Combinatorial Methods and Models: Rudolf Ahlswede's Lectures on Information Theory 4 (repost)
Combinatorial Methods and Models: Rudolf Ahlswede's Lectures on Information Theory 4 (Foundations in Signal Processing, Communications and Networking) by Rudolf Ahlswede
English | 4 July 2017 | ISBN: 3319531379 | 385 Pages | PDF | 4.84 MB
English | 4 July 2017 | ISBN: 3319531379 | 385 Pages | PDF | 4.84 MB
The fourth volume of Rudolf Ahlswede's lectures on Information Theory is focused on Combinatorics. Ahlswede was originally motivated to study combinatorial aspects of Information Theory via zero-error codes: in this case the structure of the coding problems usually drastically changes from probabilistic to combinatorial. The best example is Shannon's zero error capacity, where independent sets in graphs have to be examined. The extension to multiple access channels leads to the Zarankiewicz problem. A code can be regarded combinatorially as a hypergraph; and many coding theorems can be obtained by appropriate colourings or coverings of the underlying hypergraphs. Several such colouring and covering techniques and their applications are introduced in this book. Furthermore, codes produced by permutations and one of Ahlswede's favourite research fields – extremal problems in Combinatorics – are presented. Whereas the first part of the book concentrates on combinatorial methods in order to analyse classical codes as prefix codes or codes in the Hamming metric, the second is devoted to combinatorial models in Information Theory.