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Additive boundary of error probability in a discrete data transmission channel with noise-immune coding and grouping of errors

Introduction: Data transmission reliability analysis when using noise-immune coding in channels with grouping of errors (in particular, in radio channels with interference and fading of the received signals) is complicated by the need to use discrete data transmission channel models which take into account the error grouping, differing from the traditional binomial model. The complexity of the analytical description of such models leads to the fact that the quality indicators of data transmission over channels with error grouping are usually analyzed by simulation methods, and the development of analytical models of data transmission discrete channels with grouping of errors is one of the modern direction in the noise-immune coding theory development. Purpose: Finding the additive boundary of a bit error probability for data transmission discrete channel with grouping of symbol errors, described by Elliot — Hilbert model. Results: For the case of data transmission using a group noise-immune code, analytical expressions are obtained for calculating the additive boundary of a bit error probability in a discrete data transmission channel with grouping of symbol errors. The obtained expressions take into account the features of data transmission over a channel with error grouping, in particular, the fact that the probabilities of various combinations of the same number of errors are not equal to each other. Examples are presented of calculating a bit error probability for the case of using noise-immune codes which correct errors. It is shown that for any code length, the use of the Elliot — Hilbert model allows you to substantially refine the results of calculating the probabilistic indicators of the reliability of data transmission in channels with error grouping, as compared to the original binomial model. The obtained results are compared to the results of the simulation. Practical relevance: The results can be used in the design and analysis of the characteristics of data transmission systems for various purposes, operating under conditions of error grouping. Using analytical expressions to calculate the probability indicators of the reliability of data transfer allows you to abandon complex simulation modeling of transmitting data in channels with error grouping at the stage of choosing a noise-immune code and its parameters.