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Rate 1/2 systematic recursive convolutional codes over integer rings modulo-q are investigated for their performance. The investigation examines the performance in severe fading and additive white Gaussian noise for codes with various constraint lengths. The arithmetic for the codes is modulo-q. where the value of q is within the range of 2 to 16. An exhaustive search is carried out for codes with short constraint lengths. A reduced search is developed for larger constraint lengths which restricts the tap polynomials to irreducible polynomials over Zq. The irreducible polynomials are generated and the ones not found in the literature are presented in tables. The search algorithms are outlined and the results for the codes are tabulated. The performance of selected codes are verified by Monte-Carlo simulation techniques. Several codes have better performance than comparable codes presented in the literature for the Rayleigh fading channel. In sme of cases, the codes found have better performance on the AWGN channel than the best known ring codes. The characteristics of rotationally invariant (RI) ring codes presented in the literature are used in an exhaustive search for codes over Zq which are invariant to phase shifts of 2[pi]/q. Tables of RI codes optimized for the Rayleigh fading channel are presented along with codes which are optimized for the AWGN channel. / Graduate

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by Chunxuan Ye. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 74-[78]). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Information Theory --- p.1 / Chapter 1.2 --- Source Coding --- p.2 / Chapter 1.3 --- Fixed Length Codes and Variable Length Codes --- p.4 / Chapter 1.4 --- Prefix Codes --- p.5 / Chapter 1.4.1 --- Kraft Inequality --- p.7 / Chapter 1.4.2 --- Huffman Coding --- p.9 / Chapter 2 --- Existence of Fix-Free Codes --- p.13 / Chapter 2.1 --- Introduction --- p.13 / Chapter 2.2 --- Previous Results --- p.14 / Chapter 2.2.1 --- Complete Fix-Free Codes --- p.14 / Chapter 2.2.2 --- Ahlswede's Results --- p.16 / Chapter 2.3 --- Two Properties of Fix-Free Codes --- p.17 / Chapter 2.4 --- A Sufficient Condition --- p.20 / Chapter 2.5 --- Other Sufficient Conditions --- p.33 / Chapter 2.6 --- A Necessary Condition --- p.37 / Chapter 2.7 --- A Necessary and Sufficient Condition --- p.42 / Chapter 3 --- Redundancy of Optimal Fix-Free Codes --- p.44 / Chapter 3.1 --- Introduction --- p.44 / Chapter 3.2 --- An Upper Bound in Terms of q --- p.46 / Chapter 3.3 --- An Upper Bound in Terms of p1 --- p.48 / Chapter 3.4 --- An Upper Bound in Terms of pn --- p.51 / Chapter 4 --- Two Applications of the Probabilistic Method --- p.54 / Chapter 4.1 --- An Alternative Proof for the Kraft Inequality --- p.54 / Chapter 4.2 --- A Characteristic Inequality for ´ب1´ة-ended Codes --- p.59 / Chapter 5 --- Summary and Future Work --- p.69 / Appendix --- p.71 / A Length Assignment for Upper Bounding the Redundancy of Fix-Free Codes --- p.71 / Bibliography --- p.74

by Chan Ho Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 128-[131]). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Information Theory --- p.1 / Chapter 1.2 --- Approaches for characterizing Γ*n --- p.4 / Chapter 1.3 --- Outline of the thesis --- p.7 / Chapter 2 --- Quasi-Uniformity --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- Box Assignment --- p.9 / Chapter 2.2.1 --- Box Assignment --- p.9 / Chapter 2.2.2 --- Conditional Box Assignment --- p.17 / Chapter 2.3 --- Quasi-Uniform Random Variables --- p.18 / Chapter 2.4 --- Main Theorems --- p.20 / Chapter 2.4.1 --- Preliminaries --- p.20 / Chapter 2.4.2 --- Main Theorems --- p.25 / Chapter 2.5 --- Quasi-Uniformity and Inequality --- p.32 / Chapter 2.5.1 --- Quasi-Uniformity and Inequality --- p.32 / Chapter 2.6 --- A New Perspective of Information Inequality --- p.34 / Chapter 2.6.1 --- Combinatorial Inequality --- p.34 / Chapter 2.6.2 --- Relations between combinatorial inequalities and informa- tion inequalities --- p.36 / Chapter 2.7 --- Summary --- p.40 / Chapter 3 --- Groups and Quasi Uniformity --- p.41 / Chapter 3.1 --- Introduction --- p.41 / Chapter 3.2 --- Group --- p.42 / Chapter 3.3 --- Group Represent ability --- p.47 / Chapter 3.4 --- Tightness of Group Represent ability --- p.54 / Chapter 3.4.1 --- Tightness of γn --- p.54 / Chapter 3.5 --- Abelian group represent able --- p.58 / Chapter 3.5.1 --- Δ operator and sub cone con(γαb) --- p.63 / Chapter 3.5.2 --- Decomposition of con(γαb) --- p.67 / Chapter 3.6 --- Summary --- p.73 / Chapter 4 --- Linear Representability --- p.74 / Chapter 4.1 --- Introduction --- p.74 / Chapter 4.2 --- Preliminaries of Vector Space --- p.75 / Chapter 4.3 --- Linear Representability --- p.80 / Chapter 4.3.1 --- Orthogonal Space --- p.80 / Chapter 4.3.2 --- Linear Representability --- p.81 / Chapter 4.3.3 --- Direct Sum --- p.90 / Chapter 4.3.4 --- Conditional Entropy --- p.93 / Chapter 4.4 --- Tightness of γαb --- p.95 / Chapter 4.5 --- Reverse Representation --- p.98 / Chapter 4.6 --- Summary --- p.106 / Chapter A --- AEP and BOX ASSIGNMENT --- p.107 / Chapter B --- Proof of Chapter 4's lemma --- p.110 / Chapter C --- Tightness of and Ψαb --- p.118

Lo Ying Hang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 80-81). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Background --- p.4 / Chapter Chapter 3 --- Commutative Partition Pair Analysis --- p.9 / Chapter Chapter 4 --- Entropy Inequalities for Partition Pair --- p.19 / Chapter Chapter 5 --- Entropy Characterization of Commutative Partition Pair --- p.32 / Chapter Chapter 6 --- Ordered Commutative Partitions --- p.43 / Chapter Chapter 7 --- Running Intersection Property for Partitions --- p.45 / Chapter Chapter 8 --- Entropy Characterization of Ordered Commutative Partitions --- p.53 / Chapter Chapter 9 --- Significance and Application --- p.72 / Chapter Chapter 10 --- Future Plan --- p.78 / Chapter Chapter 11 --- Conclusion --- p.79 / Bibliography --- p.80

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.

This dissertation presents a novel problem inspired by the characteristics of sensor networks. The basic setup through-out the dissertation is that a set of sensor nodes encipher their data without collaboration and without any prior shared secret materials. The challenge is dealt by an eavesdropper who intercepts a subset of the enciphered data and wishes to gain knowledge of the uncoded data. This problem is challenging and novel given that the eavesdropper is assumed to know everything, including secret cryptographic keys used by both the encoders and decoders. We study the above problem using information theoretic models as a necessary first step towards an understanding of the characteristics of this system problem. This dissertation contains four parts. The first part deals with noiseless channels, and the goal is for sensor nodes to both source code and encipher their data. We derive inner and outer regions of the capacity region (i.e the set of all source coding and equivocation rates) for this problem under general distortion constraints. The main conclusion in this part is that unconditional secrecy is unachievable unless the distortion is maximal, rendering the data useless. In the second part we thus provide a practical coding scheme based on distributed source coding using syndromes (DISCUS) that provides secrecy beyond the equivocation measure, i.e. secrecy on each symbol in the message. The third part deals with discrete memoryless channels, and the goal is for sensor nodes to both channel code and encipher their data. We derive inner and outer regions to the secrecy capacity region, i.e. the set of all channel coding rates that achieve (weak) unconditional secrecy. The main conclusion in this part is that interference allows (weak) unconditional secrecy to be achieved in contrast with the first part of this dissertation. The fourth part deals with wireless channels with fading and additive Gaussian noise. We derive a general outer region and an inner region based on an equal SNR assumption, and show that the two are partially tight when the maximum available user powers are admissible.

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Thesis (Ph. D.)--University of Sydney, 2009. / Title from title screen (viewed November 13, 2009). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the Faculty of Architecture, Design and Planning in the Faculty of Science. Includes graphs and tables. Includes bibliographical references. Also available in print form.