Class Of Markov Sources Research Articles

Complexity of strings in the class of Markov sources

Shannon's self-information of a string is generalized to its complexity relative to the class of finite-state-machine (FSM) defined sources. Unlike an earlier generalization, the new one is valid for both short and long strings. The definition is justified in part by a theorem stating that, asymptotically, the mean complexity provides a tight lower bound for the mean length of all so-called regular codes. This also generalizes Shannon's noiseless coding theorem. For a large subclass of FSM sources a simple algorithm is described for computing the complexity.

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> th-order Markov sources with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n &gt; 2</tex> , there is a critical rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R\ast</tex> such that strong universal codes exist for rates greater than or equal to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R\ast</tex> , but not for rates less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R\ast</tex> .