| nterference alignment is a radical idea that has recently emerged out of the capacity and degrees of freedom (DoF) analysis of interference networks. In a relatively short time, this concept has challenged much of the conventional wisdom about the throughput limits of both wired and wireless networks. While the remarkable benefits of interference alignment have so far been shown mostly for wireless networks and under idealized assumptions such as global channel knowledge, we show its robustness and critical role in wired scenarios like index coding and distributed data storage networks and wireless scenarios like cellular networks with no channel state information at the transmitter (CSIT) and interference networks with delayed CSIT. In particular, we start from the index coding problem and study it from an interference alignment perspective and provide new results as well as new insights into, and generalizations of, previously known results. It has been shown that index coding problem include as special cases a number of difficult problems in both wired and wireless settings. Next, we consider the sum DoF of all one-dimensional (all nodes placed along a straight line) convex cellular networks (where cells are convex regions) when no channel knowledge is available at the transmitters except the knowledge of the network topology. Then we consider the distributed data storage problem and our focus is the design of a systematic MDS code with the additional property that a single disk failure can be repaired with minimum repair bandwidth, i.e., with the minimum possible amount of data to be downloaded for recovery of the failed disk. Finally, we show that for interference networks consisting of distributed transmitters and receivers, where interference is contributed by multiple transmitters, we can achieve more than... |
