Brillouin science and information theory
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- #BRILLOUIN SCIENCE AND INFORMATION THEORY HOW TO#
- #BRILLOUIN SCIENCE AND INFORMATION THEORY INSTALL#
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When I close the switch, you see the meter jump from 0 to 1 V.
#BRILLOUIN SCIENCE AND INFORMATION THEORY INSTALL#
We run two wires over to you and install a volt meter on your end. On my end, I have a 1-volt (V) battery and a switch. Suppose that you and I decide to set up a simple communications system ( Figure 1). What made all this possible? It is a key idea buried in a beautiful geometrical derivation of the channel capacity in Shannon's 1949 paper. Because they approach the Shannon limits, the recently developed Turbo codes promise to revolutionize communications again by providing more data transmission over the same channels.
#BRILLOUIN SCIENCE AND INFORMATION THEORY HOW TO#
The clarity of modern telecommunications, CDs, MP3s, DVDs, wireless, cellular phones, etc., came about because engineers have learned how to make electrical circuits and computer programs that do this coding and decoding. Shannon pointed out that the way to reduce errors is to encode the messages at the transmitter to protect them against noise and then to decode them at the receiver to remove the noise.
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The probability of errors can be made small but cannot be eliminated. Shannon discovered, and proved mathematically, that in this case one may transmit the information with as few errors as desired! Error is the number of wrong symbols received per second. The surprise comes when the rate is less than or equal to the capacity ( R ≤ C). There is an upper limit for how fast water can flow at some point, the resistance in the pipe will prevent further increases or the pipe will burst. A rough analogy is putting water through a pipe. First, Shannon showed that when the rate exceeds the capacity ( R > C), the communication will fail and at most C b/s will get through. Suppose one wishes to transmit some information at a rate R, also in bits per second (b/s). The channel capacity C in bits per second, depends on only three factors: the power P of the signal at the receiver, the noise N disturbing the signal at the receiver, and the bandwidth W, which is the span of frequencies used in the communication: Before delving into how he arrived at this concept, which explains why Shannon was a biologist, it is necessary to understand the surprising (Shannon's word) channel capacity theorem, and how it was developed. Of course, this immediately raised another question: How much information can we send over existing equipment, our phone lines? To answer this, Shannon developed a mathematical theory of the channel capacity. The definition, which has withstood the test of more than 50 years, precisely answered the question What is AT&T selling? The answer was information transmission in bits per second. How can information be defined precisely? Shannon, a mathematician, set down several criteria for a useful, rigorous definition of information, and then he showed that only one formula satisfied these criteria. At the time, Bell Labs was the research and development part of the American Telephone and Telegraph Company (AT&T), which was in the business of selling the ability to communicate information. It applies not only to human and animal communications, but also to the states and patterns of molecules in biological systems. In these groundbreaking papers, Shannon established information theory. Shannon's work at Bell Labs in the 1940s led to the publication of the famous paper “A Mathematical Theory of Communication” in 1948 and to the lesser known but equally important “Communication in the Presence of Noise” in 1949. By this means, one can, for example, reduce the number of transistors needed to accomplish a particular function. Thus, one can transform a circuit diagram into an equation, rearrange the equation algebraically, and then draw a new circuit diagram that has the same function. His Massachusetts Institute of Technology (MIT) master's thesis is famous because in it he showed that digital circuits can be expressed by Boolean logic. Shannon (30 April 1916-24 February 2001) is heralded for his major contributions to the fundamentals of computers and communications systems. Information theory is therefore a theory about biology, and Shannon was a biologist. Recent work using information theory to understand molecular biology has unearthed a curious fact: Shannon's channel capacity theorem only applies to living organisms and their products, such as communications channels and molecular machines that make choices from several possibilities. The theory has long been known to be closely related to thermodynamics and physics through the similarity of Shannon's uncertainty measure to the entropy function. Claude Shannon founded information theory in the 1940s.