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2. Limiting density of discrete points - Wikipedia

   en.wikipedia.org/wiki/Limiting_density_of...

   Shannon originally wrote down the following formula for the entropy of a continuous distribution, known as differential entropy: = ⁡ ().Unlike Shannon's formula for the discrete entropy, however, this is not the result of any derivation (Shannon simply replaced the summation symbol in the discrete version with an integral), and it lacks many of the properties that make the discrete entropy a ...

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. 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 ...

5. Binary entropy function - Wikipedia

   en.wikipedia.org/wiki/Binary_entropy_function

   Entropy of a Bernoulli trial (in shannons) as a function of binary outcome probability, called the binary entropy function.. In information theory, the binary entropy function, denoted ⁡ or ⁡ (), is defined as the entropy of a Bernoulli process (i.i.d. binary variable) with probability of one of two values, and is given by the formula:

6. 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).

7. 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.