Design and Analysis of Low Complexity Network Coding Schemes

In classical network information theory, information packets are treated as commodities, and the nodes of the network are only allowed to duplicate and forward the packets. The new paradigm of network coding, which was introduced by Ahlswede et al., states that if the nodes are permitted to combine the information packets and forward a function of them, the throughput of the network can dramatically increase. In this dissertation we focused on the design and analysis of low complexity network coding schemes for different topologies of wired and wireless networks. In the first part we studied the routing capacity of wired networks. We provided a description of the routing capacity region in terms of a finite set of linear inequalities. We next used this result to study the routing capacity region of undirected ring networks for two multimessage scenarios. Finally, we used new network coding bounds to prove the optimality of routing schemes in these two scenarios. In the second part, we studied node-constrained line and star networks. We derived the multiple multicast capacity region of node-constrained line networks based on a low complexity binary linear coding scheme. For star networks, we examined the multiple unicast problem and offered a linear coding scheme. Then we made a connection between the network coding in a node-constrained star network and the problem of index coding with side information. In the third part, we studied the linear deterministic model of relay networks (LDRN). We focused on a unicast session and derived a simple capacity-achieving transmission scheme. We obtained our scheme by a connection to the submodular flow problem through the application of tools from matroid theory and submodular optimization theory. We also offered polynomial-time algorithms for calculating the capacity of the network and the optimal coding scheme. In the final part, we considered the multicasting problem in an LDRN and proposed a new way to construct a coding scheme. Our construction is based on the notion of flow for a unicast session in the third part of this dissertation. We presented randomized and deterministic polynomial-time versions of our algorithm

Communication Efficiency in Information Gathering through Dynamic Information Flow

This thesis addresses the problem of how to improve the performance of multi-robot information gathering tasks by actively controlling the rate of communication between robots. Examples of such tasks include cooperative tracking and cooperative environmental monitoring. Communication is essential in such systems for both decentralised data fusion and decision making, but wireless networks impose capacity constraints that are frequently overlooked. While existing research has focussed on improving available communication throughput, the aim in this thesis is to develop algorithms that make more efficient use of the available communication capacity. Since information may be shared at various levels of abstraction, another challenge is the decision of where information should be processed based on limits of the computational resources available. Therefore, the flow of information needs to be controlled based on the trade-off between communication limits, computation limits and information value. In this thesis, we approach the trade-off by introducing the dynamic information flow (DIF) problem. We suggest variants of DIF that either consider data fusion communication independently or both data fusion and decision making communication simultaneously. For the data fusion case, we propose efficient decentralised solutions that dynamically adjust the flow of information. For the decision making case, we present an algorithm for communication efficiency based on local LQ approximations of information gathering problems. The algorithm is then integrated with our solution for the data fusion case to produce a complete communication efficiency solution for information gathering. We analyse our suggested algorithms and present important performance guarantees. The algorithms are validated in a custom-designed decentralised simulation framework and through field-robotic experimental demonstrations