Abstract

The usual assumption for proofs of the optimality of lossless encoding is a stationary ergodic source. Dynamic sources with non-stationary probability distributions occur in many practical situations where the data source is formed from a composition of distinct sources, for example, a document with multiple authors, a multimedia document, or the composition of distinct packets sent over a communication channel. There is a vast literature of adaptive methods used to tailor the compression to dynamic sources. However, little is known about optimal or near optimal methods for lossless compression of strings generated by sources that are not stationary ergodic. Here, we do not assume the source is stationary. Instead, we assume that the source produces an infinite sequence of concatenated finite strings Sl... s,, where: (i) Each finite string si is generated by a sampling of a (possibly distinct) stationary ergodic source &, and (ii) the length of each of the si is lower bounded by a function L(n) such that L(n)/log(n) grows unboundedly with the length n of all the text within $1 .. $i.

Citations