卷 61, 编号 2 (2025)

Locally thin families of sets and weak disjunctive codes are studied. The main result is obtaining new lower bounds on the rates of the studied constructions using probabilistic methods. Additionally, new lower bounds on the rates of multimedia codes that determine the coalition under averaging and noise attacks are presented, which follow from the obtained estimates for the rates of weak disjunctive codes.

An extended description of a new regularization method based on optimization aimed at inverting the sample covariance matrix without requiring complex calculations is presented. The method is designed for linear receivers in multi-user communication systems with a large number of antennas and operates under conditions of a limited number of samples. The study shows that the considered probability distributions of noise do not affect the optimal value of the regularization factor. Simulation results confirm that the method outperforms traditional approaches and provides better conditioning of the sample covariance matrix, reducing the computational complexity of calculating the weight matrix of the linear equalizer in the uplink channel of the communication system.

Practical discrete optimization problems often contain multidimensional arrays of variables with linear constraints, which complicates their conversion to QUBO (quadratic unconstrained binary optimization) form. The article proposes a systematic approach to transforming such problems, which includes three key steps: the transition from a multidimensional representation of variables to a one-dimensional one using the Kronecker product of matrices, the reduction of mixed variables to binary ones, and the introduction of linear constraints into the objective function through quadratic penalties. Explicit computational formulas are obtained for each stage, simplifying their software implementation. The developed method is illustrated with examples from graph theory and combinatorial optimization, including classical formulations, confirming its universality. The results of the article allow standardizing the process of adapting problems for solving on quantum annealing algorithms (e.g., D-Wave) and classical QUBO solvers.

Reconfigurable intelligent surfaces (RIS) is one of the promising technologies for increasing the throughput and expanding the coverage of existing and future wireless networks. It is expected that RIS will be actively used in outdoor scenarios, where it will be exposed to weather conditions such as rain. Rain, in turn, would affect the amplitude and phase frequency characteristics of the unit cells (UCs) that form the RIS, leading to a deterioration in the performance of the RIS wireless system in terms of the signal-to-noise ratio (SNR) at the receiver. This paper investigates the effect of rain of various intensity on the SNR at the receiver of a wireless system with RIS operating at a frequency of 4.8 GHz. Also, a method is proposed to compensate for this effect by thickening the dielectric and subsequently adjusting the sizes of the UCs. It is demonstrated that the proposed compensation method reduces the SNR loss at the receiver to 0.9 dB in rainy conditions.

Necessary and sufficient conditions are found for binary sequences formed by a feedback with carry shift register to have an ideal arithmetic autocorrelation for any initial state of the register.