In addition to the classical topics discussed, it provides the first comprehensive treatment of the theory of imeasure, network coding theory, shannon and nonshannon type information inequalities, and a relation between entropy and group theory. A proof of the fisher information inequality via a data processing argument abstract. Strong dataprocessing inequalities for channels and bayesian networks yury polyanskiy and yihong wu abstract the dataprocessing inequality, that is, iu. By increased the mutual information i assume you mean, increased the mutual information between the signal and the output of the highpass filter, by adding the noise. However, a fundamental theorem in information theory. Information theory and rate distortion theory by jerry d. Lecture notes for statistics 311electrical engineering 377. How big data is automating inequality the new york times. Lecture notes on information theory department of statistics, yale. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. Information theory and rate distortion theory for communications and compression. Asymptotic equipartition property theorem, consequences of the aep.
All the essential topics in information theory are covered in detail, including. Information inequality 1st edition by herbert schiller author isbn. Data compression, highprobability sets and the typical set. Artificial intelligence blog data processing inequality. Strong dataprocessing inequalities for channels and. A first course in information theory is an uptodate introduction to information theory. The number of books on the market dealing with information theory and coding has been on the rise over the past. A proof of the fisher information inequality via a data processing argument.
We prove a data processing inequality for quantum communication channels, which states that processing a received quantum state may never increase the mutual information between input and output states. Intuitively, the data processing inequality says that no clever transformation of the received code channel output y can give more information about the sent code channel input xthan y itself. Free information theory books download ebooks online textbooks. Information loss in deterministic signal processing. This is a graduatelevel introduction to mathematics of information theory. Suppose x,y, z are random variables and z is independent of x given y, then. Information theory tools for computer graphics ebook. Minimal su cient statistic is a function of all other su cient statistic maximally compresses information about in the sample dr. Korner, information theory, cambridge university press 2011 r. Wilde, recoverability for holevos justasgood fidelity, in 2018 ieee international symposium on information theory isit, colorado, usa 2018, pp. Information theory basics entropy relative entropy and mutual information inequalities jensens inequality logsum inequality jensenshannon inequality data processing inequality entropy rate entropy and coding continuous channel information bottleneck method fdivergences. Introduction to information theory and coding ee5142. The fisher information jx of a random variable x under a translation parameter appears in information theory in the classical proof of the entropypower inequality epi. Fundamentals of information theory and coding design.
Epi is one of the deepest inequalities in information theory, and has a. Elements of information theory edition 2 by thomas m. This inequality will seem obvious to those who know information theory, but i still think its cute. Sending such a telegram costs only twenty ve cents. This note will cover both classical and modern topics, including information entropy, lossless data compression, binary hypothesis testing, channel coding, and lossy data compression. An introduction to information theory and applications. We will use the dataprocessing property of mutual information to be proved. While this lower bound obviously cannot b e tighter than its classical counterpart in the limit of long blo. A proof of the fisher information inequality via a data. His research interests include statistical inference, machine learning, detection and estimation theory, information theory, statistical signal, image, and video processing, and information security. Finally, we discuss the data processing inequality, which essentially states that at every step of information processing, information cannot be gained, only lost. Find materials for this course in the pages linked along the left. Information theoretic proofs of entropy power inequalities.
Suppose x,y, z are random variables and z is independent of x given y, then mix,z information theory is an uptodate introduction to information theory. A strengthened data processing inequality for the belavkin. We also give the first optimal simultaneous protocol in the dense case for mean estimation. Vershynina, recovery and the data processing inequality for quasientropies, ieee trans. Information theory, mutual information, data processing.
Pierre moulin, university of illinois, urbanachampaign pierre moulin is a professor in the ece department at the university of illinois, urbanachampaign. Communication lower bounds for statistical estimation. Information inequality presents a telling account of the current shift in the information landscape from a model of social accountability to a more privatized corporate model. Gallager, information theory and reliable communication, wiley 1969. Two proofs of the fisher information inequality via data. Statistical inference engineers and data scientists. If ix,y is the information in common between x and y, then you can write the data processing inequality as from elements of information theory, a great book. Lecture notes on information theory preface \there is a whole book of readymade, long and convincing, lavishly composed telegrams for all occasions. Information theory, in the technical sense, as it is used today goes back to the work. C q that stems from the data processing inequality of i q. Signal or data processing operates on the physical representation of information so that users can easily access and extract that information. You see, what gets transmitted over the telegraph is not the text of the telegram, but simply the number under which it is listed in the book. But the data processing inequality doesnt say the inclusion of r1 cant increase is, r2, it only says is,r1 is,r2. Automating inequality how hightech tools profile, police, and punish the poor by virginia eubanks 260 pp.
Its impact has been crucial to the success of the voyager missions to deep space. Lecture notes information theory electrical engineering. Information theory studies the quantification, storage, and communication of information. Question feed subscribe to rss question feed to subscribe to this rss feed, copy and paste this url into your rss reader. Aracne uses the data processing inequality dpi, from information theory, to detect and prune indirect interactions that are unlikely to be mediated by an actual physical interaction. Informally it states that you cannot increase the information content of a quantum system by acting on it with. Information loss in deterministic signal processing systems. Informally it states that you cannot increase the information content of a quantum system by acting on it with a local physical operation. Search the worlds most comprehensive index of fulltext books. These are my personal notes from an information theory course taught by prof. The latest edition of this classic is updated with new problem sets and material the second edition of this fundamental textbook maintains the books tradition of clear, thoughtprovoking instruction. Jul 04, 2011 the data processing inequality dpi is a fundamental feature of information theory. Shannon 1 2 which contained the basic results for simple memoryless sources and channels and introduced more general communication systems models, including nite state sources and channels.
Thanks for contributing an answer to mathematics stack exchange. Pdf dataprocessing inequalities based on a certain. 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. Apply dataprocessing inequality twice to the map x, y y, x to get dpxy pxpy dpy x py px. Entropy, joint entropy and conditional entropy, relative entropy and mutual information, chain rules, dataprocessing inequality, fanos inequality. Aug 06, 20 aracne uses the data processing inequality dpi, from information theory, to detect and prune indirect interactions that are unlikely to be mediated by an actual physical interaction. It was originally proposed by claude shannon in 1948 to find fundamental limits on signal processing and communication operations such as data compression, in a landmark paper titled a mathematical theory of communication. However, very few, if any, of these books have been able to cover the fundamentals of the theory without losing the reader in. Data processing is a general principle in information theory, in that any quantity under the name information should obey some sort of data processing inequality.
Information theory was born in a surprisingly rich state in the classic papers of claude e. In the years since the first edition of the book, information theory celebrated. Information theory, mutual information, data processing inequality, chain rule. Lecture notes on information theory by yury polyanskiy mit and yihong wu yale other useful books recommended, will not be used in an essential way. More precisely, for a markov chain x y z, the data processing inequality states that ix. Yao xie, ece587, information theory, duke university. Data processing inequality 20612 leave a comment printable version project feature extraction, a b. An intuitive proof of the data processing inequality. Strong data processing inequalities for channels and bayesian networks yury polyanskiy and yihong wu abstract the data processing inequality, that is, iu. Y, has been the method of choice for proving impossibility converse results.
When the smooth minentropy is used as the relevant information measure. This is must reading for information professionals who maintain some sort of professional literacy. Generally data processing inequality says that the entropy cannot increase on applying a function f. Gibson 2014, paperback at the best online prices at ebay. The data processing inequality is an information theoretic concept which states that the information content of a signal cannot be increased via a local physical operation. Strong dataprocessing inequalities for channels and bayesian.
Consider a channel that produces y given xbased on the law p yjx shown. In order to evaluate a query, one first proves an upper bound on its output, by proving an information theoretic inequality. The first is a new paradigm for query processing, which we call from proofs to algorithms. Data management meets information theory data systems group. The data processing inequality adam kelleher medium. Whereas aracne considers only firstorder indirect interactions, i. Y, has been the method of choice for proving impossibility converse results in information theory and many other disciplines. This book is very specifically targeted to problems in communications and compression by providing the fundamental principles and results in information theory and rate distortion theory for these applications and presenting methods that have proved and will prove useful in analyzing and designing real systems. We discuss two novel connections between information theory and data management. It enters the proof of the epi via the debruijn identity. In this sense, zamirs data processing inequality for fisher information merely pointed out the fact that fisher information bears the real meaning as an information quantity. The data processing inequality is a nice, intuitive inequality about mutual information.
Free information theory books download ebooks online. The application of information theory to biochemical. May 04, 2018 automating inequality how hightech tools profile, police, and punish the poor by virginia eubanks 260 pp. Mutual information between continuous and discrete variables from numerical data. The data processing inequality dpi is a fundamental feature of information theory. The data processing inequality is an information theoretic concept which states that the information content of a signal cannot be increased via a local physical.
As our main technique, we prove a distributed data processing inequality, as a generalization of usual data processing inequalities, which might be of independent interest and useful for other problems. The concept of information entropy was introduced by claude shannon in his 1948 paper a mathematical theory of communication. When the smooth minentropy is used as the relevant information measure, then the dpi follows immediately from the definition of the entropy. This can be expressed concisely as post processing cannot increase information.
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