Correlation properties of symbolic M-sequences in divergent decoding

Abstract

The worldwide introduction of wireless technologies in different states of the modern life including remote controlled drones requires an increase in the resistance of the control channel to a wide range of destructive influences. These influences can have a different nature of origin, such as objectively existing changes of the transmission medium physical properties or deliberate anthropogenic impacts of a potential intruder. So the task of developing an error-correcting code is quite relevant in such conditions. The prerequisites for solving the problem of creating such codes is the implementation of the error-correcting coding optimization theory principles in decoding algorithms. In this paper we analyze the properties of symbolic M-sequence with a divisible reducible polynom as additional error detection signs in divergent decoding algorithms such as: balance, series, the same-name single symbols «specularity» with respect to mod p. We determine the conditions for the effective use of divergent correcting codes based on soft processing of segments of the symbol M-sequence. In this paper a functional diagrams of encoder, decoder and data transmission equipment with low computational complexity optimization theory of error-resistant coding principles implementation are presented. The usage of the symbolic M-sequence properties such as balance, series, «mirroring» of single symbols with respect to mod p as additional signs of error detection is sufficient to implement a divergence algorithm with multi-threshold decoding. The proposed approach allows to maintain the specified reliability when changing the transmission rate caused by a high level of interference.