# Information Theory

Coding Theorems for Discrete Memoryless Systems

Author: Imre Csiszár,János Körner

Publisher: Cambridge University Press

ISBN: 113949998X

Category: Technology & Engineering

Page: N.A

View: 659

Csiszár and Körner's book is widely regarded as a classic in the field of information theory, providing deep insights and expert treatment of the key theoretical issues. It includes in-depth coverage of the mathematics of reliable information transmission, both in two-terminal and multi-terminal network scenarios. Updated and considerably expanded, this new edition presents unique discussions of information theoretic secrecy and of zero-error information theory, including the deep connections of the latter with extremal combinatorics. The presentations of all core subjects are self contained, even the advanced topics, which helps readers to understand the important connections between seemingly different problems. Finally, 320 end-of-chapter problems, together with helpful hints for solving them, allow readers to develop a full command of the mathematical techniques. It is an ideal resource for graduate students and researchers in electrical and electronic engineering, computer science and applied mathematics.

# Information Theory

Coding Theorems for Discrete Memoryless Systems

Author: Imre Csiszár,János Körner

Publisher: Elsevier

ISBN: 1483281574

Category: Mathematics

Page: 460

View: 2405

Information Theory: Coding Theorems for Discrete Memoryless Systems presents mathematical models that involve independent random variables with finite range. This three-chapter text specifically describes the characteristic phenomena of information theory. Chapter 1 deals with information measures in simple coding problems, with emphasis on some formal properties of Shannon’s information and the non-block source coding. Chapter 2 describes the properties and practical aspects of the two-terminal systems. This chapter also examines the noisy channel coding problem, the computation of channel capacity, and the arbitrarily varying channels. Chapter 3 looks into the theory and practicality of multi-terminal systems. This book is intended primarily for graduate students and research workers in mathematics, electrical engineering, and computer science.

# Combinatorial Methods and Models

Rudolf Ahlswede’s Lectures on Information Theory 4

Author: Rudolf Ahlswede

Publisher: Springer

ISBN: 3319531395

Category: Mathematics

Page: 385

View: 3526

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. Here the code concept already relies on a rather combinatorial structure, as in several concrete models of multiple access channels or more refined distortions. An analytical tool coming into play, especially during the analysis of perfect codes, is the use of orthogonal polynomials. Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.

# Encyclopaedia of Mathematics

Volume 3 Heaps and Semi-Heaps — Moments, Method of (in Probability Theory)

Author: M. Hazewinkel

Publisher: Springer

ISBN: 1489937935

Category: Mathematics

Page: 950

View: 5320

# Encyclopaedia of Mathematics

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

ISBN: 9400959885

Category: Mathematics

Page: 534

View: 1847

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

# Inequality Theory and Applications

Author: Yeol Je Cho,Jong Kyu Kim,Sever S. Dragomir

Publisher: Nova Publishers

ISBN: 9781594548758

Category: Mathematics

Page: 189

View: 5455

Intends to introduce and exchange topics on the areas of inequality theory and their applications dealing in pure and applied mathematics.

# Mathematica

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1449

# Problemy Upravlenii͡a︡ i Teorii Informat͡s︡ii

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Information theory

Page: N.A

View: 7473

# Problems of Information Transmission

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Information theory

Page: N.A

View: 6722

# 2000 IEEE International Symposium on Information Theory

Proceedings : Sorrento Palace Hotel Conference Center, Sorrento, Italy, 25-30 June, 2000

Author: N.A

Publisher: N.A

ISBN: 9780780358584

Category: Information theory

Page: 509

View: 4531