Tight Bounds on the Rényi Entropy via Majorization with Applications to Guessing and Compression

Entropy

Igal Sason¹ 

[1] Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel;

关键词: Majorization;    Rényi entropy;    Rényi divergence;    cumulant generating functions;    guessing moments;    lossless source coding;    fixed-to-variable source codes;    Huffman algorithm;    Tunstall codes;   

DOI  :  10.3390/e20120896

来源: DOAJ

【 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.

【 授权许可】

Unknown