Information Theory

Information

Information relates to uncertainty. The Shannon information content of an outcome \(x\) is \(h(x)=-log_{2}P(x)\). The rare event has larger information than a common event. The unit of information is a bit (binary digit). Coding is a mapping from an outcome of an ensemble to binary digits \(\{0,1\}^+\). A symbol code is a code for a single ensemble. A block code is a code for a sequence ensemble. A set of sequences of the ensemble has a typical subset.