristics allow for fast generation of effective strategies and that little is lost by guessing only words that are possible solution words rather than more obscure words., Comment: 7 pages including references, 4 tables

The co-existence of terrestrial and non-terrestrial networks (NTNs) is essential for achieving global coverage in sixth-generation cellular networks. Due to increasing spectrum demand, there is discussion in the world level to share some frequencies used in terrestrial Networks (TNs) with NTNs, resulting in co-channel interference and performance degradation. This paper analyzes the interference caused by satellite networks on TN in the S-band. We examined the transmission mechanisms of satellite signals and conducted simulations to evaluate interference intensity across varying slant ranges. Our findings indicate that the angle between the user equipment direction and the sub-satellite point direction from the beam center significantly impacts the interference level., Comment: 3 pages, 6 figures, JWOC conference

The Feistel Boomerang Connectivity Table ($\rm{FBCT}$), which is the Feistel version of the Boomerang Connectivity Table ($\rm{BCT}$), plays a vital role in analyzing block ciphers' ability to withstand strong attacks, such as boomerang attacks. However, as of now, only four classes of power functions are known to have explicit values for all entries in their $\rm{FBCT}$. In this paper, we focus on studying the FBCT of the power function $F(x)=x^{2^{n-2}-1}$ over $\mathbb{F}_{2^n}$, where $n$ is a positive integer. Through certain refined manipulations to solve specific equations over $\mathbb{F}_{2^n}$ and employing binary Kloosterman sums, we determine explicit values for all entries in the $\rm{FBCT}$ of $F(x)$ and further analyze its Feistel boomerang spectrum. Finally, we demonstrate that this power function exhibits the lowest Feistel boomerang uniformity.

Localization plays an increasingly pivotal role in 5G/6G systems, enabling various applications. This paper focuses on the privacy concerns associated with delay-based localization, where unauthorized base stations attempt to infer the location of the end user. We propose a method to disrupt localization at unauthorized nodes by injecting artificial components into the pilot signal, exploiting model mismatches inherent in these nodes. Specifically, we investigate the effectiveness of two techniques, namely artificial multipath (AM) and artificial noise (AN), in mitigating location leakage. By leveraging the misspecified Cram\'er-Rao bound framework, we evaluate the impact of these techniques on unauthorized localization performance. Our results demonstrate that pilot manipulation significantly degrades the accuracy of unauthorized localization while minimally affecting legitimate localization. Moreover, we find that the superiority of AM over AN varies depending on the specific scenario., Comment: 6pages, conference paper

We introduce a group of related methods for binary classification tasks using probes of the hidden state activations in large language models (LLMs). Performance is on par with the largest and most advanced LLMs currently available, but requiring orders of magnitude fewer computational resources and not requiring labeled data. This approach involves translating class labels into a semantically rich description, spontaneous symmetry breaking of multilayer perceptron probes for unsupervised learning and inference, training probes to generate confidence scores (prior probabilities) from hidden state activations subject to known constraints via entropy maximization, and selecting the most confident probe model from an ensemble for prediction. These techniques are evaluated on four datasets using five base LLMs., Comment: 13 pages, 2 figures

The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these quantities using tools from statistical mechanics or via quantum information-based inequalities. By focusing on the second moment of one-dimensional unitary circuits where nearest neighboring gates act on sets of qudits (with open and closed boundary conditions), we show that one can exactly compute the associated spectral gaps. Indeed, having access to their functional form allows us to prove several important results, such as the fact that the spectral gap for closed boundary condition is exactly the square of the gap for open boundaries, as well as improve on previously known bounds for approximate design convergence. Finally, we verify our theoretical results by numerically computing the spectral gap for systems of up to 70 qubits, as well as comparing them to gaps of random orthogonal and symplectic circuits., Comment: 9 + 6 pages, 3 figures

This article introduces a novel non-orthogonal multiple access (NOMA) scheme for coordinated uplink channels. The scheme builds on the recently proposed sparse-regression low-density parity-check (SR-LDPC) code, and extends the underlying notions to scenarios with many concurrent users. The resulting scheme, called Multi-User SR-LDPC (MU-SR-LDPC) coding, consists of each user transmitting its own SR-LDPC codeword using a unique sensing matrix in conjunction with a characteristic outer LDPC code. To recover the sent information, the decoder jointly processes the received signals using a low-complexity and highly-parallelizable AMP-BP algorithm. At finite blocklengths (FBL), MU-SR-LDPC codes are shown to achieve a target BER at a higher spectral efficiency than baseline orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) schemes with similar computational complexity. Furthermore, MU-SR-LDPC codes are shown to match the performance of maximum a posteriori (MAP) decoding in certain regimes. For certain blocklengths and a sufficiently high number of users, MU-SR-LDPC codes may achieve a higher spectral efficiency than the approximate FBL capacity of the effective single-user Gaussian channel seen by each user in a comparable OMA scheme. Results are supported by numerical simulations., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

In the present paper we prove a family of tight upper and lower bounds for the Shannon entropy and von Neumann entropy based on the p-norms. This allows us to have an entropy estimate, a criterion for the finiteness of it and a bound on the difference of entropy, additionally, we did some numerical tests that show the efficiency of our approximations.

Upper bounds on the minimum Lee distance of codes that are linear over $\mathbb{Z}_q$ are discussed. The bounds are Singleton like, depending on the length, rank, and alphabet size of the code. Codes meeting such bounds are referred to as Maximum Lee Distance (MLD) Codes. We present some new bounds, proved using combinatorial arguments. The new bounds provide improvements over those in the literature., Comment: 12 pages

Error-correcting codes resilient to synchronization errors such as insertions and deletions are known as insdel codes. Due to their important applications in DNA storage and computational biology, insdel codes have recently become a focal point of research in coding theory. In this paper, we present several new combinatorial upper and lower bounds on the maximum size of $q$-ary insdel codes. Our main upper bound is a sphere-packing bound obtained by solving a linear programming (LP) problem. It improves upon previous results for cases when the distance $d$ or the alphabet size $q$ is large. Our first lower bound is derived from a connection between insdel codes and matchings in special hypergraphs. This lower bound, together with our upper bound, shows that for fixed block length $n$ and edit distance $d$, when $q$ is sufficiently large, the maximum size of insdel codes is $ \frac{q^{n-\frac{d}{2}+1}}{{n\choose \frac{d}{2}-1}}(1 \pm o(1))$. The second lower bound refines Alon et al.'s recent logarithmic improvement on Levenshtein's GV-type bound and extends its applicability to large $q$ and $d$., Comment: 20 pages

As machine-learning models grow in size, their implementation requirements cannot be met by a single computer system. This observation motivates distributed settings, in which intermediate computations are performed across a network of processing units, while the central node only aggregates their outputs. However, distributing inference tasks across low-precision or faulty edge devices, operating over a network of noisy communication channels, gives rise to serious reliability challenges. We study the problem of an ensemble of devices, implementing regression algorithms, that communicate through additive noisy channels in order to collaboratively perform a joint regression task. We define the problem formally, and develop methods for optimizing the aggregation coefficients for the parameters of the noise in the channels, which can potentially be correlated. Our results apply to the leading state-of-the-art ensemble regression methods: bagging and gradient boosting. We demonstrate the effectiveness of our algorithms on both synthetic and real-world datasets.

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.

This paper presents the hardware implementation of two variants of projection-aggregation-based decoding of Reed-Muller (RM) codes, namely unique projection aggregation (UPA) and collapsed projection aggregation (CPA). Our study focuses on introducing hardware architectures for both UPA and CPA. Through thorough analysis and experimentation, we observe that the hardware implementation of UPA exhibits superior resource usage and reduced energy consumption compared to CPA for the vanilla IPA decoder. This finding underscores a critical insight: software optimizations, in isolation, may not necessarily translate into hardware cost-effectiveness.

The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic distance of the associated classical code. Our new algorithms are based on the Brouwer-Zimmermann algorithm. Our experimental study shows that these new implementations are much faster than current state-of-the-art licensed implementations on single-core processors, multicore processors, and shared-memory multiprocessors. In the most computationally-demanding cases, the performance gain in the computational time can be larger than one order of magnitude. The experimental study also shows a good scalability on shared-memory parallel architectures., Comment: 14 pages, 7 figures, 1 table

In pursuit of enhanced quality of service and higher transmission rates, communication within the mid-band spectrum, such as bands in the 6-15 GHz range, combined with extra large-scale multiple-input multiple-output (XL-MIMO), is considered a potential enabler for future communication systems. However, the characteristics introduced by mid-band XL-MIMO systems pose challenges for channel modeling and performance analysis. In this paper, we first analyze the potential characteristics of mid-band MIMO channels. Then, an analytical channel model incorporating novel channel characteristics is proposed, based on a review of classical analytical channel models. This model is convenient for theoretical analysis and compatible with other analytical channel models. Subsequently, based on the proposed channel model, we analyze key metrics of wireless communication, including the ergodic spectral efficiency (SE) and outage probability (OP) of MIMO maximal-ratio combining systems. Specifically, we derive closed-form approximations and performance bounds for two typical scenarios, aiming to illustrate the influence of mid-band XL-MIMO systems. Finally, comparisons between systems under different practical configurations are carried out through simulations. The theoretical analysis and simulations demonstrate that mid-band XL-MIMO systems excel in SE and OP due to the increased array elements, moderate large-scale fading, and enlarged transmission bandwidth., Comment: 16 pages, 10 figures

The secrecy performance in both near-field and far-field communications is analyzed using two fundamental metrics: the secrecy capacity under a power constraint and the minimum power requirement to achieve a specified secrecy rate target. 1) For the secrecy capacity, a closed-form expression is derived under a discrete-time memoryless setup. This expression is further analyzed under several far-field and near-field channel models, and the capacity scaling law is revealed by assuming an infinitely large transmit array and an infinitely high power. A novel concept of "depth of insecurity" is proposed to evaluate the secrecy performance achieved by near-field beamfocusing. It is demonstrated that increasing the number of transmit antennas reduces this depth and thus improves the secrecy performance. 2) Regarding the minimum required power, a closed-form expression is derived and analyzed within far-field and near-field scenarios. Asymptotic analyses are performed by setting the number of transmit antennas to infinity to unveil the power scaling law. Numerical results are provided to demonstrate that: i) compared to far-field communications, near-field communications expand the areas where secure transmission is feasible, specifically when the eavesdropper is located in the same direction as the intended receiver; ii) as the number of transmit antennas increases, neither the secrecy capacity nor the minimum required power scales or vanishes unboundedly, adhering to the principle of energy conservation.

Along with the prosperity of generative artificial intelligence (AI), its potential for solving conventional challenges in wireless communications has also surfaced. Inspired by this trend, we investigate the application of the advanced diffusion models (DMs), a representative class of generative AI models, to high dimensional wireless channel estimation. By capturing the structure of multiple-input multiple-output (MIMO) wireless channels via a deep generative prior encoded by DMs, we develop a novel posterior inference method for channel reconstruction. We further adapt the proposed method to recover channel information from low-resolution quantized measurements. Additionally, to enhance the over-the-air viability, we integrate the DM with the unsupervised Stein's unbiased risk estimator to enable learning from noisy observations and circumvent the requirements for ground truth channel data that is hardly available in practice. Results reveal that the proposed estimator achieves high-fidelity channel recovery while reducing estimation latency by a factor of 10 compared to state-of-the-art schemes, facilitating real-time implementation. Moreover, our method outperforms existing estimators while reducing the pilot overhead by half, showcasing its scalability to ultra-massive antenna arrays., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

An exploit of the Sequential Importance Sampling (SIS) algorithm using Differential Algebra (DA) techniques is derived to develop an efficient particle filter. The filter creates an original kind of particles, called scout particles, that bring information from the measurement noise onto the state prior probability density function. Thanks to the creation of high-order polynomial maps and their inversions, the scouting of the measurements helps the SIS algorithm identify the region of the prior more affected by the likelihood distribution. The result of the technique is two different versions of the proposed Scout Particle Filter (SPF), which identifies and delimits the region where the true posterior probability has high density in the SIS algorithm. Four different numerical applications show the benefits of the methodology both in terms of accuracy and efficiency, where the SPF is compared to other particle filters, with a particular focus on target tracking and orbit determination problems., Comment: 17 Pages, 12 Figures

This paper provides a semidefinite programming hierarchy based on state polynomial optimization to determine the existence of quantum codes with given parameters. The hierarchy is complete, in the sense that if a $(\!(n,K,\delta)\!)_2$ code does not exist then a level of the hierarchy is infeasible. It is not limited to stabilizer codes and thus applicable generally. While it is formally dimension-free, we restrict it to qubit codes through quasi-Clifford algebras. We derive the quantum analog of a range of classical results: first, from an intermediate level a Lov\'asz bound for self-dual quantum codes is recovered. Second, a symmetrization of a minor variation of this Lov\'asz bound recovers the quantum Delsarte bound. Third, a symmetry reduction using the Terwilliger algebra leads to semidefinite programming bounds of size $O(n^4)$. With this we give an alternative proof that there is no $(\!(7,1,4)\!)_2$ quantum code, and show that $(\!(8,9,3)\!)_2$ and $(\!(10,5,4)\!)_2$ codes do not exist., Comment: 51 pages

In-context learning (ICL) refers to a remarkable capability of pretrained large language models, which can learn a new task given a few examples during inference. However, theoretical understanding of ICL is largely under-explored, particularly whether transformers can be trained to generalize to unseen examples in a prompt, which will require the model to acquire contextual knowledge of the prompt for generalization. This paper investigates the training dynamics of transformers by gradient descent through the lens of non-linear regression tasks. The contextual generalization here can be attained via learning the template function for each task in-context, where all template functions lie in a linear space with $m$ basis functions. We analyze the training dynamics of one-layer multi-head transformers to in-contextly predict unlabeled inputs given partially labeled prompts, where the labels contain Gaussian noise and the number of examples in each prompt are not sufficient to determine the template. Under mild assumptions, we show that the training loss for a one-layer multi-head transformer converges linearly to a global minimum. Moreover, the transformer effectively learns to perform ridge regression over the basis functions. To our knowledge, this study is the first provable demonstration that transformers can learn contextual (i.e., template) information to generalize to both unseen examples and tasks when prompts contain only a small number of query-answer pairs.