Quantization and Transmission in Wireless Multi- hop Networks

of a dissertation at the University of Miami. Dissertation supervised by Professor Manohar N. Murthi. No. of pages in text. (115) Many applications like streaming audio/video, gaming, distributed or remote computing transmit data over communication networks. The quality-of-service (QoS) of these applications depends on parameters like rate, reliability, delay, power level, etc. Furthermore, these applications need to share network resources and co-exist with other applications which run on the same network. Since these communication networks are digital communication systems, the transmitter captures the real time data, quantizes and transmits to the receiver. At the receiver not only a reconstruction of the original signal is performed but also there may be a need to classify the signal into several classes. Therefore, reconstruction fidelity and classification are also QoS requirements that many applications may demand. We are interested in the problem of transmitting data in a layered multi-hop wireless network. The QoS in our system is a function of rates and end-to-end delay from transmitters to the receivers. We are considering wireless multi-hop networks, therefore the capacity of the communication links is a function of power of transmitters and the interference from other links transmitters. Furthermore, we are not only interested in reconstructing the received quantized data but also we would like to perform signal classification on the signals based only on the characteristics of the received quantized data. We break down this problem into two separate problems to be solved at different layers of communication network as follows Problem 1 which solves a network optimization problem where QoS depends on the rate, end-to-end delay, and power of transmitters. The solution to this problem essentially entails the rate control (congestion control) in the transport later, and the power control in the physical layer to achieve bounded average queuing delay for the end-to-end transmission of the data. Problem 2 which focuses on designing a quantizer that guarantees reproduction fidelity of the signals and good classification results based on the information preserved in the reconstructed signal. Linkage and Inter-connection between Problem 1 and Problem 2 Problem 1 determines the data rate of the sessions. The data rate can be translated into bits/vector rate which is fed into the quantizer that is designed by solving Problem 2. Therefore a communication system is devised that takes advantage of the solutions of Problem 1 and 2 in order to achieve the bigger objective of this dissertation. Let us now consider the solution to Problem 1. Allocating limited resources such as bandwidth and power in a multi-hop wireless network can be formulated as a Network Utility Maximization (NUM) problem. Researchers have been using NUM in order to develop new network resource allocation algorithms by augmenting the earlier NUM problems. In the NUM framework, sources in the network measure their performance by a utility function. We augment the basic NUM problem with a constraint based on the average queueing delay requirements of the sources. Furthermore, the capacity of the links in the case of wireless networks depend on the power of transmitters. This augmented NUM formulation turns out to be a non-convex problem. We convert this non-convex problem with high-SIR assumption and a change of variable to a convex problem. We furthermore propose methods to solve this problem in an iterative distributed manner. Simulation results demonstrate the efficacy of the distributed algorithm developed. To solve Problem 2, we adopt high-rate analysis to design a quantizer that is optimized in the task of reconstruction fidelity as well as classification at the decoder. We deploy symmetric Kullback-Leibler (KL) divergence measure between the conditional probabilities of class given the signal before and after quantization as our distortion measure. We derive the optimum point density of the quantizer for minimizing the symmetric KL divergence. We study tradeoff between classification accuracy and reproduction fidelity. We also derive the effects of a mismatched distortion measure and show that for reduced complexity the original distortion measure can be replaced by a weighted mean square error (WMSE) distortion measure. We examine the performance of these methods on synthetically generated data as well as real data set and observe that our methods are superior in the task of classification of signals at the decoder. The tradeoff is the lower performance in distortion. The linkage and interrelationship of Problem 1 and 2 is shown at the end. Problem 1 determines the data rate of the sessions. The data rate can be translated into bits/vector rate which is fed into the quantizer that is designed by solving Problem 2. Therefore a communication system is devised that takes advantage of the solutions of Problem 1 and 2 in order to achieve the bigger objective of this dissertation.