Vol 61, No 1 (2025)

A sum of independent identically distributed random variables of a special form is considered. Using this sum, current posterior probabilities of messages for a randomly chosen code in a binary symmetric channel are described. The concentration function of this sum is studied.

Quantum key distribution is one of perspective directions of modern cryptography. It allows the parties of information exchange to develop a common cryptographic key, the secrecy of which is ensured by the laws of quantum mechanics. The paper studies the influence of the characteristics of the quantum channel, as well as the parameters of the applied algorithms on the maximum achievable length of a communication line for a protocol with phase-time coding and decoy states. By computational experiments with a simulation model of a quantum key distribution system based on the above protocol, it was found that the stable operation of the protocol is possible with line length of at most 210 km. It was also shown that this value can be increased by constructing more efficient sifted key correction algorithms.

The paper is devoted to the study of statistical and spectral complexity diagrams, which play an important role in solving the signal classification task. Lemmas on the construction of analytical metric grids for statistical and spectral complexity diagrams are formulated and proved. The obtained theoretical results are verified by numerical experiments, which confirmed the effectiveness of theoretical estimates.