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

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3 Author(s)
Timo, R. ; Inst. for Telecommun. Res., Univ. of South Australia, Mawson Lakes, SA, Australia ; Blackmore, K. ; Hanlen, L.

A word-valued source Y = Y1,Y2,... is discrete random process that is formed by sequentially encoding the symbols of a random process X = X1,X2,... with codewords from a codebook C. 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 Y 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 Y will satisfy a pointwise ergodic theorem and possess an AEP; and 2) if the codebook C is prefix-free, then the entropy rate of Y is equal to the entropy rate of X normalized by the average codeword length.

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Information Theory, IEEE Transactions on  (Volume:56 ,  Issue: 7 )