Editing Typical set (section)

===Typical set decoding===
In [[information theory]], typical set decoding is used in conjunction with [[random coding]] to estimate the transmitted message as the one with a codeword that is jointly ε-typical with the observation. i.e.
:<math>\hat{w}=w \iff (\exists w)( (x_1^n(w),y_1^n)\in A_{\varepsilon}^n(X,Y)) </math>
where <math>\hat{w},x_1^n(w),y_1^n</math> are the message estimate, codeword of message <math>w</math> and the observation respectively. <math>A_{\varepsilon}^n(X,Y)</math> is defined with respect to the joint distribution <math>p(x_1^n)p(y_1^n|x_1^n)</math> where <math>p(y_1^n|x_1^n)</math> is the transition probability that characterizes the channel statistics, and <math>p(x_1^n)</math> is some input distribution used to generate the codewords in the random codebook.

{{Expand section|date=December 2009}}