In wireless networks, communication links may be subject to random fatal impacts: for example, sensor networks under sudden power losses or cognitive radio networks with unpredictable primary user spectrum occupancy. Under such circumstances, it is critical to quantify how fast and reliably the information can be collected over attacked links. For a single point-to-point channel subject to a random attack, named as a dying channel, we model it as a block-fading (BF) channel with a finite and random channel length. First, we study the outage probability when the coding length K is fixed and uniform power allocation is assumed. Furthermore, we discuss the optimization over K and the power allocation vector PK to minimize the outage probability. In addition, we extend the single point to-point dying channel case to the parallel multi-channel case where each sub-channel is a dying channel, and investigate the corresponding asymptotic behavior of the overall outage probability with two different attack models: the independent-attack case and the m-dependent-attack case. It can be shown that the overall outage probability diminishes to zero for both cases as the number of sub-channels increases if the rate per unit cost is less than a certain threshold. The outage exponents are also studied to reveal how fast the outage probability improves over the number of sub-channels. Besides the information-theoretical results, we also study a practical coding scheme for the dying binary erasure channel (DBEC), which is a binary erasure channel (BEC) subject to a random fatal failure. We consider the rateless codes and optimize the degree distribution to maximize the average recovery probability. In particular, we first study the upper bound of the average recovery probability, based on which we define the objective function as the gap between the upper bound and the average recovery probability achieved by a particular degree distribution. We then seek the optimal degree distribution by minimizing the objective function. A simple and heuristic approach is also proposed to provide a suboptimal but good degree distribution.

<p>The advent of advanced communication technologies has given rise to large-scale networks comprised of numerous interconnected agents, which need to cooperate to accomplish various tasks, such as distributed message routing, formation control, robust statistical inference, and spectrum access coordination. These tasks can be formulated as distributed optimization problems, which require agents to agree on a parameter minimizing the average of their local cost functions by communicating only with their neighbors. However, distributed optimization algorithms are typically susceptible to malicious (or "Byzantine") agents that do not follow the algorithm. This thesis offers analysis and algorithms for such scenarios. As the malicious agent's function can be modeled as an unknown function with some fundamental properties, we begin in the first two parts by analyzing the region containing the potential minimizers of a sum of functions. Specifically, we explicitly characterize the boundary of this region for the sum of two unknown functions with certain properties. In the third part, we develop resilient algorithms that allow correctly functioning agents to converge to a region containing the true minimizer under the assumption of convex functions of each regular agent. Finally, we present a general algorithmic framework that includes most state-of-the-art resilient algorithms. Under the strongly convex assumption, we derive a geometric rate of convergence of all regular agents to a ball around the optimal solution (whose size we characterize) for some algorithms within the framework.</p>