基于优化的Rényi熵的紧界及其在猜测和压缩中的应用
Tight Bounds on the Rényi Entropy via Majorization with Applications to Guessing and Compression
摘要：
本文给出了离散随机变量函数的Rényi熵的严格界，其中函数的值有限，且函数不是一一对应的。为此，一个严格的下界上的Rényi熵的离散随机变量与有限的支持是作为一个功能的支持的大小，最大和最小概率质量的比率。这项工作受到Cicalese等人最近发表的论文的启发，这是集中在香农熵，它加强和推广的结果，该文件的任意正阶的雷尼熵。基于这些广义界和Arikan和Campbell的工作，导出了离散无记忆信源的矩估计和无损数据压缩的非渐近界.
英文摘要：
This paper provides tight bounds on the Rényi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the Rényi entropy of a discrete random variable with a finite support is derived as a function of the size of the support, and the ratio of the maximal to minimal probability masses. This work was inspired by the recently published paper by Cicalese et al., which is focused on the Shannon entropy, and it strengthens and generalizes the results of that paper to Rényi entropies of arbitrary positive orders. In view of these generalized bounds and the works by Arikan and Campbell, non-asymptotic bounds are derived for guessing moments and lossless data compression of discrete memoryless sources.
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。
