New Classes of Distributed Time Complexity

A number of recent papers -- e.g. Brandt et al. (STOC 2016), Chang et al. (FOCS 2016), Ghaffari & Su (SODA 2017), Brandt et al. (PODC 2017), and Chang & Pettie (FOCS 2017) -- have advanced our understanding of one of the most fundamental questions in theory of distributed computing: what are the possible time complexity classes of LCL problems in the LOCAL model? In essence, we have a graph problem $\Pi$ in which a solution can be verified by checking all radius-$O(1)$ neighbourhoods, and the question is what is the smallest $T$ such that a solution can be computed so that each node chooses its own output based on its radius-$T$ neighbourhood. Here $T$ is the distributed time complexity of $\Pi$. The time complexity classes for deterministic algorithms in bounded-degree graphs that are known to exist by prior work are $\Theta(1)$, $\Theta(\log^* n)$, $\Theta(\log n)$, $\Theta(n^{1/k})$, and $\Theta(n)$. It is also known that there are two gaps: one between $\omega(1)$ and $o(\log \log^* n)$, and another between $\omega(\log^* n)$ and $o(\log n)$. It has been conjectured that many more gaps exist, and that the overall time hierarchy is relatively simple -- indeed, this is known to be the case in restricted graph families such as cycles and grids. We show that the picture is much more diverse than previously expected. We present a general technique for engineering LCL problems with numerous different deterministic time complexities, including $\Theta(\log^{\alpha}n)$ for any $\alpha\ge1$, $2^{\Theta(\log^{\alpha}n)}$ for any $\alpha\le 1$, and $\Theta(n^{\alpha})$ for any $\alpha <1/2$ in the high end of the complexity spectrum, and $\Theta(\log^{\alpha}\log^* n)$ for any $\alpha\ge 1$, $\smash{2^{\Theta(\log^{\alpha}\log^* n)}}$ for any $\alpha\le 1$, and $\Theta((\log^* n)^{\alpha})$ for any $\alpha \le 1$ in the low end; here $\alpha$ is a positive rational number

Quantum Optical Systems for the Implementation of Quantum Information Processing

We review the field of Quantum Optical Information from elementary considerations through to quantum computation schemes. We illustrate our discussion with descriptions of experimental demonstrations of key communication and processing tasks from the last decade and also look forward to the key results likely in the next decade. We examine both discrete (single photon) type processing as well as those which employ continuous variable manipulations. The mathematical formalism is kept to the minimum needed to understand the key theoretical and experimental results

Deep Learning Framework for Wireless Systems: Applications to Optical Wireless Communications

Optical wireless communication (OWC) is a promising technology for future wireless communications owing to its potentials for cost-effective network deployment and high data rate. There are several implementation issues in the OWC which have not been encountered in radio frequency wireless communications. First, practical OWC transmitters need an illumination control on color, intensity, and luminance, etc., which poses complicated modulation design challenges. Furthermore, signal-dependent properties of optical channels raise non-trivial challenges both in modulation and demodulation of the optical signals. To tackle such difficulties, deep learning (DL) technologies can be applied for optical wireless transceiver design. This article addresses recent efforts on DL-based OWC system designs. A DL framework for emerging image sensor communication is proposed and its feasibility is verified by simulation. Finally, technical challenges and implementation issues for the DL-based optical wireless technology are discussed.Comment: To appear in IEEE Communications Magazine, Special Issue on Applications of Artificial Intelligence in Wireless Communication