Shannon entropy

Shannon entropy is one of the most important metrics in information theory. Entropy measures the uncertainty associated with a random variable, i.e. the expected value of the information in the message (in classical informatics it is
measured in bits).

The concept was introduced by Claude E. Shannon in  the paper „A Mathematical Theory of Communication” (1948). Shannon entropy allows to estimate
the average minimum number of bits needed to encode a string of symbols based on the alphabet size and the frequency of the symbols.

The Shannon entropy is calculated using formula:

当b=2时，H(X)就表示这个变量可以用几个bit来表示。bit就是H(X)的单位。如一个变量表示掷硬币正反面，如果正反面的概率都是1/2，那么H(X)就为1，1个bit就可以表示这个变量。