DEAD END OF DEVELOPMENT OR AN ERROR IN THE BASIS? THE WAY OUT OF THE CRISIS OF THE MATHEMATICAL THEORY OF COMMUNICATION AFTER 75 YEARS

The essence and reasons for the emergence of the crisis in the development of the Theory of Information Transfer are considered. Based on the analysis of the axiomatic assumptions of the basis for constructing the existing Information Theory, the reason for the erroneous canonization of the Capacity category as a fundamental physical limit of the speeds of absolutely reliable data transmission is revealed. A new mathematical procedure for processing signals at the output of a Gaussian channel has been developed. This new method is shown to provide virtually sterile separation of signals and noise. Using computational mathematical models, it has been proven that the application of the proposed algebraic procedure for processing noisy signals allows for the practical transmission of information at speeds significantly exceeding the traditionally defined Capacity value. Several examples of linear digital algebraic processing are discussed in detail, including a complete analytical description of all transformations. Despite the authors having positive results of experimental tests for real models of signals and noise, as well as corresponding patents that have passed the examination, considerable attention is paid to a detailed analytical description of the subject of consideration. This is done to facilitate understanding and openness to possible discussions. In this case, simplified but completely adequate models of elementary signals and additive Gaussian noise with a flat spectrum are used exclusively to ensure transparency and accessibility of presentation and to facilitate the assessment of the correctness of analytical transformations and descriptions.