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Topic: Shannon limit

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	Shannon's Work
		In the Shannon paradigm, information from a "source" (defined as a stochastic process) must be transmitted though a "channel" (defined by a transition probability law relating the channel output to the input).
		First he gives a fundamental limit which, for example, might say that for a given source and channel, it is impossible to achieve a fidelity or reliability level better than a certain value.
		Thus the revolutionary elements of Shannon's contribution were the invention of the source-encoder-channel-decoder-destination model, and the elegant and remarkably general solution of the fundamental problems which he was able to pose in terms of this model.
	cm.bell-labs.com /cm/ms/what/shannonday/work.html (841 words)

	Fisheries & Angling Legislation & Bye-Laws for Ireland's Shannon Region
		In the case of the Shannon Fisheries Region, the River Feale in Co Kerry and the River Mulkear in Co Limerick are open to Salmon angling and have quotas of 4,581 and 2,127 fish respectively.
		This Bye-Law provides for a season bag limit of 3 fish in the period 1 Jan to 11 May, a daily bag limit of 3 fish from 12 May to 31 August and a daily bag limit of 1 fish from 1 September to the end of the season.
		SHANNON FISHERIES REGION (Prohibition on Angling) BYE-LAW No. C.S. This Bye-Law prohibits angling for all species of fish during the period 1 March to 30 September in that section of the Lower Shannon as specified in the Bye-law i.e.
	www.shannon-fishery-board.ie /aboutus/legislation.htm (1747 words)

	Shannon–Hartley theorem - Wikipedia, the free encyclopedia
		In the 1940s, Claude Shannon developed the concept of channel capacity, based in part on the ideas of Nyquist and Hartley, and then formulated a complete theory of information and its transmission.
		The quantity 2B later came to be called the Nyquist rate, and transmitting at the the limiting pulse rate of 2B pulses per second as signalling at the Nyquist rate.
		Shannon, "Communication in the presence of noise", Proc.
	en.wikipedia.org /wiki/Shannon-Hartley_theorem (1713 words)

	Shannon's theorem
		Shannon's theorem, proved by Claude Shannon in 1948, describes the maximum possible efficiency of error-correcting methods versus levels of noise interference and data corruption.
		Shannon's theorem has wide-ranging applications in both communications and data storage applications.
		In the communication domain, Shannon's theorem is known as the Shannon limit or Shannon capacity, the maximum rate of clean data C that can be sent through an analog communication channel subject to Gaussian-distribution noise interference:
	publicliterature.org /en/wikipedia/s/sh/shannon_s_theorem.html (162 words)

	shannonbio.html
		He suggested to Shannon that algebra might be as useful in organizing genetic knowledge as it was in switching, and Shannon decided to look into this matter with a view toward using it for a doctoral thesis in mathematics.
		In 1956 Dr. Shannon was invited to be a visiting professor at M.I.T. and, in 1957-58, a fellow at the Center for the Study of the Behavioral Sciences in Palo Alto, California.
		But Shannon, who is a boyish 73, with an elfish grin and a shock of snowy hair, is tired of expounding on his past.
	www.research.att.com /~njas/doc/shannonbio.html (3740 words)

	A PERSONAL OBITUARY FOR CLAUDE SHANNON
		However, among mathematicians and computer scientists, Claude Shannon is a legend, widely recognized as one of the most brilliant men of the twentieth century.
		Shannon's original construction handled three balls, although Christopher G. Atkeson and Stefan K. Schaal of the Georgia Institute of Technology have since constructed a five-ball machine along the same lines.
		JUGGLING THEOREM proposed by Claude E. Shannon of the Massachusetts Institute of Technology is schematically represented for the three-ball cascade.
	www2.bc.edu /~lewbel/Shannon.html (1882 words)

	Claude E
		From childhood on, Shannon was fascinated by both the particulars of hardware and the generalities of mathematics.
		Shannon's initial goal was simple: to improve the transmission of information over a telegraph or telephone line affected by electrical interference, or noise.
		Sidestepping questions about meaning, Shannon showed that it is a measurable commodity: the amount of information in a given message is a function of the probability that-out of all the messages that could be sent-it would be selected.
	www.ecs.umass.edu /ece/hill/ece221.dir/shannon.html (1446 words)

	EETimes.com - Comms pioneer Claude Shannon dead at 84
		Shannon was one of the first researchers to understand the value of using Boolean logic to develop binary computer languages.
		Shannon was born in Petoskey, Mich. in 1916.
		Shannon also employed a sense of fun in his work, developing several toys such as motorized pogo sticks, as well as a mechanical mouse capable of negotiating a maze.
	www.eetimes.com /story/OEG20010227S0045 (630 words)

	Pushing the Limit: Science News Online, Nov. 5, 2005 (Site not responding. Last check: )
		Shannon showed that at any given noise level, there is an upper limit on the ratio of the information to the redundancy required for accurate transmission.
		Shannon considered how much redundancy must be added to a message so that the information in it can survive a noisy transmission.
		Shannon's law, however, says that there is a limit to how good these codes can get—whether the communication channel is a fiber-optic cable or a noisy room.
	www.sciencenews.org /articles/20051105/bob8.asp (2527 words)

	Information theory (Site not responding. Last check: )
		Proved by Claude Shannon in 1948, the theorem describes the maximum possible efficiency of error-correcting methods versus levels of noise interference and data corruption.
		If we combine both noise and bandwidth limitations, however, we do find there is a limit to the amount of information that can be transferred, even when clever multi-level encoding techniques are used.
		The V.34 modem standard advertises a rate of 33.6 kbit/s, and V.90 claims a rate of 56 kbit/s, apparently in excess of the Shannon limit (telephone bandwidth is 3.3 kHz).
	www.infomationtheory.org /theorem.html (582 words)

	Time Warner Cable - Rochester, NY
		Shannon's Law states that for any kind of data transmission medium, there is a theoretical limit to the transfer speed beyond which the signal-to-noise ratio becomes so low that no useful data can be extracted.
		The demodulation of the signal at the receiver's modem introduces quantization noise, one of the limiting factors on standard modem transmission speed.
		The so-called Shannon's Limit (theoretical maximum transmission speed) under such conditions is in fact around 35kbps.
	www.discoverrochester.com /articles/nick/view.cfm?id=436 (741 words)

	Shannon limit (Site not responding. Last check: )
		In the communication domain, Shannon's theorem is known as the Shannonlimit or Shannon capacity, the maximum rate of clean data C that can be sent through an analog communication channelsubject to Gaussian-distribution noise interference:
		With Turbo codes andthe computing power in today's digital signalprocessors, it is now possible to reach within one-tenth of one decibel of the Shannon limit.
		The speed improvement of V.90 was made possible by theelimination of an additional step of analog todigital conversion by the use of fully digital equipment at the other end of a modem connection.
	www.therfcc.org /shannon-limit-20104.html (443 words)

	Walker Stumbles Over Shannon
		Shannon's formula gives the capacity of a band-limited noisy channel, so the bandwidth term in the formula is that of the channel.
		Shannon's theorem is all about the tradeoffs between bandwidth efficiency, power efficiency and interference resistance that modulation and forward error correction coding make possible.
		Shannon's Limit with this equation is reached when Eb / N0 is about -20 dB (with Q = 100 b/s/Hz).
	www.ka9q.net /vmsk/shannon.html (1543 words)

	Neural Systems Corporation - FAQs
		The Shannon channel capacity is the maximum number of bits per sec.
		Shannon proved that it was possible to get arbitrarily close to the capacity but did not show how.
		NSC detectors have been demonstrated to achieve Shannon channel capacity at signal to noise ratios typical of cable channels, thus increasing the bit rate through a channel.
	neuralsyscorp.com /faq.html (490 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: )
		And this brings us to a thing called "The Shannon Limit." Shannon was a man (that's his last name) who studied information processing before computers were around, before information processing was a well-studied science.
		One of the things he proved is that there is a maximum amount of information that can be transmitted in a fixed number of bits.
		You probably won't need to know that, but if you study the Shannon Limit, then you will run across it.) Basically, the idea is that there is a limit to the amount you can compress data without losing any data.
	mathforum.org /library/drmath/view/65726.html (784 words)

	AT&T: AT&T Labs: AT&T Labs - Innovation - Technology Timeline - Remembering Claude Shannon
		Claude Shannon has been described as the "intellectual giant of the digital age." By the time of his death on Feb. 24, 2001, Shannon had collected a pile of prestigious prizes that proved it — the National Medal of Science, Japan's Kyoto Prize, the IEEE Medal of Honor among them.
		To approach the Shannon limit, communications engineers encode data, compress it to remove redundancy, and transmit only information essential to understanding.
		Shannon reasoned that the same types of digital codes that protect sensitive information could be used to safeguard it from noise, static or interference
	www.att.com /attlabs/reputation/timeline/16shannon.html (894 words)

	fUSION Anomaly. Claude Shannon
		Claude Shannon, a lone-wolf genius, is still known to his neighbors in Cambridge, Massachusetts, for his skill at riding a motorcycle.
		Shannon defined the basic unit of information which came to be called a "bit".
		Shannon termed this information content "entropy." In a digital message, another name for a stream of unexpected bits is random noise.
	fusionanomaly.net /claudeshannon.html (1562 words)

	What is the effect of noise (Site not responding. Last check: )
		The information carrying limit was discussed theoretically by Claude Shannon and is known as Shannon's limit, or information theory.
		Because modems run close to Shannon's limit today, no further advances will be made to traditional telephone line modems other than incremental improvement of V.90.
		V.34+ modems are limited to a maximum data rate of 33.6Kbps by an SNR of about 36dB caused mostly by network PCM (Pulse Coded Modulation) quantization noise.
	members.tripod.com /~BrunelUni/What_is_the_effect_of_noise.html (221 words)

	Coordinated Science Laboratory
		What's more, in the process they were able to boost the transmission of data to within 1.5 decibels(dB) of Shannon's limit - a milestone at the time.
		Shannon's limit, established by Claude Shannon in his landmark paper of 1949, showed that for a given source and channel, it is impossible to send error-free data beyond a certain speed or below a certain energy per bit.
		Surpassing Shannon's limit may be impossible, just as physicists will never be able to reach the absolute zero temperature.
	www.csl.uiuc.edu /news/turbocharge.asp?Number=13310 (663 words)

	[No title]
		Shannon's theory seemed to promise that almost any code chosen at random would meet the definition of "good." Researchers quickly discovered, however, this wasn't the case.
		Some suspected that forces larger than Shannon were at work, and they pointed to other testimony that the digital communications age was destined to be: "And in all your communications, let them be `Yeah, yeah' and `Nay, nay'" (Matthew 5:37).
		For applications that are strictly bandwidth limited, FEC might be appropriate only if used in combination with a larger symbol alphabet, which adds complexity to the system but avoids bandwidth expansion.
	archive.chipcenter.com /dsp/DSP000419F1.html (2568 words)

	Compression and the Huffman Code (Site not responding. Last check: )
		Shannon's Source Coding Theorem states that symbolic-valued signals require on the average at least H(A) number of bits to represent each of its values, which are symbols drawn from the alphabet A.
		In the module on the Source Coding Theorem we find that using a so-called fixed rate source coder, one that produces a fixed number of bits/symbol, may not be the most efficient way of encoding symbols into bits.
		The average number of bits required to represent this alphabet equals 1.75 bits, which is the Shannon entropy limit for this source alphabet.
	cnx.org /content/m0092/latest (752 words)

	RFC 1144 (rfc1144) - Compressing TCP/IP Headers for Low-Speed Serial Links
		Based on an ATandT study[2], the Shannon limit for a typical dialup phone line is around 22,000 bps.
		The 22Kbps Shannon limit is a hard-limit on data rate through a two-wire telephone connection.
		The connection number is limited to one byte, i.e., 256 simultaneously active TCP connections.
	www.faqs.org /rfcs/rfc1144.html (13175 words)

	Noisy channel coding theorem - Wikipedia, the free encyclopedia
		In information theory, the noisy-channel coding theorem establishes that however contaminated with noise interference a communication channel may be, it is possible to communicate digital data (information) error-free up to a given maximum rate through the channel.
		The Shannon limit or Shannon capacity of a communications channel is the theoretical maximum information transfer rate of the channel, for a particular noise level.
		Shannon, A Mathematical Theory of Communication Urbana, IL:University of Illinois Press, 1949 (reprinted 1998).
	en.wikipedia.org /wiki/Shannon_limit (1313 words)

	Shannon limit of compression
		limit of compression can be calculated by extrapolating datapoints from lower order entropies to infinity.
		limit of compression is this true entropy divided by the number of bits required for coding all the possibilities of the alphabet.
		The Shannon Limit of Compression Limit (SLC) is related to true entropy (H) of a source by dividing the entropy in bits per symbol by the number of bits that can code for all the possibilities of the alphabet.
	www.home.zonnet.nl /galien8/compression/compression.html (2653 words)

	The Shannon limit (Fred R. Goldstein) (Site not responding. Last check: )
		The limit of bps is proportional to the > logarithm of the signal to noise ratio.
		Shannon's law is, in plaintext, BPS(max) = Bw * log(2)((1+S)/N) That is, take the signal-to-noise ration (adding 1 to signal, so a negative SNR has some information present) and represent it as a power of 2.
		Today a good clean line is more likely to be digitally switched at 64000 bps, which is well above the Shannon limit (digitization is lossy), but you still get a theoretical limit closer to 40 kbps.
	yarchive.net /phone/shannon_limit.html (270 words)

	Non-parametric approach and Shannon's superresolution limit
		Due to always presenting noise there is the resolution limit for close signals, which is non-improved of principle.
		That follows from the well-known Shannon's theory on the maximum speed of the data transmission via the channel having a noise.
		the approximate expression for the superresolution limit is
	kapitza.ras.ru /people/kosarev/chep_97/node2.html (332 words)

	The VMSK Delusion
		Shannon's paper is a landmark precisely because it applies to every possible modulation and coding scheme, whether or not it had been conceived in Shannon's time.
		Other analyzer parameters include the frequency limits of the filter sweep, and the rate at which the sweep is made.
		Shannon proved that it was at least possible (though he didn't show how) to reliably communicate at any rate below the channel capacity C.
	people.qualcomm.com /karn/papers/vmsk/critique.html (5500 words)

	Shannon's Law - a Whatis.com definition
		Shannon's Law, formulated by Claude Shannon, a mathematician who helped build the foundations for the modern computer, is a statement in information theory that expresses the maximum possible data speed that can be obtained in a data channel.
		Shannon's Law says that the highest obtainable error-free data speed, expressed in bits per second (bps), is a function of the bandwidth and the signal-to-noise ratio.
		Some systems, using sophisticated encoding and decoding, can approach half of the so-called Shannon limit for a channel having fixed bandwidth and signal-to-noise ratio.
	whatis.techtarget.com /gDefinition/0,294236,sid44_gci856628,00.html (225 words)

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