Maximum Entropy Rate of Markov Sources for Systems With Non-regular Constraints

• Main Authors: Böcherer, Georg, RochaJr, Valdemar Cardoso da, Pimentel, Cecilio
• Format: Journal Article
• Language: English
• Published: 07-09-2008
• Subjects: Computer Science - Information Theory; Mathematics - Information Theory
• DOI: 10.48550/arxiv.0809.1252

Using the concept of discrete noiseless channels, it was shown by Shannon in
A Mathematical Theory of Communication that the ultimate performance of an
encoder for a constrained system is limited by the combinatorial capacity of
the system if the constraints define a regular language. In the present work,
it is shown that this is not an inherent property of regularity but holds in
general. To show this, constrained systems are described by generating
functions and random walks on trees.