The Mathematical Theory of Communication


Book Description

Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.







The Mathematical Theory of Information


Book Description

The general concept of information is here, for the first time, defined mathematically by adding one single axiom to the probability theory. This Mathematical Theory of Information is explored in fourteen chapters: 1. Information can be measured in different units, in anything from bits to dollars. We will here argue that any measure is acceptable if it does not violate the Law of Diminishing Information. This law is supported by two independent arguments: one derived from the Bar-Hillel ideal receiver, the other is based on Shannon's noisy channel. The entropy in the 'classical information theory' is one of the measures conforming to the Law of Diminishing Information, but it has, however, properties such as being symmetric, which makes it unsuitable for some applications. The measure reliability is found to be a universal information measure. 2. For discrete and finite signals, the Law of Diminishing Information is defined mathematically, using probability theory and matrix algebra. 3. The Law of Diminishing Information is used as an axiom to derive essential properties of information. Byron's law: there is more information in a lie than in gibberish. Preservation: no information is lost in a reversible channel. Etc. The Mathematical Theory of Information supports colligation, i. e. the property to bind facts together making 'two plus two greater than four'. Colligation is a must when the information carries knowledge, or is a base for decisions. In such cases, reliability is always a useful information measure. Entropy does not allow colligation.




Information: A Very Short Introduction


Book Description

We live an information-soaked existence - information pours into our lives through television, radio, books, and of course, the Internet. Some say we suffer from 'infoglut'. But what is information? The concept of 'information' is a profound one, rooted in mathematics, central to whole branches of science, yet with implications on every aspect of our everyday lives: DNA provides the information to create us; we learn through the information fed to us; we relate to each other through information transfer - gossip, lectures, reading. Information is not only a mathematically powerful concept, but its critical role in society raises wider ethical issues: who owns information? Who controls its dissemination? Who has access to information? Luciano Floridi, a philosopher of information, cuts across many subjects, from a brief look at the mathematical roots of information - its definition and measurement in 'bits'- to its role in genetics (we are information), and its social meaning and value. He ends by considering the ethics of information, including issues of ownership, privacy, and accessibility; copyright and open source. For those unfamiliar with its precise meaning and wide applicability as a philosophical concept, 'information' may seem a bland or mundane topic. Those who have studied some science or philosophy or sociology will already be aware of its centrality and richness. But for all readers, whether from the humanities or sciences, Floridi gives a fascinating and inspirational introduction to this most fundamental of ideas. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.




Information Theory


Book Description

Originally developed by Claude Shannon in the 1940s, information theory laid the foundations for the digital revolution, and is now an essential tool in telecommunications, genetics, linguistics, brain sciences, and deep space communication. In this richly illustrated book, accessible examples are used to introduce information theory in terms of everyday games like ‘20 questions’ before more advanced topics are explored. Online MatLab and Python computer programs provide hands-on experience of information theory in action, and PowerPoint slides give support for teaching. Written in an informal style, with a comprehensive glossary and tutorial appendices, this text is an ideal primer for novices who wish to learn the essential principles and applications of information theory.




Mathematical Systems Theory in Biology, Communications, Computation and Finance


Book Description

This volume contains survey and research articles by some of the leading researchers in mathematical systems theory - a vibrant research area in its own right. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists.




Information and Communication Theory


Book Description

An important text that offers an in-depth guide to how information theory sets the boundaries for data communication In an accessible and practical style, Information and Communication Theory explores the topic of information theory and includes concrete tools that are appropriate for real-life communication systems. The text investigates the connection between theoretical and practical applications through a wide-variety of topics including an introduction to the basics of probability theory, information, (lossless) source coding, typical sequences as a central concept, channel coding, continuous random variables, Gaussian channels, discrete input continuous channels, and a brief look at rate distortion theory. The author explains the fundamental theory together with typical compression algorithms and how they are used in reality. He moves on to review source coding and how much a source can be compressed, and also explains algorithms such as the LZ family with applications to e.g. zip or png. In addition to exploring the channel coding theorem, the book includes illustrative examples of codes. This comprehensive text: Provides an adaptive version of Huffman coding that estimates source distribution Contains a series of problems that enhance an understanding of information presented in the text Covers a variety of topics including optimal source coding, channel coding, modulation and much more Includes appendices that explore probability distributions and the sampling theorem Written for graduate and undergraduate students studying information theory, as well as professional engineers, master’s students, Information and Communication Theory offers an introduction to how information theory sets the boundaries for data communication.




Mathematical Foundations for Signal Processing, Communications, and Networking


Book Description

Mathematical Foundations for Signal Processing, Communications, and Networking describes mathematical concepts and results important in the design, analysis, and optimization of signal processing algorithms, modern communication systems, and networks. Helping readers master key techniques and comprehend the current research literature, the book offers a comprehensive overview of methods and applications from linear algebra, numerical analysis, statistics, probability, stochastic processes, and optimization. From basic transforms to Monte Carlo simulation to linear programming, the text covers a broad range of mathematical techniques essential to understanding the concepts and results in signal processing, telecommunications, and networking. Along with discussing mathematical theory, each self-contained chapter presents examples that illustrate the use of various mathematical concepts to solve different applications. Each chapter also includes a set of homework exercises and readings for additional study. This text helps readers understand fundamental and advanced results as well as recent research trends in the interrelated fields of signal processing, telecommunications, and networking. It provides all the necessary mathematical background to prepare students for more advanced courses and train specialists working in these areas.




A Sociological Theory of Communication


Book Description

Networks of communication evolve in terms of reflexive exchanges. The codification of these reflections in language, that is, at the social level, can be considered as the operating system of society. Under sociologically specifiable conditions, the discursive reconstructions can be expected to make the systems under reflection increasingly knowledge-intensive. This sociological theory of communication is founded in a tradition that includes Giddens' (1979) structuration theory, Habermas' (1981) theory of communicative action, and Luhmann's (1984) proposal to consider social systems as self-organizing. The study also elaborates on Shannon's (1948) mathematical theory of communication for the formalization and operationalization of the non-linear dynamics. The development of scientific communications can be studied using citation analysis. The exchange media at the interfaces of knowledge production provide us with the evolutionary model of a Triple Helix of university-industry-government relations. The construction of the European Information Society can then be analyzed in terms of interacting networks of communication. The issues of sustainable development and the expectation of social change are discussed in relation to the possibility of a general theory of communication. REVIEW In this book, LoetLeydesdorff sets out to answer the question, "Can society be considered as a self-organizing (autopoietic) system. In the process, Leydesdorff, develops a general sociological theory of communication, as well as a special theory of scientific communication designed to analyze complex systems such as the Euroean Information Society. (from review in JASIST 53[1], 2002, 62-63)




A Mind at Play


Book Description

Chronicles the life and times of the lesser-known Information Age intellect, revealing how his discoveries and innovations set the stage for the digital era, influencing the work of such collaborators and rivals as Alan Turing, John von Neumann and Vannevar Bush.