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Topic: Rate distortion theory

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	Shannon's Communication Theory
		Shannon's communication channel consisted of a sender (a source of information), a transmission medium (with noise and distortion), and a receiver (whose goal is to reconstruct the sender's messages).
		He showed that if the entropy rate, the amount of information you wish to transmit, excceds the channel capacity, then there were unavoidable and uncorrectable errors in the transmission.
		In the study of complex systems today, we view deterministic chaotic processes as information sources and use Shannon's entropy rate, as adapted by Kolmogorov and his student Y. Sinai in the late 1950s, to measure how random a chaotic system is.
	www.exploratorium.edu /complexity/CompLexicon/Shannon.html (391 words)

	Rate distortion theory - Wikipedia, the free encyclopedia
		Rate distortion theory is a major branch of information theory; it addresses the problem of determining the minimal amount of entropy (or information) R that should be communicated over a channel, so that the source (input signal) can be reconstructed at the receiver (output signal) with given distortion D.
		In rate distortion theory, the rate is usually understood as the number of bits per data sample to be stored or transmitted.
		In the most simple case (which is actually used in most cases), the distortion is defined as the variance of the difference between input and output signal (i.e., the mean-squared error of the difference).
	en.wikipedia.org /wiki/Rate_distortion_theory (1090 words)

	Rate distortion theory - Wikipedia, the free encyclopedia (Site not responding. Last check: )
		Rate distortion theory is the branch of information theory addressing the problem of determining the minimal amount of entropy (or information) R that should be communicated over a channel such that the source (input signal) can be reconstructed at the receiver (output signal) with given distortion D.
		As such, rate distortion theory gives theoretical bounds for how much compression can be achieved using lossy data compression methods.
		Rate distortion theory was created by Claude Shannon in his founding work on information theory.
	www.encyclopedia-online.info /Rate_distortion_theory (798 words)

	Rate distortion theory: Facts and details from Encyclopedia Topic (Site not responding. Last check: )
		Rate distortion theory was created by Claude Shannon[For more info, click on this link] in his founding work on information theory.
		In probability theory and information theory, the mutual information of two random variables is a quantity that measures the independence of the two variable...
		In probability theory, memorylessness is a property of certain probability distributions: the exponential distributions and the geometric distributions....
	www.absoluteastronomy.com /encyclopedia/r/ra/rate_distortion_theory.htm (1533 words)

	UofOttawa--School of Tech. Eng.: Research Areas (Site not responding. Last check: )
		In systems theory, the ingredients that put into shape dissipation are the storage function, which is a function of states, and the supply rate which is a function of the input and the output.
		Rate distortion theory was introduced to deal with cases that entropy of the source is higher than the capacity of the channel.
		Moreover rate distortion problem is extended to the case of uncertain sources, in which the uncertainty is described by a relative entropy constraint between the true and a nominal distribution.
	www.site.uottawa.ca /~chadcha/CDC2004 (2134 words)

	Information theory - Wikipedia, the free encyclopedia
		Information theory is a field of mathematics concerning the storage and transmission of data and includes the fundamental concepts of source coding and channel coding.
		Information theory is the mathematical theory of data communication and storage, generally considered to have been founded in 1948 by Claude E. Shannon.
		This division of coding theory into compression and transmission is justified by the information transmission theorems, or source-channel separation theorems that justify the use of bits as the universal currency for information in many contexts.
	www.sciencedaily.com /encyclopedia/information_theory (3631 words)

	Theory of Data Compression
		Thus, the theorem established that the entropy rate is the rate of an optimal lossless data compression code.
		Compression rate is the rate of the compressed data (which we imagined to be transmitted in ``real-time'').
		Compression ratio is the ratio of the size or rate of the original data to the size or rate of the compressed data.
	www.data-compression.com /theory.html (2876 words)

	Rate distortion theory (Site not responding. Last check: )
		Rate distortion theory is the branch of information theory addressing the problem of determining the amount of entropy (or information) R that should be communicated over a such that the source (input signal) can reconstructed at the receiver (output signal) with distortion D.
		Rate distortion theory was created by Claude Shannon in his founding work on information
		In audio compression perceptual models and perceptual distortion measures are well developed and used in compression techniques such as MP3 or Vorbis but often not easy to include rate-distortion theory.
	www.freeglossary.com /Rate_distortion_theory (863 words)

	No Title
		However, it was the year 1959 that saw the formulation of rate distortion theory as we know it today--that year marked the appearance of Shannon's paper [22] in which he laid out basic tenets of rate distortion theory, along with a rigorous proof of a lossy source coding theorem.
		However, the optimum rate for fixed-rate block coding of a non-ergodic stationary source is not given by the rate distortion function [8].
		Although the Elias code encodes at an optimal rate, it is impractical because it requires infinite precision and therefore an infinite buffer size; also, the Elias code is catastropic in the sense that finitely many errors in the code sequence may cause infinitely many errors in the decoded source sequence.
	www.itsoc.org /review/kieffer.html (1970 words)

	Bit Allocation
		The Rate-Distortion theory is often used for solving the problem of allocating bits to a set of classes, or for bitrate control in general.
		Of all the classes, the class with mininum distortion for a reduction of 1 bit is noted, and 1 bit is reduced from its quota of bits.
		The total rate for all the classes is calculated as R = p(i) * B(i), where p is the probability and B is the bit allocation for each class.
	www.debugmode.com /imagecmp/bitalloc.htm (390 words)

	Rate-distortion theory (Site not responding. Last check: )
		Postage rates worldwide Directory of mail rates (domestic and international letter rates) with links to the rate calculators or rate tables of postal services in most countries of the world.
		Rate Her Tits Rate women exposing their breast.
		Rate My Boyfriend Rate pictures of guys submitted by their girlfriend.
	www.serebella.com /encyclopedia/article-Rate-distortion_theory.html (1255 words)

	Bin Yu Lossy Data Compression (Site not responding. Last check: )
		This is called lossy compression and the theory studying its theoretical limits is called rate-distortion theory.
		This rate was asserted (for the distortion-rate function, which is the inverse of the rate-distortion function) in 1968 by Pilc, but his proof contained a major gap.
		Using the method of types and the parametric representation of the rate-distortion function, we showed in Yu and Speed (1993) that the rate $n^{-1} \log n$ is indeed an upper bound to the optimal rate.
	www.stat.berkeley.edu /users/binyu/rdt.html (263 words)

	Velikovskian Tectonics and Pangaea
		Rose proposes a theory that, essentially, they are the result of "wrinkling" of the crust due to compression as the "world mountain" collapsed.
		Nothing is presented to suggest that the actual rate at which India drifted is impossible.
		the extraordinarily high rate of drift of India is consistent with the extraordinary nature of the collision effects.
	www.talkorigins.org /faqs/egg-earth.html (1754 words)

	Definition of index.php?search=rate&limit=20&offset=80 (Site not responding. Last check: )
		Thus, given an interest rate of ''i'', an initial capital is increased by the...
		Nominal interest rate is not an interest rate at all, but the sum of two diferent concepts in e...
		1:...'''basic reproductive rate''' or the '''intrinsic rate of reproduction''' is the number of secondary [[i...
	www.wordiq.com /knowledge/index.php?search=rate&limit=20&offset=80 (749 words)

	EE372 Information Sheet
		Theory and design of codes for quantization and signal compression systems (source coding systems), systems which convert analog or high bit rate digital signals into relatively low bit rate digital signals while optimizing fidelity subject to availabile communication and storage capacity.
		Optimal theoretical tradeoffs between bit rate and fidelity, especially asymptotic results for high rate or large dimension.
		Information theory (EE376A) will certainly help, but it is not assumed and some is taught as part of this class.
	www.stanford.edu /class/ee372 (1001 words)

	Sergio Verdu Complexity of Simulation of Random Processes
		Shannon theory explores the fundamental limits on the size of codes that enable the reliable reproduction or transmission of information.
		In parallel with conventional Shannon theory, a rich theory arises when some distance (often arbitrarily small) is allowed between the desired and the resulting probability distributions.
		Resolvability of a source is shown to equal the minimum achievable source coding rate, and to be equal to the sup-entropy rate: the limsup in probability of the sequence of normalized self-information random variables.
	www.princeton.edu /~verdu/sources.html (649 words)

	Rate distortion theory
		In audio compression perceptual models, and therefore perceptual distortion measures, are well developed and routinely used in compression techniques such as mp3, but often not easy to include in rate-distortion theory.
		In the definition of the rate-distortion function, $D_Q$ and $D^$ are the distortion* between X and Y for a given $Q_{YX}(yx)$ and the prescribed maximum distortion, respectively.
		Comprehensive information about rate-distortion theory can be found for instance here: Course on signal coding (http://www-ict.its.tudelft.nl/et4_089).
	www.fastload.org /ra/Rate-distortion_theory.html (844 words)

	Rate Distortion Theory for Image and Video Coding (ResearchIndex)
		Abstract: Wegive the rate distortion function for three image sequence coders: intra-frame, interframe and motion compensating inter-frame.
		The intensity function distribution is assumed to be Gaussian, and we suppose spatio-temporal separability and an isotropic model for the spatial part of the intensity function.
		1 Rate distortion function for a source model of images (context) - Hayes, Habibi et al.
	citeseer.ist.psu.edu /609012.html (254 words)

	Rate Distortion Theory (Site not responding. Last check: )
		They're small enough to rate high on the spouse...
		the output level or the rate of growth...
		Distortion is blatant, uniform, consistent, and shocking with the...
	www.wikiverse.org /rate-distortion-theory (862 words)

	Prof. A. Eleftheriadis: Research
		Since the technique only affects the rate controller at the encoder, it can be used in a fully compatible way with practically all standards, including MPEG-1/2/4 as well as H.261 and H.263.
		We are developing the foundations of a new theory for media representation called "Complexity Distortion Theory".
		We have already proven that the bounds predicted by the new theory for stochastic sources are identical to those provided by traditional Rate Distortion theory, and are working towards practical applications of these results.
	www.ee.columbia.edu /~eleft/research.html (726 words)

	Stanford University Professor - Robert M. Gray
		``A Lagrangian formulation of fixed rate and entropy/memory constrained quantization,'' Proceedings of the 2005 IEEE Data Compression Conference, March 2005, pp.
		Not free, but much better: The book is now available from Cambridge University Press, December 2004, Cambridge, UK.
		, Scanned copy of Information Systems Laboratory Technical Report 6502-2, October 1972, an early work on conditional rate distortion functions and related theory.
	ee.stanford.edu /~gray (576 words)

	PDF
		The first part of the first course will introduce the ideal of uncertainty, which is a useful measure in studying the data compression and deriving the results related to compression.
		In particular, we shall derive the result dealing with the capacity of the channel followed by the rate distortion theory followed by the network information theory.
		Rate Distortion Theory: A Mathematical Basis for Data Compression by T. Berger, Publisher: Prentice-Hall (1971).
	www.ee.washington.edu /research/nsl/class/595/2003spr/detailsmain.html (425 words)

	Sergio Verdu Rate-Distribution Theory
		Once a fidelity criterion is chosen, the rate-distortion function reflects the optimal tradeoff between encoding rate and achievable fidelity.
		This problem was considered by Rubin in 1974 with a distortion measure equal to the normalized absolute error between the true and reproduced interarrival times.
		The rate-distortion function of the Poisson process with rate \lambda arrivals per second is equal to
	www.princeton.edu /~verdu/ratedistortion.html (473 words)

	Toby Berger
		Other problems concern applying multiterminal rate-distortion theory and multiterminal decision theory to situations in which many remote, correlated sources are connected to a common processor via separate communication links.
		The subject of random fields, which is under intense investigation in mathematics and physics, is being studied from the viewpoint of information theory.
		Work on rate-distortion theory for non-Gaussian random fields has included the establishment of a critical distortion phenomenon for the Ising model in two dimensions.
	people.ece.cornell.edu /berger (615 words)

	Rate Distortion (Site not responding. Last check: )
		Rate Distortion Function in the Spin Glass State:...
		Rate distortion theory for image and video coding...
		Theory of Data Compression :How-to.tk: :Free downloads and tutorials...
	www.scienceoxygen.com /electrical/429.html (276 words)

	NetWorking "R" Definitions and Concepts
		His experience led him to believe that they were clumsy and unnatural ways of representing data relationships.
		He therefore went back to mathematical set theory and focused on the construct known as a relation (or set).
		He extended that concept to produce the relational database model, which he introduced in a seminal paper in 1970.
	umuc.rdbprime.com /Networking/NetWorkingRDefs.html (2602 words)

	Project-Team-TEMICS
		Coding and joint source channel coding rely on fundamental concepts of information theory, such as notions of entropy, memoryless or correlated sources, of channel capacity, or on rate-distortion performance bounds.
		In lossless coding, the lower rate bound is given by the entropy of the source.
		For real signals, this function is defined as the convex-hull of all feasible (rate, distortion) points.
	www.inria.fr /rapportsactivite/RA2004/temics/uid13.html (294 words)

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