We study spectral representation and its applications for non-decaying continuous-time signals that are not necessarily bounded at ±∞ . We introduce the notions of transfer functions, spectrum degeneracy, spectrum gaps, and band-limitedness, for these unbounded signals. As an example of applications, we give explicit formulas for transfer functions of low-pass and high-pass filters suitable for these signals. As another example of applications, we show that non-decaying unbounded signals with a single point spectrum degeneracy and polynomial rate of growth are predictable. The corresponding transfer functions for the predictors are obtained explicitly. In addition, we obtain an interpolation sampling formula for unbounded bandlimited signals.
The key elements of Industrial Internet of Things networks are RTA (Real-Time Application) stations, which detect events and deliver alerts about them within a limited time with high probability. Since such stations are often located in hard-to-reach places and cannot always be connected to the power supply, they must consume little energy. A promising solution for ensuring low latency and energy consumption is the use of Target Wake Time (TWT) and Restricted Target Wake Time (R-TWT) mechanisms, introduced in the latest Wi-Fi standards: Wi-Fi 6 and Wi-Fi 7. However, the effectiveness of using these mechanisms in a heterogeneous network consisting of both RTA stations and regular stations operating in saturation mode has not been studied extensively. In this paper, we conduct a comparative study of the effectiveness of using TWT and R-TWT mechanisms in scenarios of low-intensity traffic service for RTA stations. To do this, we develop an analytical model that, for the first time, makes it possible to evaluate the probability of RTA station frame delivery within a given time and the throughput for regular stations.
We discuss modern applied problems of discrete optimization at a mathematical level, and for one of them, clustering points in multidimensional real space, we examine in detail the algorithm for solving it. A characteristic feature of these problems is the large size of the initial data, often represented by matrices with tens of thousands of rows and tens of thousands of columns. This leads to problems of processing large amounts of data in the context of a complex computational algorithm; moreover, it is often essential to obtain a reasonably accurate solution to the problem quickly, so the question of the algorithm complexity is of fundamental importance. Solving such a clustering problem leads to difficult mathematical problems: removing hidden parameters; identifying significant features; switching to optimal and informationally significant point coordinates; specific representation (manifold maps) of the vertices of a weighted graph; selection of a function depending on the current clustering of vertices, the maximization of which leads to the desired clustering; for each cluster, selection of features that individually characterize it; and, finally, reduction of the dimensionality of the source data.
Wi-Fi standardization continues: IEEE 802.11bn (Wi-Fi 8) reached Draft 1.0 in August 2025 and is progressing through comment resolution. The wireless industry now stands at a pivotal crossroads as it begins to define Wi-Fi 9. This paper analyzes technical directions and candidate features for the post-802.11bn amendment, tentatively referred to as Wi-Fi 9. We synthesize contributions from device manufacturers, network operators, and research institutions presented to the IEEE 802.11 Wireless Next Generation Standing Committee in early 2026. The emerging consensus indicates that, rather than increasing the nominal data rates, the next generation will likely prioritize deterministic performance, reliability, and expanded application domains. The paper examines the market forces driving this transition, including AI workloads that invert traditional traffic asymmetry, industrial robotics that demand sub-millisecond latency, and immersive entertainment that requires the simultaneous satisfaction of throughput, latency, and reliability constraints. Then the paper analyzes candidate technologies spanning PHY and MAC layer transformations, coordination between multiple networks, and AI integration throughout the protocol stack. Implementation challenges, including backward compatibility tradeoffs and spectrum availability, are discussed. Finally, the paper outlines the anticipated standardization timeline targeting commercial deployment of Wi-Fi 9 in the 2030s.
Among known random multiple access (RMA) algorithms, the part-and-try (splitting) algorithm demonstrates the highest throughput. However, its implementation in cellular random access channels is challenging, since the correct operation of the algorithm requires absolute time synchronization among all users to uniquely identify events in a Poisson arrival process. In this paper, we propose a modified RMA algorithm based on the principles of the part-and-try algorithm, in which the introduction of randomization eliminates the need for temporal event identification. This modification enables the algorithm to be implemented in practical random access systems. The achieved throughput of the algorithm is 0.485 .
To ensure reliable low-latency packet delivery required by real-time applications (RTAs), a new amendment to the Wi-Fi 8 standard proposes to employ the preemptive channel access method. Since this method has not been used in Wi-Fi networks before, the task of configuring its parameters to meet the Quality of Service requirements for RTA traffic is relevant. Previously, a network scenario was considered that included only one station serving priority traffic. In this paper, we investigate a more complex network scenario with N stations generating priority traffic. To this end, we have developed a Wi-Fi 8 network model that allows us to find the dependence of the RTA frame delay quantile and access point throughput on RTA traffic intensity and channel access method parameters. We give guidelines for choosing access method parameters for transmitting priority frames with a required delay quantile under which the throughput of the access point in the network is maximized.
The paper is devoted to the task of ensuring strict requirements for latency and reliability of data delivery for uplink video traffic generated by a remote vehicle control application in 5G Vehicle-to-Everything (V2X) networks. A distinctive feature of this type of traffic is that the size of video frames is variable, so we propose using a hybrid radio resource allocation scheme. According to this scheme, each user is assigned a dedicated subchannel, as well as a subchannel common to all users, which is used when the resources of the dedicated subchannel are insufficient to transmit a packet. We develop an analytical model that allows us to estimate the probability of packet loss for each user when using a hybrid resource allocation scheme. We show how to select optimal parameters for the hybrid scheme by using the developed analytical model.
The Hough transform (HT) is a cornerstone technique applied in fields ranging from classical image processing to cutting-edge neural networks. Its algorithmic implementations are primarily evaluated along two directions: computational complexity and accuracy, where the latter is typically defined as the error of approximation of continuous lines by discrete ones implicitly constructed during the HT algorithm execution. Fast HT (FHT) algorithms with optimal linearithmic complexity are well established—for instance, the Brady–Yong algorithm for images with power-of-two sizes. Extensions such as FHT2DT generalize this efficiency to images of arbitrary shape, but at the expense of accuracy, which deteriorates with increasing image size. On the other hand, HT algorithms that maintain a bounded approximation error achieve higher accuracy but approach near-cubic complexity, making them impractical for large inputs. In this work, we introduce the FHT2SP algorithm, which combines near-optimal speed with high accuracy. Within the FHT2SP algorithm formulation, we extend Brady’s original superpixel definition—applicable solely to square images with power-of-two side lengths—so that it becomes applicable to rectangular images of arbitrary dimensions. Unlike Brady’s definition, which restricted superpixels to square shapes with power-of-two linear size, our superpixel definition permits them to take any rectangular form. The FHT2SP algorithm further incorporates our extended superpixel definition into the FHT2DT algorithm. By carefully selecting the superpixel size, the FHT2SP achieves nearly optimal linear-log-cubed complexity Θ(whlog^3 w) for an image of shape w× h , while guaranteeing a constant approximation error bound λ+1/2 independent of image size, tunable via the FHT2SP meta-parameter λ∈(0,1] . The auxiliary space complexity is shown to be Θ(whlog^2 w) . We provide a summary table of experimental results, which can serve as practical guidance for selecting the value of the meta-parameter λ to balance accuracy, computational cost, and memory usage.
The proposed approach, based on introducing a coordinate system naturally associated with binocular vision, allows us to introduce the concept of a planar observable curve, formulate observability criteria, and establish the precompactness of the family of observable curves with respect to the Hausdorff metric.
We give a construction of LDPC codes from Deza graphs with parameters (v,k,1,0) . The Tanner graphs of these LDPC codes do not contain cycles of length 4. Special attention is given to the construction of LDPC codes from the Moore graphs with diameter 2. We identify and enumerate the smallest absorbing sets in the Tanner graphs of the obtained LDPC codes and analyze their structures. Furthermore, we describe a construction, based on the protograph operation, of an infinite family of LDPC codes, whose Tanner graphs have girth at least 6, obtained from each (v,k,1,0) Deza graph. We give an expression for the variance of a syndrome weight of the constructed LDPC codes, and also present simulation results.
We study the arithmetic autocorrelation of binary sequences generated by a feedback with carry shift register. We find necessary and sufficient conditions for the existence of families of such sequences with ideal arithmetic autocorrelation for arbitrary connection integer q . Under these conditions, any pair of cyclically different sequences with connection integer q also has ideal arithmetic crosscorrelation.
We study combinatorial structures known in coding theory: locally thin families of sets and weak superimposed codes. Using expurgated random coding methods, we obtain new lower bounds on the rates of the considered constructions, which generalize and improve previously known results. Furthermore, we consider traceability multimedia fingerprinting codes resistant to averaging attack and adversarial noise. We demonstrate new lower bounds on their rates, which follow from the obtained rate estimates for weak superimposed codes.
Practical discrete optimization problems often contain multidimensional arrays of variables interrelated by linear constraints such as equalities and inequalities. Values of each variable depend on its specific meaning and can be binary, integer, or discrete. These conditions make it technically difficult to reduce the original problem statement to QUBO form. We identify and examine three necessary transformations of the original problem statement to reduce it to QUBO form, namely transition from a multidimensional to a one-dimensional array, transition to binary variables in mixed problems, and incorporating linear constraints into the objective function in the form of quadratic penalties. We present and prove computationally convenient formulas to simplify these transformations. In particular, the formulas for the transition from a multidimensional to a one-dimensional array of variables are based on the application of the Kronecker product of matrices. The transformations considered are illustrated by numerous examples and used, as an application, to reduce a number of well-known problems in graph theory and combinatorial optimization to QUBO form.
Wi-Fi is evolving to support new areas such as extended reality, Industrial Internet of Things, and environments with numerous devices. Unlike previous generations that aimed to maximize peak and user-perceived throughput, Wi-Fi 8 (also known as IEEE 802.11bn Ultra High Reliability) intends to make Wi-Fi operation more reliable, i.e., to improve performance across the full range of scenarios, particularly in worst-case conditions. Specifically, 802.11bn is striving to increase throughput at various signal to interference and noise ratio levels, diminish the 95th percentile of latency, decrease packet losses, and reduce power consumption. To attain these ambitions, Wi-Fi 8 is going to introduce a series of groundbreaking mechanisms, including distributed-tone resource units, unequal modulations, prioritized and non-primary channel access, advanced roaming features, multi-AP coordination, and so on. We present the current status of Wi-Fi 8 development with an emphasis on the targets and enabling technologies. This tutorial also discusses open research directions that require the development of new intelligent methods and algorithms.
This paper presents a detailed study of a new regularization method based on optimization for the inverse sample covariance matrix. This method is highly computationally efficient and does not require complex computing resources. It is designed for linear receivers in multi-user communication systems with a large number of antennas and operates under conditions of limited sample data. The analysis showed that the probabilistic noise distributions do not significantly affect the optimal value of the regularization factor, which confirms the universality and reliability of the proposed approach. Simulation results demonstrate the superiority of this method over traditional approaches. In particular, the method provides better conditionality of the sample covariance matrix and significantly reduces the computational complexity of calculating the linear equalizer weight matrix in the uplink of a communication system, which makes it especially useful for modern communication systems with high user density and limited computing resources.
One of the main applications of quantum communication is quantum key distribution, which solves the problem of secure distribution of cryptographic keys between remote users. This paper investigates the performance of a phase-time coding quantum key distribution protocol belonging to the BB84 protocol family. We construct a simulation model that takes into account the peculiarities of hardware operation and physical properties of the transmission medium. Computational experiments with this model have shown that stable operation of the considered protocol is possible over communication lines up to 210 km long, but this parameter can be improved by constructing a more efficient error-correcting code.
We propose an analytical representation of complexity diagrams based on information about the number of discretes in the signal spectrum and the signal-to-noise ratio. This approach provides additional criteria for solving the classification problem. We formulate and prove lemmas on the construction of analytical metric grids for complexity diagrams. The obtained results are verified by numerical experiments, which have confirmed the efficiency of these methods.
We study the distribution function of a sum of independent identically distributed random variables of a special kind. This sum can be used to describe current posterior probabilities of messages for a randomly chosen code in a binary symmetric channel. These posterior probabilities are helpful in the study of feedback channels. We obtain nonasymptotic lower and upper estimates for this distribution function, which are close to each other.
In a number of LoRaWAN sensor network scenarios, it is required to deliver data with a given reliability and with minimal sensor energy consumption. To improve the reliability of data delivery in a LoRaWAN network, data can be transmitted in two modes: (i) with acknowledgments and retries of undelivered data, or (ii) without acknowledgments and with unconditional retries. In this paper, we develop a model of a LoRaWAN network in which some devices transmit data in the first mode and some in the second mode. The model makes it possible to find the dependence of packet loss probability, sensor energy consumption, and base station duty cycle on the traffic intensity. Based on the modeling results, we propose an algorithm for selecting the fraction of sensors transmitting data with confirmation and the number of repetitions for sensors transmitting data with unconditional repetitions that minimizes energy consumption, fulfills the limit on the duty cycle, and ensures the desired reliability of data transmission.
We introduce a randomized decisive rule with a Δ -layer of signal indistinguishability for the reception of binary pseudorandom signals under deliberate interference (jamming). We find that for signals with base n≤ 2 , when the layer thickness is optimal, the constructed receiver rule provides an increase in the guaranteed interference immunity of signal reception in the class of interference with limited average power, compared to the Kotelnikov receiver. The obtained value of the guaranteed error probability improves the actual upper bound for this quantity.
