信息谱熵的链式关系  

Chain rule for the information-spectrum entropy

作　　者：王晨旸 席政军[1] WANG Chenyang;XI Zhengjun(School of Computer Science,Shaanxi Normal University,Xi'an 710119,Shaanxi,China)

机构地区：[1]陕西师范大学计算机科学学院,陕西西安710119

出　　处：《陕西师范大学学报（自然科学版）》2023年第5期35-42,共8页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金(6167280)。

摘　　要：信息谱针对非独立同分布多拷贝的情形,建立了信源编码和信道编码理论。在实际中,有限码长和有限步操作才是可实现的,从而有必要对非渐近情形甚至是one-shot情形下的信息谱进行研究。该文给出信息谱相对熵及相关性质,特别给出了信息谱相对熵与假设检验相对熵的关系。依赖信息谱相对熵,考虑相关的熵、条件熵和互信息,重点讨论信息谱互信息之间的等价关系,进而讨论其链式关系。Information-spectrum methods focus on the non-independently and identically distributed setting,which have established source coding theory and channel coding theory.Typically finite and operations can be achieved only approximately,so this makes it necessary to consider the nonasymptotic scenario and even one-shot scenario.The information-spectrum relative entropy in one-shot scenario and related properties are studied.In particular,the relationship between the information-spectrum relative entropy and hypothesis testing relative entropy is given.The entropy rate,the conditional entropy and the mutual information with respect to the information-spectrum relative entropy are considered,and the equivalence relations of information-spectrum mutual information are discussed.Finally,the chain rules for them are given.

关 键 词：信息谱 相对熵 条件熵 互信息 链式关系 

分 类 号：TB565.1[交通运输工程—水声工程]