On a relation between information inequalities and group theory

被引：77

作者：

Chan, TH ^{[1
]}

Yeung, RW ^{[1
]}

机构：

[1] Chinese Univ Hong Kong, Dept Informat Engn, Shatin, Hong Kong, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2002年 / 48卷 / 07期

关键词：

entropy; groups; group-theoretic inequalities; information inequalities;

D O I：

10.1109/TIT.2002.1013138

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we establish a one-to-one correspondence between information inequalities and group inequalities. The major implication of our result is that we can prove information inequalities by proving the corresponding group inequalities, and vice versa. By giving a group-theoretic proof for all Shannon-type inequalities, we suggest that new inequalities could be discovered by making use of the rich set of tools in group theory. On the other hand, via a non-Shannon-type information inequality recently discovered by Zhang and Yeung, we obtain a new inequality in group theory whose meaning is yet to be understood.

引用

页码：1992 / 1995

页数：4

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