Weakly universal LZ-extended codes for sources with countable alphabet

Abstract

We consider the problem of designing weakly universal codes for stationary and ergodic processes with countable alphabet and present a set of algorithms. First two algorithms use a combination of an integer coding algorithm and Lempel-Ziv algorithms (incremental parsing based algorithm and one based on recurrence times). Third algorithm converts the source into a finite alphabet process in step one through an integer coding algorithm and then uses LZ-78 in second step. Asymptotic optimality of all three is proved in full generality. We make use of Shannon-McMillan-Breiman theorem for countable alphabet and its extension for asymptotically mean stationary processes