Editing Coding theory (section)

===Definition===
Data can be seen as a [[random variable]] <math>X:\Omega\to\mathcal{X}</math>, where <math>x \in \mathcal{X}</math> appears with probability <math>\mathbb{P}[X=x]</math>.

Data are encoded by strings (words) over an [[Alphabet (computer science)|alphabet]] <math>\Sigma</math>.

A code is a function

:<math>C:\mathcal{X}\to\Sigma^*</math> (or <math>\Sigma^+</math> if the empty string is not part of the alphabet).

<math>C(x)</math> is the code word associated with <math>x</math>.

Length of the code word is written as

:<math>l(C(x)).</math>

Expected length of a code is

:<math>l(C) = \sum_{x\in\mathcal{X}}l(C(x))\mathbb{P}[X=x] .</math>

The concatenation of code words <math>C(x_1, \ldots, x_k) = C(x_1)C(x_2) \cdots C(x_k)</math>.

The code word of the empty string is the empty string itself:

:<math>C(\epsilon) = \epsilon</math>