Coding for Noncausal Tracking

A source generates a random sequence that is then described to a controller who wishes to employ feedback control on a given finite-state system in order for its output to closely resemble the sequence. The tension between the best achievable expected fidelity and the description length is studied in the asymptotic regime where the length of the sequence tends to infinity, with the description rate held fixed. The solution is the source-coding dual of coding for channels with states.