Orbit-Entropy Cones And Extremal Pairwise Orbit-Entropy Inequalities
2016 IEEE International Symposium on Information Theory (ISIT)(2016)
摘要
The notion of orbit-entropy cone is introduced. Specifically, orbit-entropy cone P G Gamma*(n) is the projection of Gamma*(n) induced by G, where Gamma*(n) is the closure of entropy region for n random variables and G is a permutation group over f {0,1... , n-1 g. For symmetric group S-n (with arbitrary n) and cyclic group C-n (with n <= 5), the associated orbit-entropy cones are shown to be characterized by the Shannon type inequalities. Moreover, the extremal pairwise relationship between orbitentropies is determined completely for partitioned symmetric groups and partially for cyclic groups.
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关键词
extremal pairwise orbit-entropy inequalities,orbit-entropy cone,entropy region,random variables,permutation group,symmetric group,cyclic group,Shannon type inequalities,partitioned symmetric groups,partially symmetric groups,network coding capacity
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