The Karhunen–Loève Transform (KLT) is prevalent nowadays in communication and signal processing. This thesis aims at attaining the KLT in the encoders and achieving the minimum sum rate in the case of Gaussian multiterminal source coding. In the general multiterminal source coding case, the data collected at the terminals will be compressed in a distributed manner, then communicated the fusion center for reconstruction. The data source is assumed to be a Gaussian random vector in this thesis. We introduce the rate-distortion function to formulate the optimization problem. The rate-distortion function focuses on achieving the minimum encoding sum rate, subject to a given distortion. The main purpose in the thesis is to propose a distributed KLT for encoders to deal with the sampled data and produce the minimum sum rate. To determine the distributed Karhunen–Loève transform, we propose three kinds of algorithms. The rst iterative algorithm is derived directly from the saddle point analysis of the optimization problem. Then we come up with another algorithm by combining the original rate-distortion function with Wyner's common information, and this algorithm still has to be solved in an iterative way. Moreover, we also propose algorithms without iterations. This kind of algorithms will generate the unknown variables from the existing variables and calculate the result directly.All those algorithms can make the lower-bound and upper-bound of the minimum sum rate converge, for the gap can be reduced to a relatively small range comparing to the value of the upper-bound and lower-bound. / Thesis / Master of Applied Science (MASc)

<p>    </p> <p>This thesis studies networked Gaussian linear control systems with random delays. Networked control systems is a popular topic these years because of their versatile applications in daily life, such as smart grid and unmanned vehicles. With the development of these systems, researchers have explored this area in two directions. The first one is to derive the inherent rate-cost relationship in the systems, that is the minimal transmission rate needed to achieve an arbitrarily given stability requirement. The other one is to design achievability schemes, which aim at using as less as transmission rate to achieve an arbitrarily given stability requirement. In this thesis, we explore both directions. We assume the sensor-to-controller channels experience independently and identically distributed random delays of bounded support. Our work separates into two parts. In the first part, we consider networked systems with only one sensor. We focus on deriving a lower bound, R_{LB}(D), of the rate-cost tradeoff with the cost function to be E{| <strong>x^</strong>T<strong>x </strong>|} ≤ D, where <strong>x </strong>refers to the state to be controlled. We also propose an achievability scheme as an upper bound, R_{UB}(D), of the optimal rate-cost tradeoff. The scheme uses lattice quantization, entropy encoder, and certainty-equivalence controller. It achieves a good performance that roughly requires 2 bits per time slot more than R_{LB}(D) to achieve the same stability level. We also generalize the cost function to be of both the state and the control actions. For the joint state-and-control cost, we propose the minimal cost a system can achieve. The second part focuses on to the covariance-based fusion scheme design for systems with multiple > 1 sensors. We notice that in the multi-sensor scenario, the outdated arrivals at the controller, which many existing fusion schemes often discard, carry additional information. Therefore, we design an implementable fusion scheme (CQE) which is the MMSE estimator using both the freshest and outdated information at the controller. Our experiment demonstrates that CQE out-performances the MMSE estimator using the freshest information (LQE) exclusively by achieving a 15% smaller average L2 norm using the same transmission rate. As a benchmark, we also derive the minimal achievable L2 norm, Dmin, for the multi-sensor systems. The simulation shows that CQE approaches Dmin significantly better than LQE. </p>