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The Shannon entropy satisfies the following properties, for some of which it is useful to interpret entropy as the expected amount of information learned (or uncertainty eliminated) by revealing the value of a random variable X:
- Self-Information
In information theory, the information content,...
- Differential Entropy
Differential entropy (also referred to as continuous...
- Self-Information
The Shannon entropy (in nats) is: = = = and if entropy is measured in units of per nat, then the entropy is given by: = which is the Boltzmann entropy formula, where is the Boltzmann constant, which may be interpreted as the thermodynamic entropy per nat.
In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable given that the value of another random variable is known. Here, information is measured in shannons, nats, or hartleys.
The Shannon entropy is a statistical quantifier extensively used for the characterization of complex processes.
From this slide, it's said that the smallest possible number of bits per symbol is as the Shannon Entropy formula defined: I've read this post, and still not quite understand how is this formula derived from the perspective of encoding with bits.
Shannon’s discovery of the fundamental laws of data compression and transmission marks the birth of Information Theory. In this note, we first discuss how to formulate the main fundamental quantities in In-formation Theory: information, Shannon entropy and channel capacity.
Shannon’s entropy quantifies the amount of information in a variable, thus providing the foundation for a theory around the notion of information. Storage and transmission of information can intuitively be expected to be tied to the amount of information involved.
