Optimal routing and scheduling for a simple network coding scheme

We consider jointly optimal routing, scheduling, and network coding strategies to maximize throughput in wireless networks. While routing and scheduling techniques for wireless networks have been studied for decades, network coding is a relatively new technique that allows for an increase in throughput under certain topological and routing conditions. In this work we introduce k-tuple coding, a generalization of pairwise coding with next-hop decodability, and fully characterize the region of arrival rates for which the network queues can be stabilized under this coding strategy. We propose a dynamic control policy for routing, scheduling, and k-tuple coding, and prove that our policy is throughput optimal subject to the k-tuple coding constraint. We provide analytical bounds on the coding gain of our policy, and present numerical results to support our analytical findings. We show that most of the gains are achieved with pairwise coding, and that the coding gain is greater under 2-hop than 1-hop interference. Simulations show that under 2-hop interference our policy yields median throughput gains of 31% beyond optimal scheduling and routing on random topologies with 16 nodes.National Science Foundation (U.S.) (grant CNS-0915988)United States. Office of Naval Research (grant N00014-12-1-0064)United States. Office of Naval Research. Multidisciplinary University Research Initiative (grant number W911NF-08-1-0238)United States. Air ForceUnited States. Dept. of Defense (Contract No. FA8721-05-C-0002

Distributed CSMA with pairwise coding

We consider distributed strategies for joint routing, scheduling, and network coding to maximize throughput in wireless networks. Network coding allows for an increase in network throughput under certain routing conditions. We previously developed a centralized control policy to jointly optimize for routing and scheduling combined with a simple network coding strategy using max-weight scheduling (MWS) [9]. In this work we focus on pairwise network coding and develop a distributed carrier sense multiple access (CSMA) policy that supports all arrival rates allowed by the network subject to the pairwise coding constraint. We extend our scheme to optimize for packet overhearing to increase the number of beneficial coding opportunities. Simulation results show that the CSMA strategy yields the same throughput as the optimal centralized policy of [9], but at the cost of increased delay. Moreover, overhearing provides up to an additional 25% increase in throughput on random topologies.United States. Dept. of Defense. Assistant Secretary of Defense for Research & EngineeringUnited States. Air Force (Air Force Contract FA8721-05-C-0002

Topics in Routing and Network Coding for Wireless Networks

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

Towards a Queueing-Based Framework for In-Network Function Computation

We seek to develop network algorithms for function computation in sensor networks. Specifically, we want dynamic joint aggregation, routing, and scheduling algorithms that have analytically provable performance benefits due to in-network computation as compared to simple data forwarding. To this end, we define a class of functions, the Fully-Multiplexible functions, which includes several functions such as parity, MAX, and k th -order statistics. For such functions we exactly characterize the maximum achievable refresh rate of the network in terms of an underlying graph primitive, the min-mincut. In acyclic wireline networks, we show that the maximum refresh rate is achievable by a simple algorithm that is dynamic, distributed, and only dependent on local information. In the case of wireless networks, we provide a MaxWeight-like algorithm with dynamic flow splitting, which is shown to be throughput-optimal

Robust And Optimal Opportunistic Scheduling For Downlink 2-Flow Network Coding With Varying Channel Quality and Rate Adaptation

This paper considers the downlink traffic from a base station to two different clients. When assuming infinite backlog, it is known that inter-session network coding (INC) can significantly increase the throughput of each flow. However, the corresponding scheduling solution (when assuming dynamic arrivals instead and requiring bounded delay) is still nascent. For the 2-flow downlink scenario, we propose the first opportunistic INC + scheduling solution that is provably optimal for time-varying channels, i.e., the corresponding stability region matches the optimal Shannon capacity. Specifically, we first introduce a new binary INC operation, which is distinctly different from the traditional wisdom of XORing two overheard packets. We then develop a queue-length-based scheduling scheme, which, with the help of the new INC operation, can robustly and optimally adapt to time-varying channel quality. We then show that the proposed algorithm can be easily extended for rate adaptation and it again robustly achieves the optimal throughput. A byproduct of our results is a scheduling scheme for stochastic processing networks (SPNs) with random departure, which relaxes the assumption of deterministic departure in the existing results. The new SPN scheduler could thus further broaden the applications of SPN scheduling to other real-world scenarios