Grant: Discovery Grants Program - Individual

We live in an information age where every aspect of our lives is influenced and empowered by information that is being collected and communicated at ever increasing rates. Whether the information is collected through millions of sensors that are deployed every single day in our appliances, security/surveillance systems and infrastructure, or through social media, the information needs to be stored, processed and communicated. The goal of this research is to address some of the most pressing challenges in today's information systems and push the existing limits of such systems in terms of speed, complexity and reliability. On the topic of sensing, we devise compressed sensing techniques that combine the operations of sensing and compression, and lend themselves to simple implementations at high speeds. For the storage, we develop coding/processing algorithms for the state--of--the--art high--speed high-density memory architectures that would make the reliable application of such architectures possible. On the topic of coding/processing for the reliable communication of information, we devise error correction and coded modulation schemes that can accommodate high--speed transmission at very low error rates. Since many communication scenarios involve multiple users that communicate through a network, we also extend our results to such cases, and consider techniques such as network coding. Our general approach in research is to first use our extensive industrial collaborations together with our knowledge of the state--of--the--art literature to identify some of the major challenges/problems that face today's information systems. We then use a variety of mathematical tools including probability theory, stochastic processes, graph theory and combinatorics along with Monte Carlo simulations to investigate such problems, develop mathematical models, and devise viable solutions. Many of the proposed topics fall into a unifying framework that describes the system as a graph with many interconnections. An important aspect of the proposed research is to investigate the structure of such graphs and examine the relationships between the properties of the graph, such as the cycle distribution, and the properties of the system, such as the error rate. In addition to the theoretical aspects of problems, we also consider implementations of our proposed techniques and algorithms both in hardware and software. The outcomes of this research are technologies and algorithms that enable faster communication links and devices, as well as smart phones and sensors that not only communicate faster and more reliably but also have a longer battery life.