Word-valued sources: an ergodic theorem, an AEP, and the conservation of entropy
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2010
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Timo, R.C.
Blackmore, K.
Hanlen, L.
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IEEE Transactions on Information Theory, 2010; 56(7):3139-3148
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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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