Fixed-rate universal codes for Markov sources
The existence of a fixed-rate block source code whose performance for each source in a class of Markov sources is uniformly close to the distortion-rate function of that source is investigated. Such a code is called strong universal. It is found that strong universal codes of all rates exist for the class of all binary first-order Markov sources. But for a larger alphabet or for the class of all n th-order Markov sources with n > 2 , there is a critical rate R\ast such that strong universal codes exist for rates greater than or equal to R\ast , but not for rates less than R\ast .