published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

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M.Ing. (Electrical and Electronic Engineering) / In this thesis, spectral shaping techniques are applied to the insertion/deletion error correcting codes. Spectral shaping techniques are introduced and applied to insertion/deletion error correcting codes. The attainable rates for subcodes with spectral properties are computed and presented. The theory of comma-free codes is briefly reviewed and a new construction method is given : for comma-free insertion/deletion correcting codes. This method serves as a lower bound on the cardinality of comma-free insertion/deletion codes. The idea of a marker is introduced as an alternative method of finding word boundaries. Rules are given for governing the construction of marker code books that can differentiate between additive and insertion/deletion errors. The marker code books are then used in such: a way as not to violate the spectral properties of the abovementioned insertion/deletion correcting codes. A new class of codes is presented that has higher order spectral zeros at both DC and the Nyquist frequency. It is shown that these codes are insertion/deletion and additive error correcting. Besides this, it is shown that the abovementioned class of codes can correct two adjacent additive errors.

This dissertation consists of four essays in economic theory. All of them fall under the umbrella of economics of information; we study various models of game-theoretic interaction between players who are communicating with others, and have (or are able to produce) information of some sort. There is a large emphasis on the interplay of information, incentives and beliefs. In the first chapter we study a model of communication and persuasion between a sender who is privately informed and has state independent preferences, and a receiver who has preferences that depend on the unknown state. In a model with two states of the world, over the interesting range of parameters, the equilibria can be pooling or separating, but a particular novel refinement forces the pooling to be on the most informative information structure in interesting cases. We also study two extensions - a model with more information structures as well as a model where the state of the world is non-dichotomous, and show that analogous results emerge. In the second chapter, which is coauthored with Joseph E. Stiglitz and Jungyoll Yun, we study the Rothschild-Stiglitz model of competitive insurance markets with endogenous information disclosure by both firms and consumers. We show that an equilibrium always exists, (even without the single crossing property), and characterize the unique equilibrium allocation. With two types of consumers the outcome is particularly simple, consisting of a pooling allocation which maximizes the well-being of the low risk individual (along the zero profit pooling line) plus a supplemental (undisclosed and nonexclusive) contract that brings the high risk individual to full insurance (at his own odds). We also show that this outcome is extremely robust and Pareto efficient. In the third chapter we study a game of strategic information design between a sender, who chooses state-dependent information structures, a mediator who can then garble the signals generated from these structures, and a receiver who takes an action after observing the signal generated by the first two players. Among the results is a novel (and complete, in a special case) characterization of the set of posterior beliefs that are achievable given a fixed garbling. We characterize a simple sufficient condition for the unique equilibrium to be uninformative, and provide comparative statics with regard to the mediator’s preferences, the number of mediators, and different informational arrangements. In the fourth chapter we study a novel equilibrium refinement - belief-payoff monotonicity. We introduce a definition, argue that it is reasonable since it captures an attractive intuition, relate the refinement to others in the literature and study some of the properties.

One of the most fundamental and least understood elements of evolution is the mapping between genotype and phenotype. Recent work on genotype-phenotype (GP) maps suggests that these maps show properties which may have important evolutionary implications. These properties include a skewed distribution of genotypes over phenotypes, linear scaling between phenotype robustness and the logarithm of phenotype frequency, and a positive correlation between phenotype robustness and evolvability. However, most of these properties have only been studied for self-assembling systems, such as protein complexes or RNA folding. In this thesis, we ask ourselves if these properties are more general. First, we apply tools from algorithmic information theory to a wide class of inputoutput maps, of which GP maps are a subset. We find that these maps show a strong bias towards simple phenotypes, a pattern known as simplicity bias. We also define a matrix map of tunable complexity, with which we can study the conditions under which simplicity bias is present. Next, we investigate multiple models of GP maps for gene regulatory networks (GRNs). These include Boolean threshold networks, where we fix the strength of gene interactions, while varying the network topology, as well as systems of differential equations, where we fix the network topology while varying interaction strengths. For both modelling frameworks, the GRN GP maps exhibit all the structural properties found in the literature, as well as simplicity bias. We also find that the number of genotypes mapping to the wild-type phenotypes for various GRNs is unusually large, and argue that this is evidence that the structure of the GP map plays an important role in determining evolutionary outcomes. Finally, we return to more general input-output maps, and show that in addition to simplicity bias these maps also present randomness deficiency, that is, their output spectrum is less complex than expected. We argue that this additional property combines with simplicity bias in GP maps, and more generally, in input-output maps, and suggest a general trend towards simplicity in nature.

Ho Siu-wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 103-104). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Classical Information Theory --- p.2 / Chapter 1.1.1 --- Shannon Entropy --- p.3 / Chapter 1.1.2 --- "Shannon Joint Entropy, Conditional Entropy, Mutual Information and Conditional Mutual Information" --- p.5 / Chapter 1.1.3 --- Applications of Shannon Entropy --- p.7 / Chapter 1.2 --- Mathematical background for Quantum Mechanics --- p.8 / Chapter 1.2.1 --- Dirac Notation --- p.8 / Chapter 1.2.2 --- Linear Operators and Matrices --- p.11 / Chapter 1.2.3 --- Spectral Decomposition and Diagonalization --- p.11 / Chapter 1.2.4 --- Functions of Normal Matrices --- p.12 / Chapter 1.2.5 --- Trace --- p.13 / Chapter 1.2.6 --- Kronecker Product --- p.13 / Chapter 1.3 --- Elementary Quantum Mechanics --- p.14 / Chapter 1.3.1 --- State Space --- p.15 / Chapter 1.3.2 --- Evolution --- p.16 / Chapter 1.3.3 --- Quantum Measurements --- p.17 / Chapter 1.3.4 --- Joint Systems --- p.20 / Chapter 1.3.5 --- Quantum Mixtures --- p.22 / Chapter 1.3.6 --- Subsystems --- p.28 / Chapter 1.4 --- von Neumann Entropy --- p.31 / Chapter 1.4.1 --- Definition --- p.32 / Chapter 1.4.2 --- Applications of the von Neumann Entropy --- p.34 / Chapter 1.4.3 --- Conditional Entropy --- p.34 / Chapter 1.5 --- Organization of The Thesis --- p.36 / Chapter Chapter 2 --- Problem Formulations --- p.38 / Chapter 2.1 --- Measurements that Produce Pure States --- p.39 / Chapter 2.2 --- The Shannon Entropy of a Quantum States --- p.41 / Chapter 2.3 --- An Equivalent Density Matrix Obtained by Mixing Orthogonal States --- p.44 / Chapter Chapter 3 --- Pure Post-Measurement States (PPMS) Measurements --- p.46 / Chapter 3.1 --- Introduction --- p.46 / Chapter 3.2 --- Definition of PPMS measurements --- p.46 / Chapter 3.3 --- Properties of PPMS Measurement --- p.52 / Chapter 3.4 --- An Alternative Definition of von Neumann entropy in terms of PPMS Measurements --- p.73 / Chapter Chapter 4 --- Mental Measurement of a Quantum State --- p.75 / Chapter 4.1 --- Introduction --- p.75 / Chapter 4.2 --- An Alternative Definition of a Projective Measurement --- p.76 / Chapter 4.3 --- Characteristics of a Projective PPMS Measurement --- p.81 / Chapter 4.4 --- The Choice of the Mental Measurement --- p.84 / Chapter 4.5 --- An Alternative Definition of von Neumann Entropy by Means of a Mental Measurement --- p.86 / Chapter 4.6 --- Construction of the Mental Measurement --- p.86 / Chapter Chapter 5 --- Completeness of Density Matrix Postulate --- p.92 / Chapter 5.1 --- Introduction --- p.92 / Chapter 5.2 --- Complete Specification of Quantum Ensemble by Density Matrix --- p.93 / Chapter 5.3 --- An Alternative Definition of von Neumann Entropy by Shannon Entropy --- p.98 / Chapter Chapter 6 --- Conclusion and Future Works --- p.99 / Chapter 6.1 --- Conclusion --- p.99 / Chapter 6.2 --- Future Work --- p.101 / Reference --- p.103

In some practical systems, most of the errors are of 1 → 0 type and 0 → 1 errors occur very rarely. In this thesis, first, the capacity of the asymmetric channel is derived. The capacity of the binary symmetric channel (BSC) and the Z-channel can be derived from this expression as special cases. Second, the error detecting capability of Bose-Lin codes beyond the maximum designed error detection capability are described. Third, a new class of a systematic t-unidirectional error detecting codes over Z [subscript m], m≥2 is designed. These codes can detect 2 errors using r=2 check bits and up to m[superscript (r-2)] + r-2 errors using r>2 check bits. Some upper bound on the maximum number of detectable errors when using r check bits are given. Finally, some analysis on the data throughput when using the following protocols over the m-ary Z-Channel, m≥2 are derived: (1) ARQ protocols using t-Asymmetric Error Detecting (t-AED) codes. (2) ARQ protocols using All Asymmetric Error Detecting (AAED) codes. (3) Type-I Hybrid ARQ protocols using t-Asymmetric Error Correcting and All Asymmetric Error Detecting (t-EC/AAED) codes. (4) ARQ Protocols with diversity combining using t-Asymmetric Error Correcting and All Asymmetric Error Detecting (t-EC/AAED) codes. Finally, some open research problems are described. / Graduation date: 2005

The rise in the popularity of smartphones such as Blackberry and iPhone creates a strain on the world's mobile networks. The extensive use of these mobile devices leads to increasing congestion and higher rate of node failures. This increasing demand of mobile wireless clients forces network providers to upgrade their wireless networks with more efficient and more reliable services to meet the demands of their customers. Therefore, there is a growing interest in strategies to resolve the problem and reduce the stress on the wireless networks. One strategy to reduce the strain on the wireless networks is to utilize cooperative communication. The purpose of this thesis is to provide more efficient and reliable solutions for direct information exchange problems. First, algorithms are presented to increase the efficiency of cooperative communication in a network where the clients can communicate with each other through a broadcast channel. These algorithms are designed to minimize the total transmission cost so that the communication will be less expensive and more efficient. Second, we consider a setting in which several clients exchange data through a relay. Our algorithms have provable performance guarantees. We also verify the performance of the algorithms in practical settings through extensive simulations.

Thesis (Ph. D.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 97-102). Also available in print.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 155-161).