A survey of Bratteli information source theory
John C. Kieffer · 2016
We survey recent results on Bratteli-Vershik information sources, which are sources that live on a Bratteli diagram, a type of graph with a countable infinity of vertices and edges that are split into levels. The results are valid when the underlying Bratteli diagram satisfies a regularity condition. These results include an ergodic decomposition theorem, Shannon-McMillan-Breiman theorem, and theorems in source coding theory. The results are obtained using the Vershik transformation that is associated with a Bratteli diagram. It is explained how some previously known results in source coding for finite-alphabet stationary sequential information sources are obtainable from source coding results for Bratteli-Vershik sources.