本論文考慮對於二值輸入廣播信道在沒有公共信息要求的情況下，如何評估Marton 內界。對於雙用戶廣播信道而言，該內界是最好的，而最好的外界是UV 外界。最近我們證明了UV 外界不是容量區域，但是Marton 內界是否是容量區域尚未可知。 / 在論文的第一部份，我們介紹了一個由Jog 和Nair 獲得的基於二值輸入斜對稱廣播信道的不等式，該不等式被用於首次證明Marton 內界嚴格包含在UV 外界里。我們將該不等式推廣到任意二值輸入廣播信道。在證明中，我們採用擾動分析的方法，幫助刻劃了不等式在非平凡情況下的性質。 / 在第二部份，我們專注于研究輸出對稱的二值輸入廣播信道。我們證明了Marton 內界是否嚴格包含于UV 外界里是與特定偏序密切相關的，同時找到了另一個嚴格包含的例子。 / 對於評估內界而不僅僅是其中的總傳輸率，我們考慮邊界的支撐超平面，然後提出一個猜想，利用凸包的概念推廣了之前提及的不等式。對於大部份情況，我們證明了該猜想。 / 本論文的主要貢獻在於，我們拓展了評估特定可達傳輸率的新工具和方法，同時證明了某些非基於凸性質的不等式。 / This thesis concerns the evaluation of Marton's inner bound for binary input broadcast channel without common message.This inner bound is the best one for two-receiver broadcast channel, while the best outer bound is UV outer bound. Recently we have shown that UV outer bound is not optimal, however the optimality of Marton's inner bound is still unknown. / In the first part, we introduce a binary inequality obtained by Jog and Nair for binary-skew symmetric broadcast channel, which helps to show for the first time that Marton's inner bound is strictly included in UV outer bound. We generalize this inequality to be true for arbitrary binary input broadcast channel. The method applied here is perturbation analysis, which helps to characterize the properties of non-trivial cases in the proof. / In the second part, we study a class of broadcast channel consisting of binary input symmetric-output channels. We show that whether Marton's inner bound is strictly included in UV outer bound is closely related to the more capable partial order, and we find a second example that demonstrates the strict inclusion. / To evaluate the inner bound beyond the sum-rate, we consider the supporting hyperplanes of the boundary points and conjecture the binary inequality to a stronger one, where we utilize the notion of concave envelope. We prove the extended inequality for certain cases. / The main contribution of the thesis is in the development of new tools and techniques for evaluating certain achievable regions as well as for proving certain information inequalities that are not based on convexity. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Geng, Yanlin. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 64-66). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Broadcast channel and capacity region --- p.2 / Chapter 1.2 --- Inner bounds to capacity region --- p.3 / Chapter 1.3 --- Outer bounds to capacity region --- p.6 / Chapter 1.4 --- Partial orders --- p.7 / Chapter 1.5 --- Examples where inner and outer bounds differ --- p.11 / Chapter 2 --- A binary inequality --- p.14 / Chapter 2.1 --- Proof of special settings --- p.20 / Chapter 2.2 --- Two nontrivial cases --- p.20 / Chapter 2.3 --- Proof of XOR case --- p.22 / Chapter 2.4 --- Proof of AND case --- p.26 / Chapter 3 --- BISO broadcast channel --- p.30 / Chapter 3.1 --- BISO channel --- p.32 / Chapter 3.2 --- Partial orders on BISO broadcast channel --- p.34 / Chapter 3.2.1 --- More capable comparability --- p.34 / Chapter 3.2.2 --- More capable and essentially less noisy --- p.39 / Chapter 3.3 --- Comparison of bounds for BISO broadcast channel --- p.42 / Chapter 3.4 --- A new partial order --- p.46 / Chapter 4 --- Extended binary inequality --- p.56 / Chapter 4.1 --- Proof of XOR case --- p.57 / Chapter 4.2 --- A conjecture on extending the inequality --- p.61 / Chapter 5 --- Conclusion --- p.62 / Bibliography --- p.64
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328402 |
| Date | January 2012 |
| Contributors | Geng, Yanlin., Chinese University of Hong Kong Graduate School. Division of Information Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (x, 66 leaves) : ill. (some col.) |
| 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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