Том 59, № 4 (2023)

A key problem of low-density parity-check (LDPC) codes analysis is estimation of an extremely low error floor that occurs at a high level of the signal-to-noise ratio (SNR). The importance sampling (IS) method is a popular approach to address this problem. Existing works typically use a normal sampling probability density function (PDF) with shifted mean, which yields a large variance of the estimate. In contrast, uniform distribution has equally probable samples on the entire range and thus should reduce the variance, but results in a biased estimation. This paper proposes a modified IS approach (IS-U) that allows considering the uniform distribution as a sampling PDF, and shows that this estimation is better than the traditional one. Also, this paper demonstrates that the existing criteria cannot be applied to evaluate the accuracy of the IS-U on the whole SNR range. To address this issue, a new metric is proposed, which uses only the convergence rate and does not depend on the true data.

Time synchronization is one of the most crucial issues that must be addressed in developing quantum key distribution (QKD) systems. It not only lets the transmitter and the receiver to assign a sequence number to each event and then do correct basis reconciliation, but also allows to increase signal-to-noise ratio. Time synchronization in satellite communications is especially complicated due to such factors as high loss, signal fading, and Doppler effect. In this work, a simple, efficient, and robust algorithm for time synchronization is proposed. It was tested during experiments on QKD between Micius, the world’s first quantum communications satellite, and an optical ground station located in Russia. The obtained synchronization precision lies in the range from 467 to 497 ps. The authors compare their algorithm for time synchronization with the previously used methods. The proposed approach can also be applied to terrestrial QKD systems.

An attempt is made to give an accurate mathematical interpretation of the energy–time uncertainty relation.

We propose an approach for generalization of formulas previously obtained by the authors for the first and second queue length moments in a queueing system with a nonordinary Poissonian arrival flow, single server, and constant service time to the case of a variable service time. The service time is assumed to be a random variable with a finite set of values. This model is adequate for a vast class of batch transmission systems, since the batch transmission time in real-world systems can take only finitely many values.