Reliability Criteria in Information Theory and in Statistical Hypothesis Testing

This survey is devoted to one of the central problems of Information Theory -- the problem of determination of interdependence between coding rate and error probability exponent for different information transmission systems. The overview deals with memoryless systems of finite alphabet setting. It presents material complementary to the contents of the series of the most remarkable in Information Theory books of Feinstain, Fano, Wolfowitz, Gallager, Csiszar and Korner, Kolesnik and Poltirev, Blahut, Cover and Thomas and of the papers by Dobrushin, Gelfand and Prelov. We briefly formulate fundamental notions and results of Shannon theory on reliable transmission via coding and give a survey of results obtained in last two-three decades by the authors, their colleagues and some other researchers. The paper is written with the goal to make accessible to a broader circle of readers the theory of rate-reliability. We regard this concept useful to promote the noted problem solution in parallel with elaboration of the notion of reliability-reliability dependence relative to the statistical hypothesis testing and identification.