1 research outputs found
Word-Valued Sources: an Ergodic Theorem, an AEP and the Conservation of Entropy
A word-valued source is discrete random process
that is formed by sequentially encoding the symbols of a random process
with codewords from a codebook . These
processes appear frequently in information theory (in particular, in the
analysis of source-coding algorithms), so it is of interest to give conditions
on and for which will satisfy an
ergodic theorem and possess an Asymptotic Equipartition Property (AEP). In this
correspondence, we prove the following: (1) if is asymptotically
mean stationary, then will satisfy a pointwise ergodic theorem and
possess an AEP; and, (2) if the codebook is prefix-free, then the
entropy rate of is equal to the entropy rate of
normalized by the average codeword length.Comment: 21 page