Abstracts Communications and the Arts

Uniformly Bounded State Estimation over Multiple Access Channels

by Ghassen Zafzouf

In this doctoral thesis, a characterization of the zero-error capacity region for three different classes of multiple access channels (MACs) is derived. The first type of channels considered in this work is a two-user MAC with a common message that captures the correlation between transmitters. Next, this model is extended by considering an arbitrary number of users M >= 2. The last class of MACs represents a further extension to a more general case where inter-user correlation is modeled by a common message seen by all users as well as pairwise shared messages. In this research, we look at the zero-error capacity, which differs from the more commonly studied small-error capacity, from a nonprobabilistic angle. In fact, the obtained characterization is based on the so-called nonstochastic information, and is valid not only for asymptotically large coding block-lengths but also for finite lengths. Understanding how to coordinate unambiguous communication through MACs, such that several unrelated senders can simultaneously send as much information as possible is of great interest, especially with the emergence of new paradigms such as the Internet of Things (IoT) and Machine-to-Machine (M2M) communication. Next, using the characterization of the zero-error capacity region for the two-user MAC, we investigate the problem of distributed state estimation under the criterion of uniformly bounded estimation errors. It is shown that if there exists a coder-estimator tuple that achieves the desired criterion, namely uniformly bounded estimation error, the vector of topological entropies of the linear systems, whose state is being estimated, must lie within the zero-error capacity region of the communication channel. Additionally, we prove that if the to-be-observed plants have a topological entropy vector inside the interior of the zero-error capacity region, the existence of a coder-estimator tuple achieving uniformly bounded state estimation errors is guaranteed. This result relates the channel properties to the plant dynamics and paves the way toward understanding information flows in networked control systems with multiple transmitters. Finally, we seek to characterize the fundamental tradeoff between the communication data rate, code-length, system dynamics and state estimation performance. To this end, a universal lower bound on the time-asymptotic estimation error is obtained using volume-based analysis. Additionally, to provide a guarantee on the estimation performance, an upper bound on the error is derived when the measurements are quantized. When the code-length is large, we show that these lower and upper bounds converge to the same limit.