General theory of information transfer: Updated

We report on ideas, problems and results, which occupied us during the past decade 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 Shannon's 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 data compression for identification. Finally we are led beyond information theory to new concepts of solutions for probabilistic algorithms. The original paper [R. Ahlswede, General theory of information transfer, Preprint 97-118, SFB 343 Diskrete Strukturen in der Mathematik, Universitat Bielefeld, 1997] gave to and received from the ZIF-project essential stimulations which resulted in contributions added as GTIT-Supplements Search and channels with feedback and Noiseless coding for multiple purposes: a combinatorial model. Other contributions-also to areas initiated-are published in the recent book [R. Ahlswede et al. (Eds.), General Theory of Information Transfer and Combinatorics, Lecture Notes in Computer Science, vol. 4123, Springer, Berlin, 2006]. The readers are advised to study always the pioneering papers in a field-in this case the papers [R. Ahlswede, G. Dueck, Identification via channels, IEEE Trans. Inform. Theory 35 (1989) 15-29; R. Ahlswede, G. Dueck, Identification in the presence of feedback-a discovery of new capacity formulas, IEEE Trans. Inform. Theory 35 (1989) 30-39] on identification. It is not only the most rewarding way to come to new ideas, but it also helps to more quickly grasp the more advanced formalisms without going through too many technicalities. Perhaps also the recent Shannon Lecture [R. Ahlswede, Towards a General Theory of Information Transfer, Shannon Lecture at ISIT in Seattle 13th July 2006, IEEE Information Theory Society Newsletter, 2007], aiming at an even wider scope, gives further impetus. (C) 2007 Elsevier B.V. All rights reserved.