词值信源：遍历定理、AEP和熵守恒
Word-Valued Sources: an Ergodic Theorem, an AEP and the Conservation of Entropy
摘要：
字值源$\mathbf{Y} = Y_1,Y_2,...$是通过用来自码本$\mathscr{C}$的码字顺序地编码随机过程$\mathbf{X} = X_1,X_2,...$的符号而形成的离散随机过程。这些过程经常出现在信息论中（特别是在信源编码算法的分析中），因此给出关于$\mathbf{X}$和$\mathscr{C}$的条件，使$\mathbf{Y}$满足遍历定理并具有渐近均分性质（AEP）是很有意义的。证明了：（1）若$\mathbf{X}$是渐近平均平稳的，则$\mathbf{Y}$满足逐点遍历定理并具有AEP;（2）若码本$\mathscr{C}$是无前缀的，则$\mathbf{Y}$的熵率等于$\mathbf{X}$的平均码字长度归一化的熵率.
英文摘要：
A word-valued source $\mathbf{Y} = Y_1,Y_2,...$ is discrete random process that is formed by sequentially encoding the symbols of a random process $\mathbf{X} = X_1,X_2,...$ with codewords from a codebook $\mathscr{C}$. 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 $\mathbf{X}$ and $\mathscr{C}$ for which $\mathbf{Y}$ will satisfy an ergodic theorem and possess an Asymptotic Equipartition Property (AEP). In this correspondence, we prove the following: (1) if $\mathbf{X}$ is asymptotically mean stationary, then $\mathbf{Y}$ will satisfy a pointwise ergodic theorem and possess an AEP; and, (2) if the codebook $\mathscr{C}$ is prefix-free, then the entropy rate of $\mathbf{Y}$ is equal to the entropy rate of $\mathbf{X}$ normalized by the average codeword length.
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