Coding for Wireless Broadcast and Network Secrecy

TL;DR: A cross-layer framework with wireless broadcast is developed, which integrates rate control, network coding and scheduling in transport, network and link layers, and it is shown that the link scheduling problem is the maximum weighted hypergraph matching problem, which is NP-complete.

Abstract: In the first part of this thesis, we exploit wireless broadcast across different layers in wireless networks. The wireless channel is distinguished by its broadcast nature. Wireless broadcast provides a fertile ground to improve the efficiency of existing wireless networks and design new ones. Specifically, we first consider relaying strategies for memoryless two-way relay channels at the physical layer. We generalize networking layer network coding operating on a finite field to physical layer network coding, which is a mapping from the relay's received signal to its transmitted signal. We analyze the symbol-error performance of several relay strategies, and optimize the relay function via functional analysis. Our results indicate that the interference caused by wireless broadcast can be exploited to improve the spectrum efficiency. We then develop a cross-layer framework with wireless broadcast, which integrates rate control, network coding and scheduling in transport, network and link layers. Under the primary interference model, we show that the link scheduling problem is the maximum weighted hypergraph matching problem, which is NP-complete. We propose several distributed approximation algorithms and bound their worst case performance. Next, we describe a new class of medium access control (MAC) protocol, which uses successive interference cancelation to resolve packet collision due to wireless broadcast. Each user is allowed to transmit at different data rates chosen randomly from an appropriately determined set of rates. We characterize the throughput of the proposed protocol compared to that with a centralized controller. A game-theoretic framework along with the dynamic algorithms is proposed to achieve the desired throughput optimal equilibrium, which provides a valuable perspective to understand existing MAC protocols and a general framework to design new ones to improve the system performance. In the second part of this thesis, we consider the problem of secure transmission in the presence of a wiretapper. Due to wireless broadcast, wireless signals are particularly easy to jam and intercept. We derive the secrecy capacity region for the case when the location of the wiretapped links is known and propose several achievable strategies for the case when such information is unknown. We give an example to show that the secrecy capacities of the two cases are generally unequal and show that in both cases computing the secrecy capacity is NP-complete.