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The channel coding methods development mainly for point-to-point applications provides an approximation to the Shannon limit. The development of telecommunication networks with dynamically changing topology and heterogeneous networks led to the idea of transferring coding processes to the network structure. The network codes studied to date, when establishing a correspondence between information bits and encoded bits, use linear algebraic relations defined, as a rule, on two variables. The latter factor limits the use of such linear network codes only on topologies - two sources, one or more coding nodes. In this work, a class of network codes based on the use of a non-linear function of an unlimited number of variables (the logical function of the absolute majority), which allows them to be applied to a wider class of network topologies, is investigated. Variants of network topologies with an arbitrary number of sources encoded in one coding - switching node are proposed. The possibilities of combining such star-shaped fragments of the network using clustering are considered. The characteristics of noise immunity of non-linear network codes of arbitrary redundancy were investigated using statistical and analytical models. Recommendations for choosing the structure of non-linear network codes with the best efficiency have been developed. The adequacy of statistical and analytical models is confirmed by simulation modeling.
Vyacheslav A. Shevtsov
Moscow Aviation Institute (National Research University) (Russia, 125080, Moscow, Volokolamsk ave., 4)
Vitaly O. Kazachkov
Moscow Aviation Institute (National Research University) (Russia, 125080, Moscow, Volokolamsk ave., 4)
Ilgam R. Letfullin
Moscow Aviation Institute (National Research University) (Russia, 125080, Moscow, Volokolamsk ave., 4)

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