**Csiszár Imre**: Information theory. Coding theorems for discrete memoryless systems - Disquisitiones mathematicae Hungaricae 12. (Budapest, 1986)

INFORMATION THEORY Coding Theorems for Discrete Memoryless Systems by IMRE CSISZÁR and JÁNOS KÖRNER The book is a comprehensive new presentation of the central problems of information theory in the Shannon sense. Starting from the very rudiments, it reaches the most recent developments with particular emphasis on multi-terminal systems. The approach is basically combinatorial and relies on no prerequisites. The coding theorems for discrete memoryless (stochastic) models of various communication situations including exponential error estimates are treated within a unified mathematical theory. An outline of the intuitive background is given in the Introduction. Chaper 1 starts with the introduction of information measures via simple coding and hypothesis testing problems. After a compact presentation of the technical tools use throughout the book, source coding is treated in detail. Chapter 2 offers a parallel treatment of the noisy channel coding problem and source coding with a distortion measuring. Exponential error bounds are derived by an elegant combinatorial method, highlighting their universal coding aspects. This chapter concludes with a section on arbitrarily varying channels. Chapter 3 is the first systematic presentation of the wide spectrum of multi-terminal source and channel coding problems emerged in the seventies, including many new results of the authors. The text is supplemented by about 300 problems, complete with hints. Their majority is selfcontained and presents important results. AKADÉMIAI KIADÓ BUDAPEST ISBN 963 05 4330 3