On the AEP of word-valued sources

We consider a new class of information sources called word-valued sources in order to investigate coding algorithms based upon string parsing. A word-valued source is defined as a pair of an independent and identically distributed (i.i.d.) source with a countable alphabet and a function that maps each symbol into a finite sequence over a finite alphabet. A word-valued source is a nonstationary process and has countable states. If the function of a word-valued source is prefix-free, the entropy rate is characterized with a simple expression and the AEP (asymptotic equipartition property) holds