4 research outputs found
Mixing, Ergodic, and Nonergodic Processes with Rapidly Growing Information between Blocks
We construct mixing processes over an infinite alphabet and ergodic processes
over a finite alphabet for which Shannon mutual information between adjacent
blocks of length grows as , where . The processes
are a modification of nonergodic Santa Fe processes, which were introduced in
the context of natural language modeling. The rates of mutual information for
the latter processes are alike and also established in this paper. As an
auxiliary result, it is shown that infinite direct products of mixing processes
are also mixing.Comment: 21 page
Variable-Length Coding of Two-Sided Asymptotically Mean Stationary Measures
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 -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.Comment: 20 pages. A few typos corrected after the journal publicatio