Fluid antenna (FA) technology has recently emerged as an effective means of exploiting spatial diversity through position-domain reconfigurability. This paper investigates the integration of FA into over-the-air federated learning (OTA-FL) systems with the aim of improving aggregation reliability and user participation under realistic channel conditions. By dynamically selecting antenna positions, FA-equipped users can exploit additional spatial degrees of freedom to realize more favorable channel conditions, thereby increasing the probability of successful contribution to the OTA aggregation process in each communication round. We consider an uplink OTA-FL framework consisting of a single fixed-antenna access point and multiple FAenabled users operating over spatially correlated fading channels. Unlike existing studies that primarily rely on optimization-based designs or numerical evaluations, we develop a tractable analytical framework that enables a rigorous performance characterization of FA-assisted OTA-FL. In particular, closed-form expressions are derived for the aggregation error outage probability and the expected number of participating users per round. Spatial channel correlation across FA ports is modeled using a copula-based approach, where the Clayton copula is adopted to capture lower-tail dependence relevant to worst-case fading conditions. Numerical results validate the analytical findings and demonstrate that FA-assisted OTA-FL significantly outperforms conventional fixed-antenna schemes in terms of aggregation reliability and participation efficiency, while providing insights under practical system considerations.

This paper investigates an over-the-air federated learning (OTA-FL) system that employs fluid antennas (FAs) at an access point. The system enhances learning performance by leveraging the additional degrees of freedom provided by antenna mobility. We analyze the convergence of the OTA-FL system and derive the optimality gap to illustrate the influence of FAs on learning performance. With these results, we formulate a nonconvex optimization problem to minimize the optimality gap by jointly optimizing the positions of the FAs, the beamforming vector, and the transmit power allocation at each user. To address the dynamic environment, we cast this optimization problem as a Markov decision process and propose the recurrent deterministic policy gradient (RDPG) algorithm. Finally, extensive simulations show that the FA-assisted OTA-FL system outperforms systems with fixed-position antennas and that the RDPG algorithm surpasses the existing methods.

This paper proposes an innovative approach to improve over-the-air federated learning (OTA-FL) systems by integrating fluid antennas (FAs) at the access point. By exploiting the mobility of FAs, we aim to increase the correlation among the users’ channels, thereby improving the learning performance. We analyze the performance of over-the-air computation and the convergence behavior of the OTA-FL system, highlighting the benefits of FAs. Since the learning performance improves as more devices participate in the FL aggregation, we formulate a non-convex optimization problem that maximizes the number of selected users by jointly optimizing FA positions and the beamforming vector, coupled with a user selection policy subject to a mean-squared error constraint. To address environmental dynamics, we describe the problem as a Markov decision process and develop a long short-term memory (LSTM)-based algorithm for efficient decision-making. Simulation results demonstrate that the proposed FA-assisted OTA-FL framework significantly outperforms conventional setups, achieving higher user selection rates and improved learning performance compared to existing benchmarks.

Abstract Hierarchical temporal memory (HTM) is a promising unsupervised machine-learning algorithm that models key principles of neocortical computation. One of the main components of HTM is the spatial pooler (SP), which encodes binary input streams into sparse distributed representations (SDRs). In this paper, we propose an information-theoretic framework for the performance comparison of HTM-spatial pooler (SP) algorithms, specifically, for quantifying the similarities and differences between sparse distributed representations in SP algorithms. We evaluate SP's standalone performance, as well as HTM's overall performance. Our comparison of various SP algorithms using Renyi mutual information, Renyi divergence, and Henze–Penrose divergence measures reveals that the SP algorithm with learning and a logarithmic boosting function yields the most effective and useful data representation. Moreover, the most effective SP algorithm leads to superior HTM results. In addition, we utilize our proposed framework to compare HTM with other state-of-the-art sequential learning algorithms. We illustrate that HTM exhibits superior adaptability to pattern changes over time than long short term memory (LSTM), gated recurrent unit (GRU) and online sequential extreme learning machine (OS-ELM) algorithms. This superiority is evident from the lower Renyi divergence of HTM (0.23) compared to LSTM6000 (0.33), LSTM3000 (0.38), GRU (0.41), and OS-ELM (0.49). HTM also achieved the highest Renyi mutual information value of 0.79, outperforming LSTM6000 (0.73), LSTM3000 (0.71), GRU (0.68), and OS-ELM (0.62). These findings not only confirm the numerous advantages of HTM over other sequential learning algorithm, but also demonstrate the effectiveness of our proposed information-theoretic approach as a powerful framework for comparing and evaluating various learning algorithms.

Abstract In a nervous system propagation of spikes among neurons can be interpreted as an information transmission process, where, a neural response carries information about the stimulus. Quantification of this information might be of theoretical and practical importance. In this paper, (i) The interaction between two neurons with an electrically coupled transport of ions is modelled mathematically, where the communication through the junction gap between very close neurons occurs with a specific time delay; (ii) then, the connection structure of neurons is proposed based on a particular Rulkov network model. The corresponding process is modelled as a non‐linear binary channel with memory; and (iii) by assuming a recurrence relation for number of available membrane potential changing due to the arrival of the spike to the axonal terminal, the mutual information between channel input and output is obtained and the input range maximizing mutual information, and hence, the information rate of channel is derived.

Abstract Two‐user multiple‐access relay channel (MARC) with side information (SI) non‐causally known at one encoder is studied, where transmitters send a common message with rate R 0 , and private messages with rates R 1 and R 2 ; and derive a general achievable rate region by appropriately using superposition block Markov encoding, binning scheme, Gel'fand–Pinsker (GP) coding and partial decode‐forward (PDF) strategy at the relay. Also, it is shown that this capacity inner bound can be tight for two special classes of degraded and reversely degraded multiple‐access relay channels with one informed encoder. In order for the theoretical findings to be potentially applicable in communications performance metrics evaluations, the obtained general achievable rate region, while having all of the previous works on the point to point, relay and multiple access channels with and without SI as its special cases, is extended to the corresponding Gaussian version, the dirty paper coding of which has been a challenging and widely studied problem, and the result of which includes a variety of previously studied important Gaussian results. Finally, mathematical results are evaluated numerically.

In this article, we consider the massive nonorthogonal multiple access (NOMA) with a hybrid automatic repeat request (HARQ) for short packet communications. To reduce the latency, each user can perform one retransmission provided that the previous packet was not decoded successfully. The system performance is evaluated for both coordinated and uncoordinated transmissions. We first develop a Markov model (MM) to analyze the system dynamics and characterize the packet error rate (PER) and throughput of each user in the coordinated scenario. The power levels are then optimized for two scenarios, including the power constrained and reliability constrained scenarios. A simple yet efficient dynamic cell planning is also designed for the uncoordinated scenario. Numerical results show that both coordinated and uncoordinated NOMA-HARQ with a limited number of retransmissions can achieve the desired level of reliability with the guaranteed latency using a proper power control strategy. The results also show that NOMA-HARQ achieves a higher throughput compared to the orthogonal multiple access scheme with HARQ under the same average received power constraint at the base station.

This paper studies performance analysis of physical layer security in a Rayleigh fading wiretap channel, where, the main (transmitter-to-legitimate receiver) and eavesdropper (transmitter-to-eavesdropper) channel coefficients are correlated. By exploiting the novel approach called Copula theory, we derive closed-form expressions for average secrecy capacity (ASC), secrecy outage probability (SOP), and secrecy coverage region (SCR). Moreover, to more evaluate the impact of channel correlation, the asymptotic behavior of SOP in high signal-to-noise ratio (SNR) regime and other scenarios is studied, and finally, the analytical results are illustrated numerically under the positive dependence, independence, and negative dependence structures. Based on the insights from this analysis, we found that the effect of correlated fading on the performance of physical layer security can be helpful or harmful in different scenarios, depending on the structure of dependency between the main and eavesdropper channels.

From practical and theoretical viewpoints, performance analysis of communications with correlated fading channels is important. In this study, the authors exploit a novel approach based on Copula function concept to investigate the impact of correlation of Rayleigh fading channels on communication performances. One of the most convenient ways to describe the dependence between several variables is using Copula functions. For this purpose, by applying the Farlie–Gumbel–Morgenstern Copula function, they derive closed‐form expressions for outage probability as well as coverage region in a wireless multiple access channel. It is shown that the fading correlation improves the outage probability and coverage region for negative dependence structure. Specifically, whenever the dependence structure tends to negative values, the outage and coverage region performance improvement is increased. Finally, the efficiency of the analytical results is illustrated numerically.

Image classification is very important in pattern recognition and computer vision, where, for integrating final representation, feature pooling methods of the max‐pooling, sum‐pooling and average‐pooling have been widely used. In this study, the authors propose a new method called K ‐strongest responses (KSRs) on the dictionary atoms for integrating the coding coefficients to generate the final representation that is compared with the previous pooling methods, produces better performance for the image classification task. On the basis of the KSR method, to improve classification accuracy and generate more compact and discriminative final representation, a new framework consisting of two‐part KSR and bag‐of‐features is proposed. To evaluate the performance of the proposed method and framework, they apply it to locality‐constrained linear coding, linear distance coding and sparse coding by using two datasets from benchmarks of scene classification: 19‐class satellite scene and UC Merced Land. The results show that the coding coefficients integrated by their method and framework are more discriminative than other methods.

A wireless ad hoc network consisting of one‐hoping relay channel and some interfering nodes with possible arbitrary correlation between wireless channels coefficients is studied. By exploiting a novel approach called Copula theory, enabling us to describe joint probability distribution function for arbitrarily correlated random variables, the authors derive a closed‐form expression for success probability in different dependence structures of channels. Specifically, by applying the Farlie–Gumbel–Morgenstern (FGM) Copula and the popular Archimedean (Clayton, Gumbel, and Frank) Copulas, they analyse the network performance in terms of success probability, and show that the channels correlation improves the performance of success probability so that whenever the dependence structure tends to higher values, the performance improvement is increased. Besides, it is found that the investigation of channel correlation effects by FGM Copula is more tangible compared to Archimedean Copulas. Finally, the efficiency of the analytical results is illustrated numerically.

The discrete alphabet and memoryless relay channel (RC) with side information (SI) and its extension to the continuous alphabet Gaussian version with uncorrelated noises have been studied by Zaidi et al . Zhang et al. have studied a Gaussian RC with correlated noises and uninformed relay. Aggarwal et al. have analysed a coverage region for a RC without any SI and with uncorrelated noises. In this study, the authors have investigated the impact of SI on the coverage region as an important wireless performance factor for a wireless RC, and also derived the capacity upper and lower bounds for such a channel with SI and correlated noises. The results of this research include previous studies as special cases, and that under special circumstances, noise correlation can tighten the upper bound, and furthermore, SI enlarges the coverage region as expected intuitively. Mathematical derivations and numerical results are obtained to support the claims.

The past decade has seen the rapid development of information theoretic learning and its applications in signal processing and machine learning. Specifically, minimum error entropy (MEE) and maximum correntropy criterion (MCC) have been widely studied in the literature. Although MEE and MCC are applied in many branches of knowledge and could outperform statistical criteria (such as mean square error), they have not been compared with each other from theoretical point of view. In some cases, MEE and MCC perform similarly to each other; however, under some conditions (e.g., in non-Gaussian environments), they act differently. This letter derives a new information theoretic relation between MEE and MCC, leading to better understanding of the theoretical differences, and illustrates the findings in a common example.

Mean square error (MSE) is the most prominent criterion in training neural networks and has been employed in numerous learning problems. In this paper, we suggest a group of novel robust information theoretic backpropagation (BP) methods, as correntropy-based conjugate gradient BP (CCG-BP). CCG-BP algorithms converge faster than the common correntropy-based BP algorithms and have better performance than the common CG-BP algorithms based on MSE, especially in nonGaussian environments and in cases with impulsive noise or heavy-tailed distributions noise. In addition, a convergence analysis of this new type of method is particularly considered. Numerical results for several samples of function approximation, synthetic function estimation, and chaotic time series prediction illustrate that our new BP method is more robust than the MSE-based method in the sense of impulsive noise, especially when SNR is low.

Point‐to‐point communication channels with phase noise have been studied extensively. To the best of the authors’ knowledge, the broadcast channel (BC) with phase noise has not been studied yet. In this study, having reviewed definitions of the channels with phase noise, the authors analyse capacity region of the BC impaired by Wiener phase noise and additive white Gaussian noise and obtain an outer bound for the capacity region. Also, its high signal‐to‐noise ratio analysis is presented. Their outer bound includes the known outer bound for the point‐to‐point phase noise channel as its special case. Mathematical findings are explained more by simulation results.

Spectrum sensing is a significant issue in cognitive radio networks which enables estimation of the frequency spectrum and hence provides frequency reuse. In the large‐scale cognitive radio networks, secondary users cannot share a common spectrum since the coverage area of primary users is limited. In this study, the authors suggest a diffusion adaptive learning algorithm based on correntropy cooperation policy, which first categorises received data of secondary users into several groups, and then learns a common spectrum inside each group. The mean‐square performance of proposed algorithm is analysed and supported by simulations. Experimental results show that, in a multitask cognitive network, the proposed algorithm can achieve a better mean‐square deviation learning performance both in transient and steady‐state regimes in comparison with other conventional algorithms.

The two-user discrete memoryless cognitive multiple-access channel with confidential messages (DM-CMAC-CM) has been studied in the literature with a result for the secrecy capacity region. In this paper, we study a more general and practical model (three-user DM-CMAC-CM), although similar generalizations have been intractable in some studied cases, and obtain a capacity-equivocation and secrecy capacity region results including previous results as its special cases.

From practical and theoretical viewpoints, performance analysis of communication systems by using information‐theoretic results is important. In this study, first, the authors obtain a general achievable rate region for three‐user discrete memoryless multiple‐access relay channel (MARC) via partial decode and forward strategy and regular block Markov encoding/backward decoding. Also by extending the discrete alphabet results to the continuous alphabet channel, an inner bound for three‐user Gaussian MARC (GMARC) is achieved. Next, based on the inner bound of three‐user GMARC, they analyse the impact of a relay on the coverage region of MARC, as a basic model for uplink communications between a base station and users with the help of a relay. This analysis includes the coverage region for the multiple‐access channel and two‐user GMARC as special cases. Considering rate regions for the GMARC and fading GMARC, it is proved that in a fixed transmission rate, the relay extends coverage region of the MARC. Numerical illustrations confirm their theoretical results.

Discovery of gene regulatory network (GRN) from gene expression data gives an insight into tumor developments and underlying structures. Granger causality (GC) is considered as a powerful tool to detect the interactions between elements of a network. Among the various methods suggested for GC, we use Pairwise GC (PGC), Kernel GC (KGC) and Correntropy method. Also GC is defined in two domains. In time domain, GC cannot correctly determine how strongly one time series influences the other when there is directional causality between them, this limitation necessitates an alternative method. In this regard, GC in frequency domain is being applied as a solution. In this paper, first, we conduct a frequency domain analysis on these methods theoretically. We then evaluate the performance of PGC in both domains by applying real HeLa dataset with three experiments and compare it with previous work. Finally, we apply all methods to both synthetic data and a 94-gene HeLa data to illustrate the discovered networks. We show that frequency domain has better performance in discovery of relations at all experiments.

The fact that the results for 2‐receiver broadcast channels (BCs) are not generalised to the 3‐receiver ones is of information theoretical importance. In this study, the authors study two classes of discrete memoryless BCs with non‐causal side information, that is, multilevel BC (MBC) and 3‐receiver less noisy BC. First, they obtain an achievable rate region and a capacity outer bound for the MBC. Second, they provide the capacity region for a special class of 3‐receiver less noisy BC. Third, the obtained special capacity region for the 3‐receiver less noisy BC is evaluated for the continuous alphabet fading Gaussian version. It is worth mentioning that the previous works are special cases of the authors works.

In this paper, we study the two transmitter multiple-access channel (MAC) with noncausal side information at one (single-sided) or both (two-sided) of the encoders in the presence of an external wiretapper (WT) and under individual and collective secrecy constraints. Our work consists of four parts. First, we consider the discrete memoryless (DM-MAC-WT) case of the model and derive inner and outer bounds on the secrecy capacity region under both of the secrecy constraints. Second, the results are extended to the Gaussian memoryless case [Gaussian multiple-access channel WT (GMAC-WT)] in detail and are used to illustrate numerically that the secrecy rate region is enlarged by increasing the power of the interference signal which is known noncausally at the encoder. Third, we analyze the strong interference regime as an important regime in GMAC with side information and show that under collective secrecy constraint, we can achieve the secrecy capacity region of the single-sided channel asymptotically for a special case in which the signal and noise powers satisfy specific constraints. To the best of our knowledge, this capacity region is the first one obtained for GMAC-WT. Finally, we show that our results include previous works as its special cases for both the single-sided and two-sided channel models.

In this study, the authors study a two‐user Gaussian doubly dirty compound multiple‐access channel with partial side information (GDD‐CMAC‐PSI) where two independent additive interference signals are considered, each one known non‐causally and partially to one of the encoders but unknown to either of the receivers. This channel, first, can model two users communicating with two base stations suffering from interference, and second, includes many previously studied channels as its special cases. For such a communication scenario, first, a general capacity outer bound is derived. Depending on the values of cross link gains, they classify the channel into three classes: weak, strong and mixed GDD‐CMAC‐PSI. Next, assuming that the interference signals have infinite variances, they obtain capacity outer bounds for these classes. Then, an achievable sum‐rate is derived for the GDD‐CMAC‐PSI using Costa's strategy and thereby, they show that when both interference signals have infinite variances, this achievable sum‐rate vanishes. Later, by utilising the lattice strategies and deriving achievable rate regions, independent of the interference powers, they show that in contrast with Costa's strategy, lattice‐strategies can achieve positive rates. Finally, depending on signal‐to‐noise ratio gaps at receivers, various achievable rates are obtained.

A new, reliable and computationally efficient blind method is proposed for joint estimation of channel order and number of active users in a direct sequence code‐division multiple‐access system with multi‐path fading channel. The proposed method (i) exploits a parametric model used for equalisation of multi‐path channels in finite impulse response multi‐input multi‐output systems, (ii) first, estimates rank of correlation matrix of observation, by combining the subspace method and information‐theoretic criteria, (iii) then, estimates simultaneously channel order and number of active users, by using the estimated rank and the model parameter, without any prior information, (iv) uses only a single antenna, in contrast to the previous methods, while having the ability to jointly estimate higher numbers of active users and channel order in lower signal‐to‐noise ratios. Numerical results show that the proposed method can estimate higher number of users and also has higher detection probability when using minimum mean square error algorithm.

In this paper we derive a new upper bound for the input-output mutual information of FSO channels with input-dependent Gaussian noise by using a simple mathematical inequality. Then, by maximizing the obtained upper bound over all the discrete input distributions with equally spaced mass points, and approximating, we reach to a third order equation for the optimum input distribution. Our equation (i) determines the optimum input distribution directly in contrary to the Farid-Hranilovic (FH) work where it is found numerically, and also, (ii) gives a previously derived second order equation for the optimum input distribution of FSO channels with input-independent Gaussian noise in a special case. Using numerical illustrations, we compare our input distribution with previous works.

In this paper, we derive an inner bound for two-user state-dependent multiple-access relay channel (MARC) via decode and forward strategy (DF) in which the states of channel are known non-causally at the relay. The inner bound is obtained by using a combination of binning scheme and codeword splitting. Codeword splitting at the relay is applied to generating two codebooks, one for utilizing a joint codebook between the relay and the transmitters and another for utilizing the channel state information. Furthermore, we obtain an outer bound for this model. Actually, our work is a generalization of Zaidi et al. work on the relay channel with informed relay to the MARC.

In this study, the authors establish achievable rate and capacity regions for three kinds of Gaussian multiple access channels (MACs) with side information (SI) partially (estimated or sensed version) and non‐causally known at the transmitters. Actually, the authors show that the lattice strategy is optimal for Gaussian MACs with partial SI, the same as it is for Gaussian MACs with full SI studied by Philosof–Zamir. The rate and capacity regions, while showing that partiality in SI reduces the achievable rates, subsumes directly the Philosof–Zamir rate regions and also the Gueguen–Sayrac work and the Costa theorem indirectly as special cases.

In this study, the authors obtain a general and new achievable rate region and some certain capacity theorems for multiple‐access relay channel (MARC), using partial decode‐and‐forward (PDF) strategy at the relay, superposition coding at the transmitters and multiple‐access and relay channel (RC) decoding schemes. (a) The authors general rate region (i) generalises the achievability part of Slepian–Wolf multiple‐access capacity theorem to the MARC, (ii) extends the Cover–El Gamal best achievable rate for the RC with PDF strategy to the MARC, (iii) gives the Kramer–Wijengaarden anticipated rate region for the MARC and (iv) meets max‐flow min‐cut outer bound for some important classes of the MARC. (b) They extend the results to the Gaussian case as an important practical aspect of MARC and obtain (v) a general and new achievable rate region for Gaussian Slepian–Wolf MARC. Finally, they evaluate their inner bounds for Gaussian MARC numerically, and illustrate specifically that when the relay is closer to the transmitters, their rates are greater than the previous corresponding rates.

In this paper, we establish achievable rate regions for the multiple access channel (MAC) with side information partially known (estimated or sensed version) at the transmitters. Actually, we extend the lattice strategies used by Philosof-Zamir for the MAC with full side information at the transmitters to the partially known case. We show that the sensed or estimated side information reduces the rate regions, the same as that occurs for Costa Gaussian channel.

Three-receiver broadcast channel (BC) is of interest due to its information theoretical differences with two receiver one. In this paper, we derive achievable rate regions for two classes of 3-receiver BC with side information available at the transmitter, Multilevel BC and 3-receiver less noisy BC, by using superposition coding, Gel'fand-Pinsker binning scheme and Nair-El Gamal indirect decoding. Our rate region for multilevel BC subsumes the Steinberg rate region for 2-receiver degraded BC with side information as its special case. We also find the capacity region of 3-receiver less noisy BC when side information is available both at the transmitter and at the receivers.

We study the two-user discrete memoryless compound multiple access channel (MAC) with common message and two specially correlated channel states each known non-causally by one of the encoders. Two channel states are correlated in the sense of Slepian-Wolf (SW) in which two correlated states are modeled by three independent states: a common state and two private states. By using superposition coding, binning scheme and jointly decoding, we propose several achievable rates for various cases of the two-user compound MAC with non-causal Slepian-Wolf channel states available at encoders and common message or conferencing encoders. Also, we show that the obtained achievable rate regions are optimal when perfect states are known at both decoders as well.

Gastpar and Vetterli named the ad hoc networks with one randomly selected source-destination pair as relay networks, and they suggested using arbitrary network coding in order to increase the overall efficiency. Here, the relay network is investigated with two relays, no interference and a new achievable rate is obtained using a new network coding (decode-and-broadcast). The obtained achievable rate (i) gives the lower bound for general relay channel, obtained by Cover and El Gamal, but with a slight difference owing to no interference assumption at the receiver, (ii) includes the one relay rates of a two-level relay channel studied by Gupta and Kumar using point-to-point coding, (iii) includes the rates of two-relay Aref network and other special two-relay networks, (iv) meets the max-flow min-cut upper bound under certain additional assumptions resulting in certain capacity theorems that include the related previous capacities, (v) is validated by its consistency with previous results relevant to special cases of broadcast channels.

The authors indicate the dependence between the inputs of the relay channel with one auxiliary random variable as Cover, El-Gamal and Salehi have done for the multiple access channel with arbitrarily correlated sources. Then, by considering broadcast and multiple access sub-channels in the relay channel, the authors describe the essential role of the relay with special Markovity conditions on the auxiliary random variable and channel input–outputs, and unify most of known capacity theorems into one capacity theorem. The capacity theorem potentially may be applicable to a more general class of relay channels including at least the relay channels with known capacity.

An achievable rate region for the genie-aided cognitive radio channel is obtained using the celebrated Han-Kobayashi jointly decoding strategy for the interference channel and the Gel'fand-Pinsker coding scheme for channels with side information known at the transmitter. The achievable rate region is then simplified by Fourier-Motzkin elimination. The obtained achievable rate region (i) extends the Chong-Motani-Garg region for the interference channel to the cognitive channel and (ii) is a simplified description of the Devroye-Mitran-Tarokh rate region for the genie-aided cognitive radio channel.