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It represents nothing other than itself. However the spectrum is not a sequence of digital symbols. Sunlight is not a code and neither is a rainbow. A rainbow is a spectrum of light and it represents nothing other than itself. Radioactive decay is just atomic particles decomposing. There is no symbolic relationship. Same with water. Water is water.

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But as a molecule it just has two atoms that we call Hydrogen and one atom that we call Oxygen. Noise and Information Entropy. One of the most important things in a communication system is noise and how well the system deals with it. Noise destroys information.

Noise introduces uncertainty as to what the original message was. When Claude Shannon worked out the math, he found something very surprising: The formula for noise in an information system was identical to the formula for entropy in thermodynamics. Entropy is the irreversible process of useful energy becoming useless energy. The heat coming out of the exhaust pipe in your car is cooler and a whole lot less useful than the heat inside your engine, and that process is irreversible. All audio engineers know that noise is also irreversible. All you can do is try to disguise it. There are a few very narrow applications in digital signal processing where noise can be put to good use i.

What is information theory?

It never creates it. Shannon measured information in bits, the exact same way that we measure the size of computer files. So one thing that confuses a lot of people is that when you add noise to a signal, it adds bit information to the signal and the signal appears to have more information. In one sense it does — if you add noise to a signal, the signal does contain more data. The ideal amount of noise to have in a signal is ZERO. Shannon pointed out that the best way to combat noise was through redundancy: Extra letters or numbers in the signal that help you fill in the blanks if there are missing letters.

You can usually figure out what the original sentence was as long as at least half the letters are still there. Layers of Communication. Right now, you are seeing a detailed 2-dimensional image on your computer screen. One of the essential aspects of communication systems is that the codes, the encoders and decoders have layers. Layers operate like this — multiple encoders and decoders cascaded together:. Information is encoded from the top layer down, and it is decoded from the bottom layer up.

You can edit text in Microsoft Word. If you want to successfully edit an email message, you have to edit it in an email program. If you want to change one of the information layers to make it say something different, you have to be IN that layer to change it. Because it only takes a very small injury to the packet to irreparably damage the whole thing, to the point where it cannot be decoded at all. Even a tiny flaw in a strand of DNA can cause a birth defect, for example. These very simple ideas that Claude Shannon introduced have profound and far-reaching implications for Origin of Life Research and Evolutionary Theory:.

All communication systems rely on prior agreement between encoder and decoder, otherwise no communication can take place. This agreement between the two sides must be made in advance. The agreement begins as an immaterial idea, just like the information itself is immaterial. All communication systems that we know of are designed. There are no known exceptions to this. Symbols are immaterial. The symbols have to be chosen in advance. The meaning of the message is independent of the medium that carries it. The very existence of information overturns the materialistic worldview.

This view is in sharp contrast with the common conception of information, in which meaning has an essential role. Shannon also realized that the amount of knowledge conveyed by a signal is not directly related to the size of the message. Similarly, a long, complete message in perfect French would convey little useful knowledge to someone who could understand only English.

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Shannon thus wisely realized that a useful theory of information would first have to concentrate on the problems associated with sending and receiving messages, and it would have to leave questions involving any intrinsic meaning of a message—known as the semantic problem—for later investigators. Clearly, if the technical problem could not be solved—that is, if a message could not be transmitted correctly—then the semantic problem was not likely ever to be solved satisfactorily.

Solving the technical problem was therefore the first step in developing a reliable communication system. It is no accident that Shannon worked for Bell Laboratories. The practical stimuli for his work were the problems faced in creating a reliable telephone system. A key question that had to be answered in the early days of telecommunication was how best to maximize the physical plant—in particular, how to transmit the maximum number of telephone conversations over existing cables.

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Shannon produced a formula that showed how the bandwidth of a channel that is, its theoretical signal capacity and its signal-to-noise ratio a measure of interference affected its capacity to carry signals. In doing so he was able to suggest strategies for maximizing the capacity of a given channel and showed the limits of what was possible with a given technology.

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This was of great utility to engineers, who could focus thereafter on individual cases and understand the specific trade-offs involved. Shannon also made the startling discovery that, even in the presence of noise, it is always possible to transmit signals arbitrarily close to the theoretical channel capacity. This discovery inspired engineers to look for practical techniques to improve performance in signal transmissions that were far from optimal.

Before Shannon, engineers lacked a systematic way of analyzing and solving such problems. Though information theory does not always make clear exactly how to achieve specific results, people now know which questions are worth asking and can focus on areas that will yield the highest return. They also know which sorts of questions are difficult to answer and the areas in which there is not likely to be a large return for the amount of effort expended.

The section Applications of information theory surveys achievements not only in such areas of telecommunications as data compression and error correction but also in the separate disciplines of physiology, linguistics, and physics.

Unfortunately, many of these purported relationships were of dubious worth. I personally believe that many of the concepts of information theory will prove useful in these other fields—and, indeed, some results are already quite promising—but the establishing of such applications is not a trivial matter of translating words to a new domain, but rather the slow tedious process of hypothesis and experimental verification. Information theory.

Information Theory part 11: Claude Shannon: A Mathematical Theory of Communication