Variable-Length Coding of Two-sided Asymptotically Mean Stationary Measures |
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Authors: | Łukasz Dębowski |
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Institution: | (2) Department of Computer Science and Engineering, Florida Atlantic University, Boca Raton, FL, USA; |
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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 σ-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. |
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Keywords: | |
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