Network Coding for Error Correction

In this thesis, network error correction is considered from both theoretical and practical viewpoints. Theoretical parameters such as network structure and type of connection (multicast vs. nonmulticast) have a profound effect on network error correction capability. This work is also dictated by the practical network issues that arise in wireless ad-hoc networks, networks with limited computational power (e.g., sensor networks) and real-time data streaming systems (e.g., video/audio conferencing or media streaming). Firstly, multicast network scenarios with probabilistic error and erasure occurrence are considered. In particular, it is shown that in networks with both random packet erasures and errors, increasing the relative occurrence of erasures compared to errors favors network coding over forwarding at network nodes, and vice versa. Also, fountain-like error-correcting codes, for which redundancy is incrementally added until decoding succeeds, are constructed. These codes are appropriate for use in scenarios where the upper bound on the number of errors is unknown a priori. Secondly, network error correction in multisource multicast and nonmulticast network scenarios is discussed. Capacity regions for multisource multicast network error correction with both known and unknown topologies (coherent and noncoherent network coding) are derived. Several approaches to lower- and upper-bounding error-correction capacity regions of general nonmulticast networks are given. For 3-layer two-sink and nested-demand nonmulticast network topologies some of the given lower and upper bounds match. For these network topologies, code constructions that employ only intrasession coding are designed. These designs can be applied to streaming erasure correction code constructions.</p

Equitable Marketplace Mechanism Design

We consider a trading marketplace that is populated by traders with diverse trading strategies and objectives. The marketplace allows the suppliers to list their goods and facilitates matching between buyers and sellers. In return, such a marketplace typically charges fees for facilitating trade. The goal of this work is to design a dynamic fee schedule for the marketplace that is equitable and profitable to all traders while being profitable to the marketplace at the same time (from charging fees). Since the traders adapt their strategies to the fee schedule, we present a reinforcement learning framework for simultaneously learning a marketplace fee schedule and trading strategies that adapt to this fee schedule using a weighted optimization objective of profits and equitability. We illustrate the use of the proposed approach in detail on a simulated stock exchange with different types of investors, specifically market makers and consumer investors. As we vary the equitability weights across different investor classes, we see that the learnt exchange fee schedule starts favoring the class of investors with the highest weight. We further discuss the observed insights from the simulated stock exchange in light of the general framework of equitable marketplace mechanism design

Optimal Stopping with Gaussian Processes

We propose a novel group of Gaussian Process based algorithms for fast approximate optimal stopping of time series with specific applications to financial markets. We show that structural properties commonly exhibited by financial time series (e.g., the tendency to mean-revert) allow the use of Gaussian and Deep Gaussian Process models that further enable us to analytically evaluate optimal stopping value functions and policies. We additionally quantify uncertainty in the value function by propagating the price model through the optimal stopping analysis. We compare and contrast our proposed methods against a sampling-based method, as well as a deep learning based benchmark that is currently considered the state-of-the-art in the literature. We show that our family of algorithms outperforms benchmarks on three historical time series datasets that include intra-day and end-of-day equity stock prices as well as the daily US treasury yield curve rates

Acknowledgements

To my parents