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The mathematical information theory for using in biology and medicine

Keywords:

G.I. Khudiakov – technical science doctor, professor of the medical radioelectronics department of Saint-Petersburg state university of aerospace instrumentation. E-mail: khudgi@mail.ru


The paper presents the main results of theoretical investigations in the field of clarification of the information theory’s basic notions which were carried out by the author during the last five years. In the field of statistical signal theory: there have been refined the signal/noise ratio (required for power: Q = s2/σп2 – because it provides additively quantities Q), the sampling theorem for stationary random signals, and also the problem of optimal resolution of two Gaussian signals in Gaussian noise was solved. In the field of applied information theory. The formula for the amount of information I(wk| uj), contained in the output symbol wk, about information contained in the input sign uj – if the interferences are in a transmission channel of information, which is determined by equality I(wk| uj) = log [P(wk| uj)/P(wk)], qualifies as the fifth postulate of Shannon's information theory, that results in all the laws of information transmitting over a noisy communication channels. Shannon formally introduced the notion of "entropy of source of discrete messages" is interpreted as the specific informatively of the source, which has the dimension [bit/sign]. Clarified the condition of a complete loss of information in binary communication channels with interference: p + q = 1, where p is the probability of the output channel "unit" subject to the submission to the input channel "unit", and q – the probability of "zero" in the filing "zero." Condition of the absolute reliability binary channel is not only p + q = 2, but p + q = 0. It was also found that in the case of the so-called "continuous messages" as a measure of the quantity of metrological information should be no differential (relative, reduced) entropy of measurement errors but the inverse dispersion of these errors (which satisfies all the postulates of the theory of information, including the postulate of additively), then there is R. Fisher’s information measure. In the mathematical theory of information: there was offered a simple digital method, which allows you to estimate not only the capacity of the communication channel, but also the optimal number of signal levels. This method allowed us to determine the capacity of a communication channel with additive white Gaussian noise with limited peak power for example, which (capacity) can not be evaluated analytically, and to evaluate the information characteristics of modern telecommunication links with various digital modulation techniques.
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