# Shannon Lecture: Musing upon Information Theory

### Te Sun Han, *NICT*

## Thursday, June 17, 08:30 - 09:30

#### Abstract

Basic logics underlying typical theorems in informtion theory are
scrutinized from the viewpoint of information-spectra. Very general sources,
which may be neither stationary nor ergodic, are introduced to establish
conceptually simple formulars holding for the generalized AEP theorem, the
optimal source coding theorem along with the reliability function, the
fundamental limits of random number generation, the folklore theorem about
source coding, the invariance theorem of information-spectra in the process of
optimal source coding, the type II error rate function for hypothesis testing,
etc. To do so, it plays the key role to define the limit superior in
probability and the limit inferior in probability, which look like reasonable
extentions of the well-established concept of "limit in probablity." It turns
out also that source coding may be regarded as being a mere special case of
hypothesis testing in the generalized sense.