Rudolf Ahlswede Livres

The lectures concentrate on highlights in Combinatorial (ChaptersII and III) and Number Theoretical (ChapterIV) Extremal Theory, in particular on the solution of famous problems which were open for many decades. However, the organization of the lectures in six chapters does neither follow the historic developments nor the connections between ideas in several cases. With the speci? ed auxiliary results in ChapterI on Probability Theory, Graph Theory, etc., all chapters can be read and taught independently of one another. In addition to the 16 lectures organized in 6 chapters of the main part of the book, there is supplementary material for most of them in the Appendix. In parti- lar, there are applications and further exercises, research problems, conjectures, and even research programs. The following books and reports [B97], [ACDKPSWZ00], [A01], and [ABCABDM06], mostly of the authors, are frequently cited in this book, especially in the Appendix, and we therefore mark them by short labels as [B], [N], [E], and [G]. We emphasize that there are also “Exercises” in [B], a “Problem Section” with contributions by several authors on pages 1063–1105 of [G], which are often of a combinatorial nature, and “Problems and Conjectures” on pages 172–173 of [E].

This book collects 63 revised, full-papers contributed to a research project on the "General Theory of Information Transfer and Combinatorics" that was hosted from 2001-2004 at the Center for Interdisciplinary Research (ZIF) of Bielefeld University and several incorporated meetings. Topics covered include probabilistic models, cryptology, pseudo random sequences, quantum models, pattern discovery, language evolution, and network coding.

Focusing on arbitrarily varying channels (AVC), this volume showcases Rudolf Ahlswede's expertise in Information Theory. It includes a survey on AVC and wiretap channels by Holger Boche and Ahmed Mansour. The book also covers continuous data compression and extensively discusses distributed information, highlighting key topics like "multiple descriptions" and "network coding," where Ahlswede made significant contributions. The final section addresses statistical inference under communication constraints, based on a highly acclaimed joint paper with Imre Csiszar.

The volume "Storing and Transmitting Data" is based on Rudolf Ahlswede's introductory course on "Information Theory I" and presents an introduction to Shannon Theory. For the two next, Shannon presented an impressive mathematical theory called Information Theory, which he based on probabilistic models.

This volume focuses on information security, starting with a brief course on cryptography, based on lectures by Rudolf Ahlswede at the University of Bielefeld in the mid-1990s. It continues from his introductory course on basic coding theorems presented in the first volume. The text details Shannon’s foundational work on secrecy systems and introduces an information-theoretic model of wiretap channels, along with key concepts like homophonic coding and authentication. Following the theoretical discussions, it provides comprehensive technical details of AES and includes a brief history of public-key cryptology, covering RSA and El Gamal cryptosystems, as well as the basic theory of elliptic curves and efficient addition algorithms. The significant topic of “oblivious transfer,” related to privacy in communication, is also explored, highlighting its growing importance in today's context. This is the third volume in a series documenting Ahlswede’s lectures on information theory, featuring insights from invited experts, including Rüdiger Reischuk. The content is aimed at graduate students in Mathematics and those in Theoretical Computer Science, Physics, and Electrical Engineering with a basic Mathematics background. It serves as a foundation for courses or supplementary material, presenting research problems and conjectures suitable for Ph.D. students and advanced researchers seeking new avenues for exploration.

The fourth volume of Rudolf Ahlswede’s lectures on Information Theory emphasizes Combinatorics, driven by his interest in zero-error codes, which shift coding problems from probabilistic to combinatorial frameworks. A key example is Shannon’s zero-error capacity, which involves analyzing independent sets in graphs, and extends to the Zarankiewicz problem in multiple access channels. Codes are viewed combinatorially as hypergraphs, allowing for the application of various colouring and covering techniques to derive coding theorems. The book also explores codes generated by permutations and delves into extremal problems in Combinatorics. The first part focuses on combinatorial methods for analyzing classical codes, such as prefix codes and those in the Hamming metric, while the second part addresses combinatorial models in Information Theory, where codes are based on combinatorial structures in multiple access channels and refined distortions. Orthogonal polynomials serve as analytical tools, particularly in the study of perfect codes. Covering classical information processing tasks—knowledge acquisition, data storage, transmission, and concealment—the lectures are designed for graduate students in Mathematics and those in Theoretical Computer Science, Physics, and Electrical Engineering. They can serve as course foundations or supplements, while Ph.D. students may find research problems and conjectures for thesis topics, and adv

The calculation of channel capacities is a key focus of Rudolf Ahlswede's second volume in his Lectures on Information Theory. This volume provides an in-depth exploration of classical material from the early days of Information Theory, highlighting developments from the USA, Russia, Hungary, and notably the German school associated with his supervisor, Konrad Jacobs. Ahlswede's lectures aim to rigorously justify the foundations of Information Theory. Each volume includes insights from a distinguished expert, with Gerhard Kramer contributing to this one. The core of classical information processing involves acquiring knowledge and the storage, transmission, and concealment of data. The primary goal of Statistics aligns with knowledge acquisition, while Shannon's groundbreaking work established Information Theory, grounded in probabilistic models for data transmission and concealment. This theory emphasizes codes with minimal error probabilities despite transmission noise, modeled by channels. The lectures are designed for graduate students in Mathematics and those in Theoretical Computer Science, Physics, and Electrical Engineering with a foundational understanding of Mathematics. They serve as a basis for courses or as supplementary material. Ph.D. students will encounter research problems and conjectures suitable for thesis topics, while advanced researchers may discover questions that could lead to extensive research progra

In den letzten drei Jahrzehnten sind in theoretisch und anwendungsorientierten Zeitschriften zunehmend Beiträge zum Thema „Suchen“ erschienen. Dabei werden sehr unterschiedliche Probleme als Suchprobleme klassifiziert, und Forscher aus verschiedenen Fachrichtungen sind oft wenig über Ergebnisse in unbekannten Gebieten informiert. Dieses Buch versucht, das umfangreiche Material so aufzubereiten, dass Leser schnell in die Thematik einsteigen und einen umfassenden Überblick erhalten. Es behandelt die wesentlichen Arbeiten auf dem neuesten Stand, erhebt jedoch keinen Anspruch auf Vollständigkeit, da der Rahmen des Buches dies nicht zulässt. Einige bedeutende Arbeiten werden nur in ihren Ergebnissen dargestellt. Der interessierte Forscher wird so in die Lage versetzt, sich eigenständig durch die Literatur zu navigieren. Das Buch kann für Experten als Nachschlagewerk nützlich sein. Unser Hauptanliegen ist es, jedem Leser mit der Fähigkeit zu abstraktem, formalem Denken Zugang zu den grundlegenden Ideen, Methoden und Resultaten des Gebiets zu ermöglichen, die bisher nicht in Büchern veröffentlicht wurden, aber eine breitere Verbreitung verdienen.