the following properties: Applications of typicality Typical set encoding In information theory, typical set encoding encodes only the sequences in the typical set of a stochastic source with fixed length block codes. Since the size of the typical set is about 2nH(X), only nH(X) bits are required for the coding, while at the same time ensuring that the chances of encoding error is limited to ε. Asymptotically, it is, by the AEP, lossless and achieves the minimum rate equal to the entropy rate of the source. 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. where are the message estimate, codeword of message and the observation respectively. is defined with respect to the joint distribution where is the transition probability that characterizes the channel statistics, and is some input distribution used to generate the codewords in the random codebook. Universal null-hypothesis testing Universal channel code See also Asymptotic equipartition property Source coding theorem Noisy-channel coding theorem References C. E. Shannon, "A Mathematical Theory of Communication", Bell System Technical Journal, vol. 27, pp. 379–423, 623-656, July, October, 1948 David J. C. MacKay. Information Theory, Inference, and Learning Algorithms Cambridge: Cambridge University Press, 2003. Information theory Probability theory