Title: Topics in Routing and Network Coding for Wireless Networks
Description: This dissertation presents topics in routing and network coding for wireless networks. We present a multipurpose multipath routing mechanism. We propose an efficient packet encoding algorithm that can easily integrate a routing scheme with network coding. We also discuss max-min fair rate allocation and scheduling algorithms for the flows in a wireless network that utilizes coding. We propose Polar Coordinate Routing (PCR) to create multiple paths between a source and a destination in wireless networks. Our scheme creates paths that are circular segments of different radii connecting source-destination pairs. We propose a non-euclidean distance metric that allows messages to travel along these paths. Using PCR it is possible to maintain a known separation among the paths, which reduces the interference between the nodes belonging to two separate routes. Our extensive simulations show that while PCR achieves a known separation between the routes, it does so with a small increase in overall hop count.

Moreover, we demonstrate that the variances of average separation and hop count are lower for the paths created using PCR compared to the existing schemes, indicating a more reliable system. Existing multipath routing schemes in wireless networks do not perform well in the areas with obstacles or low node density. To overcome adverse areas in a network, we integrate PCR with simple robotic routing, which lets a message circumnavigate an obstacle and follow the multipath trajectory to the destination as soon as the obstacle is passed. Next we propose an efficient packet encoding algorithm to integrate a routing scheme with network coding. Note that this packet encoding algorithm is not dependent on PCR. In fact it can be coupled with any routing scheme in order to leverage the benefits offered by both an advanced routing scheme and an enhanced packet encoding algorithm. Our algorithm, based on bipartite graphs, lets a node exhaustively search its queue to identify the maximum set of packets that can be combined in a single transmission.

We extend this algorithm to consider multiple next hop neighbors for a packet while searching for an optimal packet combination, which improves the likelihood of combining more packets in a single transmission. Finally, we propose an algorithm to assign max-min fair rates to the flows in a wireless network that utilizes coding. We demonstrate that when a network uses coding, a direct application of conventional progressive filling algorithm to achieve max-min fairness may yield incorrect or suboptimal results. To emulate progressive filling correctly for a wireless networks with coding, we couple a conflict graph based framework with a linear program. Our model helps us directly select a bottleneck flow at each iteration of the algorithm, eliminating the need of gradually increasing the rates of the flows until a bottleneck is found. We demonstrate the caveats in selecting the bottleneck flows and setting up transmission scheduling constraints in order to avoid suboptimal results. We first propose a centralized fair rate allocation algorithm assuming the global knowledge of the network.

We also present a novel yet simple distributed algorithm that achieves the same results as the centralized algorithm. We also present centralized as well as distributed scheduling algorithms that help flows achieve their fair rates. We run our rate allocation algorithm on various topologies. We use various fairness metrics to show that our rate allocation algorithm outperforms existing algorithms (based on network utility maximization) in terms of fairness.