Word-Valued Sources: An Ergodic Theorem, an AEP, and the Conservation of Entropy

作者：Timo Roy^*; Blackmore Kim; Hanlen Leif

来源：IEEE Transactions on Information Theory, 2010, 56(7): 3139-3148.

DOI：10.1109/TIT.2010.2046251

• Asymptotic equipartition property (AEP)
• asymptotically mean stationary (AMS)
• ergodic theorem

A word-valued source Y = Y-1,Y-2,... is discrete random process that is formed by sequentially encoding the symbols of a random process X = X-1,X-2,... 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 X and C for which will satisfy an ergodic theorem and possess an asymptotic equipartition property (AEP). In this paper, we prove the following: 1) if X is asymptotically mean stationary (AMS), 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 X normalized by the average codeword length.

• 出版日期2010-7