General theory of information transfer

We report on ideas, problems and results, which occupied us during the past two decades and which seem to extend the frontiers of information theory in several directions. The main contributions concern information transfer by channels. There are also new questions and some answers in new models of source coding. While many of our investigations are in an explorative state, there are also hard cores of mathematical theories. In particular we present a unified theory of information transfer, which naturally incorporates Shannonʹs theory of information transmission and the theory of identification in the presence of noise as extremal cases. It provides several novel coding theorems. On the source coding side we introduce the concept of identification entropy. Finally we are led beyond information theory to new concepts of solutions for probabilistic algorithms.