Optimal lossless compression of a class of dynamic sources

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 constructed by 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. We present a number of asymptotically efficient algorithms that address, at least from the theoretical point of view, optimal lossless compression of dynamic sources. We assume the source produces an infinite sequence of concatenated finite strings generated by sampling a stationary ergodic source