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

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Thesis (Ph. D. business administration)--Washington State University, May 2008. / Includes bibliographical references (p. 113-121).

Thesis (doctoral)--Freie Universität, Berlin. / Includes bibliographical references (p. 491-504).

This investigation is concerned with improvements that can be made in communication systems to enable them to transmit efficiently signals containing occasional transient. A method of improving delta modulation by the use of variable step size is discussed in detail and the design and construction of a suitable coder and step size control unit are described. The results of tests made on the equipment constructed are given. From these results it is concluded that considerably better response to sudden large changes in input signal can be obtained with only slight deterioration in the performance under normal conditions of input signal. The method used to effect this improvement is applicable to more complex modulation schemes. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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The application of information theory to music may provide both a means for measuring the information content of the messages .of the system and for studying the effects of such messages in the field of psychology of music (e.g., the group at Iowa University which is carrying on work commenced by Carl Seashore 3 ). Before the techniques of information theory may be applied to a study of music much statistical data about the music system must be compiled. Masking data must be compiled dealing with many simultaneous tones as are encountered in music; the effects of timbre in overcoming or adding to masking effects must be investigated; the effects of masking on and by the singing voice must be tabulated; and similar data must be compiled dealing with the effects of other types of tonal interactions. This data of the effects of tonal interactions may be used both to reduce the effects of such auditory phenomena and to determine which components of a message pass through the communication channel (i.e., the ear). The masking problem, as illustrated in Figures 19 and 20, may be so acute in some compositions that the part of the signal carrying the information content may be obliterated. These illustrations indicate, however, that effects of masking and other forms of tonal interactions may be reduced This study has indicated, further, that elimination of the effects of tonal interactions is impossible if a wide range of dynamic intensities is used, but that these effects are limitations of the transmission channel and thus restrict the choice of tones of the musical system which may be used at one time.

In network information theory, the relay channel models a communication scenario where there is one or more relay nodes that can help the information transmission between the source and the destination. Although the capacity of the relay channel is still unknown even in the single-relay case, two fundamentally different relay schemes have been developed by (Cover and El Gamal, 1979) for such channels, which, depending on whether the relay decodes the information or not, are generally known as Decode-and-Forward (D-F) and Compress-and-Forward (C-F). In the D-F relay scheme, the relay first decodes the message sent by the source and then forwards it to the destination, and the destination decodes the message taking into account the inputs of both the source and the relay. In contrast, the C-F relay scheme is used when the relay cannot decode the message sent by the source, but still can help by compressing its observation into some compressed version, and forwarding this compression into the destination; the destination then either successively or jointly decodes the compression of the relay's observation and the original message of the source. For the single-relay case, it is known that joint compression-message decoding, although providing more freedom in choosing the compression at the relay, cannot achieve higher rates for the original message than successive decoding. This thesis addresses some fundamental issues in generalizing and unifying the above D-F and C-F relay schemes to the multiple-relay case. We first generalize the C-F scheme to multiple-relay channels, and investigate the question of whether compression-message joint decoding can improve the achievable rate compared to successive decoding in the multiple-relay case. It is demonstrated that in the case of multiple relays, there is no improvement on the achievable rate by joint decoding either. More interestingly, it is discovered that any compressions not supporting successive decoding will actually lead to strictly lower achievable rates for the original message. Therefore, to maximize the achievable rate for the original message, the compressions should always be chosen to support successive decoding. Furthermore, it is shown that any compressions not completely decodable even with joint decoding will not provide any contribution to the decoding of the original message. We also develop a new C-F relay scheme with block-by-block backward decoding. This new scheme improves the original C-F relay scheme to achieve higher rates in the multiple-relay case as the recently proposed noisy network coding scheme. However, compared to noisy network coding which uses repetitive encoding/all blocks united decoding, our new coding scheme is not only simpler, but also reveals the essential reason for the improvement of the achievable rate, that is, delayed decoding until all the blocks have been finished. Finally, to allow each relay node the freedom of choosing either the D-F or C-F relay strategy, we propose a unified relay framework, where both the D-F and C-F strategies can be employed simultaneously in the network. This framework employs nested blocks combined with backward decoding to allow for the full incorporation of the best known D-F and C-F relay strategies. The achievable rates under our unified relay framework are found to combine both the best known D-F and C-F achievable rates and include them as special cases. It is also demonstrated through a Gaussian network example that our achievable rates are generally better than the rates obtained with existing unified schemes and with D-F or C-F alone.

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