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2. Shannon–Hartley theorem - Wikipedia

   en.wikipedia.org/wiki/Shannon–Hartley_theorem

   This formula's way of introducing frequency-dependent noise cannot describe all continuous-time noise processes. For example, consider a noise process consisting of adding a random wave whose amplitude is 1 or −1 at any point in time, and a channel that adds such a wave to the source signal. Such a wave's frequency components are highly ...

3. Entropy (information theory) - Wikipedia

   en.wikipedia.org/wiki/Entropy_(information_theory)

   The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication", [2] [3] and is also referred to as Shannon entropy. Shannon's theory defines a data communication system composed of three elements: a source of data, a communication channel, and a receiver. The "fundamental problem ...

4. Entropy coding - Wikipedia

   en.wikipedia.org/wiki/Entropy_coding

   More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies ⁡ [(())] ⁡ [⁡ (())], where is the number of symbols in a code word, is the coding function, is the number of symbols used to make output codes and is the probability of the source symbol. An entropy coding attempts to ...

5. Noisy-channel coding theorem - Wikipedia

   en.wikipedia.org/wiki/Noisy-channel_coding_theorem

   In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible (in theory) to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel.

6. Channel capacity - Wikipedia

   en.wikipedia.org/wiki/Channel_capacity

   Information-theoretic analysis of communication systems that incorporate feedback is more complicated and challenging than without feedback. Possibly, this was the reason C.E. Shannon chose feedback as the subject of the first Shannon Lecture, delivered at the 1973 IEEE International Symposium on Information Theory in Ashkelon, Israel.

7. Information content - Wikipedia

   en.wikipedia.org/wiki/Information_content

   As a quick illustration, the information content associated with an outcome of 4 heads (or any specific outcome) in 4 consecutive tosses of a coin would be 4 shannons (probability 1/16), and the information content associated with getting a result other than the one specified would be ~0.09 shannons (probability 15/16).

8. Hartley function - Wikipedia

   en.wikipedia.org/wiki/Hartley_function

   If the base of the logarithm is 2, then the unit of uncertainty is the shannon (more commonly known as bit). If it is the natural logarithm , then the unit is the nat . Hartley used a base-ten logarithm , and with this base, the unit of information is called the hartley (aka ban or dit ) in his honor.

9. Binary entropy function - Wikipedia

   en.wikipedia.org/wiki/Binary_entropy_function

   When = /, the binary entropy function attains its maximum value, 1 shannon (1 binary unit of information); this is the case of an unbiased coin flip. When p = 0 {\displaystyle p=0} or p = 1 {\displaystyle p=1} , the binary entropy is 0 (in any units), corresponding to no information, since there is no uncertainty in the variable.