EVALUATION OF THE CHARACTERISTICS OF A TWO-STAGE SYNCHRONIZATION ALGORITHM BASED ON THE SELECTION OF AN ADJACENT PAIR OF SEGMENTS WITH THE MAXIMUM TOTAL COUNT IN THE QKD SYSTEM

Abstract

A two-stage synchronization algorithm is proposed based on the selection of an adjacent pair of segments with the maximum total count in the QKD system. The algorithm is based on a well–known approach to reducing the time of entering into synchronism - the analysis of adjacent pairs of time segments. A distinctive feature of the proposed algorithm is to ensure that the probability of successful search and testing is not worse than the required level. It should be noted that due to the testing stage, erroneous decisions made at the search stage are rejected, which minimizes the probability of false synchronization due to the registration of noise pulses. At the search stage, the equipment sequentially registers the total counts from all adjacent pairs of segments. Next, a pair of segments with the maximum total count is selected, and the count in one of the pairs of segments reliably exceeds the values of the counts from all other pairs of segments, and the equipment proceeds to the testing stage. Testing consists of polling the photodetector during the gating pulse to re-register the count. In case of positive testing, the process of «rough» estimation of the moment of reception of the sync pulse is considered successfully completed, otherwise the equipment returns to the search in the next frame. Note that the maximum allowable number of frames and tests correspond to the search and testing stages, respectively. Analytical expressions are obtained for calculating the time and probabilistic characteristics of the search and testing stages of the proposed detection algorithm based on the selection of an adjacent pair of segments with the maximum total count, including for calculating the allowable number of frames and tests while ensuring the required probabilities of successful search and testing, respectively. It has been found that with an increase in the average number of photons in the sync pulse, the average number of frames and tests, as well as the average time of successful search and testing, decrease significantly. For example, when the average number of photons in a sync pulse increases by 5 times, the average number of tests for successful testing and the average time for successful testing decrease by 1.5 times, and the permissible number of tests by 5 times.