Information, entropy, and coding princeton university. This approach has been described as information theory. A characterization of entropy in terms of information loss. Entropy is a central concept in both classical and quantum information theory, measuring the uncertainty and the information content in the state of a physical system. Motivationinformation entropy compressing information an introduction to information theory. Prasang upadhyaya 1 introduction in the previous lecture we looked at the application of entropy to derive inequalities that involved counting. Pinskers classic information and information stability of random variables and processes and by the seminal work of a. Information entropy is occasionally called shannons entropy in honor of claude e.
Information theory an overview sciencedirect topics. Penghua wang, may 14, 2012 information theory, chap. Entropy in classical and quantum information theory. Information theory georgia institute of technology. This book is an updated version of the information theory classic, first published in 1990.
Entropy and information theory 3 march 20 this site provides the current version of the first edition of the book entropy and information theory by r. Such a theory is not yet well developed, for several historical reasons. Entropy information theory provides a theoretical foundation to quantify the information content, or the uncertainty, of a random variable represented as a distribution. In shannons information theory, the entropy is analogous to the thermodynamic concept of entropy, which measures the amount of disorder in physical systems. Also, it arises as answers to speci c operational problems, e. Online matlab and python computer programs provide handson experience of information theory in action, and powerpoint slides give support for teaching. This is a fascinating subject, which arose once the notion of information got precise and quantifyable. Problems with arnheims \entropy and art 1 problems with the scienti c notion of entropy overly emphasizes entropy disorder confuses equilibrium with order appears to miss entirely the fact that shannons \information content is a statistical notion confuses entropyinformation with complexity misunderstands the information theory. Relation of differential entropy to discrete entropy. June 2010 contents 1 introduction 1 2 entropy in thermodynamics 2 3 information theory 4 4 statistical mechanics 9 5 dynamical systems theory 18 6 fractal geometry 26 7 conclusion 30 1 introduction entropy is ubiquitous in physics, and it plays important roles in numerous. Rotermankonieczna, in protein folding in silico, 2012.
Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. Entropy a guide for the perplexed roman frigg and charlotte werndl. Harvard seas es250 information theory entropy, relative entropy, and mutual information. Systems science and cybernetics entropy systems theory kenneth d. Examples are entropy, mutual information, conditional entropy, conditional information, and relative entropy discrimination, kullbackleibler.
Then we define each concept of information entropy for a probability sequence and two kinds of probability matrices, joint and conditional, that are defined in article 25. There are a number of entropyrelated concepts that mathematically quantify information content in some way. These two heuristics have different units of measure. The information entropy, often just entropy, is a basic quantity in information theory associated to any random variable, which can be interpreted as the average level of information, surprise, or uncertainty inherent in the variables possible outcomes. It is a characteristic of probability distribution providing a measure of uncertainty associated with the probability distribution. Using work by faddeev and furuichi, we derive a very simple characterization.
This type of result is often known as singleletterization in information theory. Digital communication information theory tutorialspoint. It measures a very important character of random variab. An introduction to information theory and entropy csustan. Entropy is a basic concept in physics and information science, being the basic measure to compare different states of an isolated system the information content of a description. From a physical point of view, information theory has nothing to do with physics.
The concept of information entropy was introduced by claude shannon in his 1948 paper a mathematical theory of communication. Jan 16, 2018 content1 entropy formula, unit, properties. Motivationinformation entropy compressing information an introduction to information theory carlton downey november 12, 20. Notice that alices actions give information about the weather in toronto. The notion of entropy, which is fundamental to the whole topic of this book, is introduced here. Differential entropy elements of information theory. Lecture notes on information theory statistics, yale university.
Information theory clearly indicates that the quantity of information carried by a sequence of amino acids is only sufficient to generate the earlystage es folding intermediate and that additional information must be provided in order to correctly model the remainder of the folding process. Information theory is a mathematical approach to the study of coding of information along with the quantification, storage, and communication of information. Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along. Sinai and kolmogorov in 1959 extended this read more. Information theory, the mathematical theory of communication, has two.
We explore the history of communication technology leading to the modern field of information theory. To do so, the transmitter sends a series possibly just one partial messages that give clues towards the original message. Bailey encyclopedia of life support systems eolss entropy systems theory kenneth d. Minimum mutual information and nongaussianity through the maximum entropy method. Because of its dependence on ergodic theorems, however, it can also be viewed as a branch of ergodic theory, the theory of invariant transformations and transformations related to invariant transformations. Properties of differential entropy, relative entropy, and mutual information. The information entropy, often just entropy, is a basic quantity in information theory associated. Information is the source of a communication system, whether it is analog or digital. Motivationinformation entropy compressing information introduction i todays recitation will be an introduction to information theory i information theory studies the quanti. Entropy, thermodynamic entropy, boltzmanns entropy, informationtheory. The minimum average number of binary digits needed to specify a source output. I believe a good intuitive explanation enables you to apply a concept without the mental overhead of too many mathematical details.
What is an intuitive explanation of the concept of entropy. Much of the book is concerned with their properties, es. Entropy in thermodynamics and information theory from wikipedia, the free encyclopedia there are close parallels between the mathematical expressions for the thermodynamic entropy, usually denoted by s, of a physical system in the statistical thermodynamics established by. View enhanced pdf access article on wiley online library html.
Information theory a tutorial introduction o information. Information theory is used in information retrieval, intelligence gathering, gambling, and even in musical composition. When we observe the possibilities of the occurrence of. Entropy is particularly friendly to such logical shortcuts. Entropy is the basic thermodynamic variable that serves to. Three tutorial lectures on entropy and counting1 david galvin2 1st lake michigan workshop on combinatorics and graph theory, march 1516 2014 1these notes were prepared to accompany a series of tutorial lectures given by the author at the 1st lake michigan workshop on combinatorics and graph theory, held at western michigan. Shannon entropy is the key concept of information theory 1. There are numerous characterizations of shannon entropy and tsallis entropy as measures of information obeying certain properties.
Definition and some properties of information entropy in. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Differential entropy elements of information theory wiley. Entropy and information theory stanford ee stanford university. Diversityindex entropy is one of several ways to measure diversity. Alice toronto goes jogging whenever it is not snowing heavily. The information content of one of these partial messages is a measure of how much uncertainty. It is a characteristic of probability distribution providing a measure of uncertainty associated with the.
Yet it is exactly what is needed to simplify the teaching and understanding of fundamental concepts. We thank the denizens of the ncategory cafe, especially david cor eld, steve lack, mark meckes and josh shadlen, for encouragement and helpful suggestions. Entropy properties of entropy entropy, as we have defined it, has some dependence on the resolution to which the energy of macrostates is measured. A characterization of entropy in terms of information loss john c. Information theory a tutorial introduction o information theory. Shannon entropy this chapter is a digression in information theory. Its properties and its interpretation as the data compression limit of a quantum information source will be discussed. Nevertheless, differential entropy shares many functional properties with the usual. Shannon, who formulated many of the key ideas of information theory. Information theory in computer science october 6, 2010 lecture 3 lecturer. Recall that is the number of accessible microstates with energy in the range to. In information theory, the major goal is for one person a transmitter to convey some message over a channel to another person the receiver. Text using standard ascii representation, each character letter, space. Shannon entropy, tsallis entropy, information theory, measure preserving function.
Introduction the concept of entropy in information theory describes how much information there is in a signal or event. When this is the case, the units of entropy are bits. Properties of entropy university of texas at austin. This format can be read from a web browser by using the acrobat reader helper application, which is available for free downloading from adobe the current version is a. In particular, if xk has probability density function pdf p, then hxk elog 1. Further, we discuss some properties of information entropy including shannons lemma, maximum property, additivity and superadditivity properties. Properties of entropy entropy, as we have defined it, has some dependence on the resolution to which the energy of macrostates is measured. Entropy information theory provides a theoretical foundation to quantify the information content, or the. Entropy is a concept in thermodynamics see entropy, statistical mechanics and information theory. Pdf information entropy is introduced as a measure of quantum mechanical uncertainty.
Entropy in information theory basics, property and. Dobrushin on information measures for abstract alphabets and their convergence properties. Using this definition we can confirm that it has the wanted property of additivity. Along the way, well give some intuitive reasoning behind these values in addition to the formulas. Entropy and mutual information 1 introduction imagine two people alice and bob living in toronto and boston respectively. Information theory can be viewed as simply a branch of applied probability theory. This article consists of a very short introduction to classical and quantum information theory. Both concepts of entropy have deep links with one another, although it took many years for the development of the theories of statistical mechanics and information theory to make this connection apparent. The entropy of a source a fundamental quantity in information theory.
Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along with the limiting normalized versions of these quantities such as entropy rate and information rate. Today, we cover some of the basics of information theory. About onethird of the book is devoted to shannon source and channel coding theorems. In this lecture we step back and introduce the concepts of relative entropy and mutual information that. Suppose that we choose a new resolution and define a new density of states which is.
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