The ergodic decomposition of asymptotically mean stationary random sources

TL;DR

This paper extends the ergodic decomposition to asymptotically mean stationary sources, enabling broader application of source coding theorems to more realistic, non-ergodic sources.

Contribution

It introduces a method to represent AMS sources as mixtures of ergodic AMS sources, generalizing the stationary source decomposition.

Findings

Provides a framework for ergodic decomposition of AMS sources

Facilitates generalization of source coding theorems

Enables analysis of non-ergodic, real-world sources

Abstract

It is demonstrated how to represent asymptotically mean stationary (AMS) random sources with values in standard spaces as mixtures of ergodic AMS sources. This an extension of the well known decomposition of stationary sources which has facilitated the generalization of prominent source coding theorems to arbitrary, not necessarily ergodic, stationary sources. Asymptotic mean stationarity generalizes the definition of stationarity and covers a much larger variety of real-world examples of random sources of practical interest. It is sketched how to obtain source coding and related theorems for arbitrary, not necessarily ergodic, AMS sources, based on the presented ergodic decomposition.