Communication With Reconstruction and Privacy Constraints
Sammanfattning: Communication networks are an integral part of the Internet of Things (IoT) era. They enable endless opportunities for connectivity in a wide range of applications, leading to advances in efficiency of day-to-day life. While creating opportunities, they also incur several new challenges. In general, we wish to design a system that performs optimally well in all aspects. However, there usually exist competing objectives which lead to tradeoffs. In this thesis, driven by several applications, new features and objectives are included into the system model, making it closer to reality and needs. The results presented in this thesis aim at providing insight into the fundamental tradeoff of the system performance which can serve as a guideline for the optimal design of real-world communication systems.The thesis is divided into two parts. The first part considers the aspect of signal reconstruction requirement as a new objective in the source and channel coding problems. In this part, we consider the framework where the quality and/or availability of the side information can be influenced by a cost-constrained action sequence. In the source coding problem, we impose a constraint on the reconstruction sequence at the receiver that it should be reproduced at the sender, and characterize the fundamental tradeoff in the form of the rate-distortion-cost region, revealing the optimal relation between compression rate, distortion, and action cost. The channel coding counterpart is then studied where a reconstruction constraint is imposed on the channel input sequence such that it should be reconstructed at the receiver. An extension to the multi-stage channel coding problem is also considered where inner and outer bounds to the capacity region are given. The result on the channel capacity reveals interesting consequence of imposing an additional reconstruction requirement on the system model which has a causal processing structure.In the second part, we consider the aspect of information security and privacy in lossy source coding problems. The sender wishes to compress the source sequence in order to satisfy a distortion criterion at the receiver, while revealing only limited knowledge about the source to an unintended user. We consider three different aspects of information privacy. First, we consider privacy of the source sequence against the eavesdropper in the problem of source coding with action-dependent side information. Next, we study privacy of the source sequence due to the presence of a public helper in distributed lossy source coding problems. The public helper is assumed to be either a user who provides side information over a public link which can be eavesdropped, or a legitimate user in the network who helps to relay information to the receiver, but may not ignore the information that is not intended for it. Lastly, we take on a new perspective of information privacy in the source coding problem. That is, instead of protecting the source sequence, we are interested in the privacy of the reconstruction sequence with respect to a user in the system. For above settings, we provide the complete characterization of the rate-distortion(-cost)-leakage/equivocation region or corresponding inner and outer bounds for discrete memoryless systems.
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