Variable-Length Coding of Two-Sided Asymptotically Mean Stationary Measures

Abstract

We collect several observations that concern variable-length coding of two-sided infinite sequences in a probabilistic setting. Attention is paid to images and preimages of asymptotically mean stationary measures defined on subsets of these sequences. We point out sufficient conditions under which the variable-length coding and its inverse preserve asymptotic mean stationarity. Moreover, conditions for preservation of shift-invariant $\sigma$-fields and the finite-energy property are discussed and the block entropies for stationary means of coded processes are related in some cases. Subsequently, we apply certain of these results to construct a stationary nonergodic process with a desired linguistic interpretation.

20 pages. A few typos corrected after the journal publication

Cited by in corpus (6)

• Excess entropy in natural language: present state and perspectives
• On Hidden Markov Processes with Infinite Excess Entropy
• Mixing, Ergodic, and Nonergodic Processes with Rapidly Growing Information between Blocks
• Regular Hilberg Processes: An Example of Processes with a Vanishing Entropy Rate
• Bounds for Algorithmic Mutual Information and a Unifilar Order Estimator
• From Letters to Words and Back: Invertible Coding of Stationary Measures