Source and Channel Coding for Compressed Sensing and Control

Abstract: Rapid advances in sensor technologies have fueled massive torrents of data streaming across networks. Such large volume of information, indeed, restricts the operational performance of data processing, causing inefficiency in sensing, computation, communication and control. Hence, classical data processing techniques need to be re-analyzed and re-designed prior to be applied to modern networked data systems. This thesis aims to understand and characterize fundamental principles and interactions in and among sensing, compression, communication, computation and control, involved in networked data systems. In this regard, the thesis investigates four problems. The common theme is the design and analysis of optimized low-delay transmission strategies with affordable complexity for reliable communication of acquired data over networks with the objective of providing high quality of service for users.In the first three problems considered in the thesis, an emerging framework for data acquisition, namely, compressed sensing, is used which performs acquisition and compression simultaneously. The first problem considers the design of iterative encoding schemes, based on scalar quantization, for transmission of compressed sensing measurements over rate-limited links. Our approach is based on an analysis-by-synthesis principle, where the motivation is to reflect non-linearity in reconstruction, raised by compressed sensing, via synthesis, on choosing the best quantized value for encoding, via analysis. Our design shows significant reconstruction performance compared to schemes that only consider direct quantization of compressed sensing measurements.In the second problem, we investigate the design and analysis of encoding--decoding schemes, based on vector quantization, for transmission of compressed sensing measurements over rate-limited noisy links. In so realizing, we take an approach adapted from joint source-channel coding framework. We show that the performance of the studied system can approach the fundamental theoretical bound by optimizing the encoder-decoder pair. The price, however, is increased complexity at the encoder. To address the encoding complexity of the vector quantizer, we propose to use low-complexity multi-stage vector quantizer whose optimized design shows promising performance.In the third problem considered in the thesis, we take one step forward, and study joint source-channel coding schemes, based on vector quantization, for distributed transmission of compressed sensing measurements over noisy rate-limited links. We design optimized distributed coding schemes, and analyze theoretical bounds for such topology. Under certain conditions, our results reveal that the performance of the optimized schemes approaches the analytical bounds.In the last problem and in the context of control under communication constraints, we bring the notion of system dynamicity into the picture. Particularly, we study relations among stability in dynamical networked control systems, performance of real-time coding schemes and the coding complexity. For this purpose, we take approaches adapted from separate source-channel coding, and derive theoretical bounds on the performance of two types of coding schemes: dynamic repetition codes, and dynamic Fountain codes. We analytically and numerically show that the dynamic Fountain codes, over binary-input symmetric channels, with belief propagation decoding, are able to provide system stability in a networked control system.The results in the thesis evidently demonstrate that impressive performance gain is feasible by employing tools from communication and information theory to control and sensing. The insights offered through the design and analysis will also reveal fundamental pieces for understanding real-world networked data puzzle.