Diversity and Reliability in Erasure Networks: Rate Allocation, Coding, and Routing

Recently, erasure networks have received significant attention in the literature [1–7] as they are used to model both wireless and wireline packet-switched networks. Many packetswitched data networks like wireless mesh networks [8–10], the Internet [11–13], and Peerto-peer networks [14] can be modeled as erasure networks. The reason is that each packet contains an internal error detection code, like the Cyclic Redundancy Check (CRC), which allows the receiver to detect and discard erroneous packets [12,15–17]. In any erasure network (wireless mesh network, the Internet, or Peer-to-peer network), path diversity works by setting up multiple parallel connections between the end points using the topological path redundancy of the network. Our analysis of diversity over erasure networks studies the problem of rate allocation (RA) across multiple independent paths, coding over erasure channels, and the trade-off between rate and diversity gain in three consecutive chapters. In chapter 2, Forward Error Correction (FEC) is applied across multiple independent paths to enhance the end-to-end reliability. We prove that the probability of irrecoverable loss (PE) decays exponentially with the number of paths. Furthermore, the RA problem across independent paths is studied. Our objective is to find the optimal RA, i.e. the allocation which minimizes PE. The RA problem is solved for a large number of paths. Moreover, it is shown that in such asymptotically optimal RA, each path is assigned a positive rate iff its quality is above a certain threshold. Finally, using memoization technique, a heuristic suboptimal algorithm with polynomial runtime is proposed for RA over a finite number of paths. This algorithm converges to the asymptotically optimal RA when the number of paths is large. For practical number of paths, the simulation results demonstrate the close-to-optimal performance of the proposed algorithm. Chapter 3 addresses the problem of lower-bounding the probability of error (PE) for any block code over an input-independent channel. First, we define an input-independent chan-