令N = {1, ..., n}. 一組n個隨機變量{Xi : i ∈ N} 的熵函數h是一個2n維的向量，該向量的每個分量h(A) = H(XA);A ⊂ N, 即該組隨機變量的子集的(聯合)熵且空集的熵按傳統看做為0。所有n個隨機變量的熵函數組成的區 域稱為n階熵函數區域，記作Γ* n。熵函數區域Γ* n及其閉包Γ* n的表徵是信息論中著名的開放問題。 / 在本文中，我們研究劃分對稱熵函數。令p = {N₁... ,Nt}為N的 一個t-劃分 。一個熵函數h稱為p-對稱的，若h滿足:對於N的所有子集A，B，對於p的每一 個分塊，只要A和該分塊的交集的基數與B和該分塊交集的基數相等，那麼h(A) = h(B)。所有p-對稱熵函數的集合稱作p-對稱熵函數區域。我們證明p-對稱熵函數區域的 閉包可以由香農型信息不等式完全表徵當且僅當p為1-劃分或者有一個分塊為單元 素集合的2-劃分。 / 劃分對稱熵函數的表徵能應用於那些結構中含有對稱的信息論問題及其相關問題。 / Let N = {1, ..., n}. The entropy function h of a set of n discrete randomvariables {Xi : i ∈ N} is a 2n-dimensional vector whose entries are h(A)H(XA),ACN, the (joint) entropies of the subsets of the set of n randomvariables with H(X) = 0 by convention. The set of all entropy functions for n discrete random variables, denoted by Γ* n , is called the entropy function region for n. Characterization of Γ* n and its closure Γ* n are well-known open problems in information theory. They are important not only because they play key roles in information theory problems but also they are related to other subjects in mathematics and physics. / In this thesis, we consider partition-symmetrical entropy functions. Let p ={N₁... ,Nt} be a t-partition of N. An entropy function h is called p-symmetricalif for all A,B ⊂ N, h(A) = h(B) whenever / The characterization of the partition-symmetrical entropy functions can beuseful for solving some information theory and related problems where symmetryexists in the structure of the problems. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chen, Qi. / Thesis (Ph.D.) Chinese University of Hong Kong, 2014. / Includes bibliographical references (leaves 70-73). / Abstracts also in Chinese.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_1077699 |
| Date | January 2014 |
| Contributors | Chen, Qi (author.), Yeung, Raymond W. , 1962- (thesis advisor.), Chinese University of Hong Kong Graduate School. Division of Information Engineering, (degree granting institution.) |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography, text |
| Format | electronic resource, electronic resource, remote, 1 online resource (73 leaves), computer, online resource |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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