Dispersion theorems via second order analysis of functions of distributions

We revisit old and recent “dispersion” theorems for lossless and lossy source coding, channel coding and joint source-channel coding, showing that they can be proven in a general unified framework. In all of these cases, an error (or excess distortion) event occurs, to the level of interest in the asymptotic analysis, if some function of the empirical distribution crosses a threshold. Thus, second order analysis for general functions of distributions is studied, and a technical result which allows to prove the various dispersion theorems is derived.