This dissertation studies a family of the state-of-the-art PNC schemes called compute-and-forward (C&F). C&F was originally proposed and studied from an information-theoretic perspective. As such, it typically relies on several strong assumptions: very long block length, almost unbounded complexity, perfect channel state information, and no decoding errors at the relays; its benefit is often analyzed for simple network configurations. The aim of this dissertation is two-fold: first, to relax the above assumptions while preserving the performance of C&F, and second, to understand the benefit of C&F in more realistic network scenarios, such as random-access wireless networks.There are four main results in this dissertation. First, an algebraic framework is developed, which establishes a direct connection between C&F and module theory. This connection allows us to systematically design lattice codes for C&F with controlled block length and complexity. In particular, explicit design criteria are derived, concrete design examples are provided, and it is shown that nominal coding gains from 3 to 7.5 dB can be obtained with relatively short block length and reasonable decoding complexity. Second, a new C&F scheme is proposed, which, unlike conventional C&F schemes, does not require any channel state information (CSI). It is shown that this CSI-free scheme achieves, for a certain class of lattice codes, almost the same throughput as its CSI-enabled counterpart. Third, an end-to-end error control mechanism is designed, which effectively mitigates decoding errors introduced at wireless relays. In particular, the end-to-end error control problem is modeled as a finite-ring matrix channel problem, for which tight capacity bounds and capacity-approaching schemes are provided. The final part of this dissertation studies the benefit of C&F in random-access wireless networks. In particular, it is shown that C&F significantly improves the network throughput and delay performance of slotted-ALOHA-based random-access protocols.ii Acknowledgements This thesis is the result of the support, help, and advice that I have received from an amazing group of scholars and students at the University of Toronto. Without them this dissertation wouldn't have been possible. First, I feel very fortunate to have two great supervisors: Prof. Frank R. Kschischang and Prof.Baochun Li. As an advisor, Frank has consistently exceeded my expectation. He is not only a brilliant researcher and excellent teacher, but also truly a kind and caring person. He has given me a tremendous amount in the past six years, I can only thank him for a subset. In particular, I have benefited greatly from his focus on fundamental problems, his taste for beautiful mathematics, his emphasis on clarity and grace, and his dedication in developing his students to their full potential. I am very grateful to Frank for making my PhD journey so exciting and rewarding! Frank also has a great sense of humor.I will always remember how much fun we had together during our endless discus...

Blockchain technology has attracted tremendous attention in both academia and capital market. However, overwhelming speculations on thousands of available cryptocurrencies and numerous initial coin offering (ICO) scams have also brought notorious debates on this emerging technology. This paper traces the development of blockchain systems to reveal the importance of decentralized applications (dApps) and the future value of blockchain. We survey the state-of-the-art dApps and discuss the direction of blockchain development to fulfill the desirable characteristics of dApps. The readers will gain an overview of dApp research and get familiar with recent developments in the blockchain.

The problem of designing new physical-layer network coding (PNC) schemes via lattice partitions is considered. Building on a recent work by Nazer and Gastpar, who demonstrated its asymptotic gain using information-theoretic tools, we take an algebraic approach to show its potential in non-asymptotic settings. We first relate Nazer-Gastpar's approach to the fundamental theorem of finitely generated modules over a principle ideal domain. Based on this connection, we generalize their code construction and simplify their encoding and decoding methods. This not only provides a transparent understanding of their approach, but more importantly, it opens up the opportunity to design efficient and practical PNC schemes. Finally, we apply our framework for PNC to a Gaussian relay network and demonstrate its advantage over conventional PNC schemes.Comment: 5 pages, 3 figures, accepted to IEEE Int. Symp. Information Theory, 201

Quantum communication holds the promise of creating disruptive technologies that will play an essential role in future communication networks. For example, the study of quantum communication complexity has shown that quantum communication allows exponential reductions in the information that must be transmitted to solve distributed computational tasks. Recently, protocols that realize this advantage using optical implementations have been proposed. Here we report a proof-of-concept experimental demonstration of a quantum fingerprinting system that is capable of transmitting less information than the best-known classical protocol. Our implementation is based on a modified version of a commercial quantum key distribution system using off-the-shelf optical components over telecom wavelengths, and is practical for messages as large as 100 Mbits, even in the presence of experimental imperfections. Our results provide a first step in the development of experimental quantum communication complexity.