无限字母表上的通用编码：指数递减包络
Universal Coding on Infinite Alphabets: Exponentially Decreasing Envelopes
摘要：
本文研究可数无限字母表上的通用无损编码问题。它侧重于一些类的源定义的包络条件的边缘分布，即指数下降包络类的指数$α$。证明了指数递减包络类的极大极小冗余等价于$\frac{1}{4 α\log e} \log^2 n$.然后提出了一种编码策略，贝叶斯冗余等价于最大最小冗余。最后给出了一种自适应算法，其冗余度等价于极小极大冗余度
英文摘要：
This paper deals with the problem of universal lossless coding on a countable infinite alphabet. It focuses on some classes of sources defined by an envelope condition on the marginal distribution, namely exponentially decreasing envelope classes with exponent $α$. The minimax redundancy of exponentially decreasing envelope classes is proved to be equivalent to $\frac{1}{4 α\log e} \log^2 n$. Then a coding strategy is proposed, with a Bayes redundancy equivalent to the maximin redundancy. At last, an adaptive algorithm is provided, whose redundancy is equivalent to the minimax redundancy
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
