Study of the corrective ability of sync codes for the matched processing decoder

Abstract

Increase of the operation reliability of the frame synchronization schemes of communication systems affected by interferences might be achieved by using sync sequences optimal according to the minimax criterion and having the best ratio of the maximum side-lobe level to the main peak of the non-periodic autocorrelation function. Obviously, the longer the minimax sequence, the higher its correction ability. However, with the increase in the length of the sync code, a conflict arises between the corrective ability and the speed of data transfer. This is caused by the decrease in the duration of the information section of the frame. At the same time, as the length of the code increases, the complexity of the technical implementation of the decoder synchronization scheme increases as well.
This means that when developing an information transmission system, it is necessary to find a compromise between the complexity of the technical implementation of the decoder and the required noise immunity. To solve this problem, it is necessary to study the correcting ability of binary sync codes. The purpose of this work was to study the correcting ability of binary sequences with good non-periodic auto-correlation properties using a reception scheme with matched processing. This article discusses the possibility of using Barker sequences of lengths 7, 11, and 13 and M-sequences as corrective sync codes. The authors carry out an analysis of the correcting ability of the decoder model with matched processing for Barker codes of different lengths under the conditions of a one, two, and threefold error. Analytical expressions have been obtained to determine the decoding error probability of a binary minimax code depending on the length of the sync code. The dependence of the corrective ability of the code and the maximum level of the side lobe on the length of the sync code in the range from 4 to 128 with the best nonperiodic autocorrelation functions (NPAF) is obtained. It has been established that there are length ranges for minimax sequences within which their correction ability remains constant, that is, a sync code of shorter length has the same correction ability as a longer code. Thus, the research results allow us to optimize the complexity of the technical implementation of a sync signal decoder depending on the requirements for general noise immunity and information transfer rate in a communication system. The proposed approach can be successfully used to modify the existing synchronization schemes of communication systems with code division of channels.