无记忆信源压缩的尾冗余及其特征
Tail redundancy and its characterization of compression of memoryless sources
摘要：
我们正式的尾部冗余的分布在一个可数无限字母的集合，并表明，这个基本的数量特征的渐近每符号冗余的普遍压缩序列产生的IID从一个集合$\mathcal P$的分布在一个可数无限字母。与通用压缩的最坏情况公式相反，$\mathcal P$的有限单个字母（平均情况）冗余并不自动暗示从$\mathcal P$采样的iid描述长度- $n$字符串的预期冗余随着$n$次线性地增长。相反，我们证明了通用的压缩长度$n$ \iid序列从$\mathcal P$的特点是如何以及分布在$\mathcal P$的尾部可以普遍描述，表明渐近每符号冗余的iid字符串是等于尾部冗余。
英文摘要：
We formalize the tail redundancy of a collection of distributions over a countably infinite alphabet, and show that this fundamental quantity characterizes the asymptotic per-symbol redundancy of universally compressing sequences generated iid from a collection $\mathcal P$ of distributions over a countably infinite alphabet. Contrary to the worst case formulations of universal compression, finite single letter (average case) redundancy of $\mathcal P$ does not automatically imply that the expected redundancy of describing length-$n$ strings sampled iid from $\mathcal P$ grows sublinearly with $n$. Instead, we prove that universal compression of length-$n$ \iid sequences from $\mathcal P$ is characterized by how well the tails of distributions in $\mathcal P$ can be universally described, showing that the asymptotic per-symbol redundancy of iid strings is equal to the tail redundancy.
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